---
title: "OncoSimulR: forward genetic simulation in asexual populations with arbitrary epistatic interactions and a focus on modeling tumor progression."
author: "

         Ramon Diaz-Uriarte\\

         Dept. Biochemistry, Universidad Autónoma de Madrid, Instituto de
         Investigaciones Biomédicas 'Alberto Sols' (UAM-CSIC), Madrid,
         Spain.\\ 
		 
		 <rdiaz02@gmail.com>, <http://ligarto.org/rdiaz>
		 "
date: "`r paste0(Sys.Date(),'. OncoSimulR version ', packageVersion('OncoSimulR'), '. Revision: ', system('git rev-parse --short HEAD', intern = TRUE))`"
output: 
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classoption: a4paper
geometry: margin=3cm
fontsize: 12pt
bibliography: OncoSimulR.bib
link-citations: true
vignette: >
  %\VignetteIndexEntry{OncoSimulR: forward genetic simulation in asexual populations with arbitrary epistatic interactions and a focus on modeling tumor progression.}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignettePackage{OncoSimulR}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
  %\VignetteKeywords{OncoSimulR simulation cancer oncogenetic trees}
  %\VignetteDepends{OncoSimulR}
---

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<!-- ##    <rdiaz02@gmail.com>, <http://ligarto.org/rdiaz> -->
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```{r setup, include=FALSE}
## use collapse for bookdown, to collapse all the source and output
## blocks from one code chunk into a single block
knitr::opts_chunk$set(echo = TRUE, collapse = TRUE)
options(width = 70)
require(BiocStyle)
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# Introduction {#intro}
 
OncoSimulR was originally developed to simulate tumor progression
using several models of tumor progression with emphasis on allowing
users to set restrictions in the accumulation of mutations as
specified, for example, by Oncogenetic Trees
[OT: @Desper1999JCB; @Szabo2008] or Conjunctive Bayesian Networks
[CBN: @Beerenwinkel2007; @Gerstung2009; @Gerstung2011], with the
possibility of adding passenger mutations to the simulations and
allowing for several types of sampling.


Since then, OncoSimulR has been vastly extended to allow you to
specify other types of restrictions in the accumulation of genes, as
such as the XOR models of @Korsunsky2014 or the "semimonotone" model
of Farahani and Lagergren [@Farahani2013]. Moreover, different
fitness effects related to the order in which mutations appear can
also be incorporated, involving arbitrary numbers of genes. This is
different from "restrictions in the order of accumulation of
mutations". With order effects, shown empirically in a recent cancer
paper by Ortmann and collaborators [@Ortmann2015], the effect of
having both mutations "A" and "B" differs depending on whether "A"
appeared before or after "B". More generally, now OncoSimulR also
allows you to specify arbitrary epistatic interactions between
arbitrary collections of genes and to model, for example, synthetic
mortality or synthetic viability (again, involving an arbitrary
number of genes, some of which might also depend on other genes, or
show order effects with other genes). Moreover, it is possible to
specify the above interactions in terms of modules, not genes. This
idea is discussed in, for example, @Raphael2014a and @Gerstung2011:
the restrictions encoded in, say, CBNs or OT can be considered to
apply not to genes, but to modules, where each module is a set of
genes (and the intersection between modules is the empty set) that
performs a specific biological function. Modules, then, play the
role of a "union operation" over the set of genes in a module. In
addition, arbitrary numbers of genes without interactions (and with
fitness effects coming from any distribution you might want) are
also possible.


The models so far implemented are all continuous time models, which
are simulated using the BNB algorithm of @Mather2012. The core of
the code is implemented in C++, providing for fast execution.  To
help with simulation studies, code to simulate random graphs of the
kind often seen in CBN, OTs, etc, is also available. Finally,
OncoSimulR also allows for the generation of random fitness
landscapes and the representation of fitness landscapes.

## Key features of OncoSimulR {#key}

As mentioned above, OncoSimulR is now a very general package for forward
genetic simulation, with applicability well beyond tumor progression. This
is a summary of some of the key features:

<!-- FIXME: add the tables of the poster -->


 
* You can specify arbitrary interactions between genes, with   arbitrary fitness effects, with  explicit support for:
    - Restrictions in the accumulations of mutations, as specified by
      Oncogenetic Trees (OTs), Conjunctive Bayesian Networks (CBNs),
      semimonotone progression networks, and XOR relationships.
		  
    - Epistatic interactions, including, but not limited to, synthetic
       viability and synthetic lethality.
    - Order effects.
	
* You can add passenger mutations.
* You can add mutator/antimutator effects.
* Fitness and mutation rates can be gene-specific.
* More generally, you can add arbitrary numbers of non-interacting
      genes with arbitrary fitness effects.
  
* You can allow for deviations from the OT, CBN, semimonotone, and
      XOR models, specifying a penalty for such deviations (the $s_h$
      parameter).
      
* You can conduct multiple simulations, and sample from them with
      different temporal schemes and using both whole tumor or single cell
      sampling. 
  
* Right now, three different models are available, two that lead
      to exponential growth, one of them loosely based on @Bozic2010, and
      another that leads to logistic-like growth, based on @McFarland2013.
      
<!-- * Code in C++ is available (though not yet callable from R) for -->
<!--       using several other models, including the one from @Beerenwinkel2007b. -->
      
* You can use very large numbers of genes (e.g., see an example of
      50000 in section \@ref(mcf50070) ).
      
* Simulations are generally very fast as I use C++ to implement
      the BNB algorithm.
      
* You can obtain the true sequence of events and the phylogenetic
      relationships between clones.
    
* You can generate random fitness landscapes (under the House of
      Cards, Rough Mount Fuji, or additive models, or combinations of the
      former) and use those landscapes as input to the simulation
      functions.
      
* You can plot fitness landscapes.
      



Further details about the motivation for wanting to simulate data this way
in the context of tumor progression can be found in
@Diaz-Uriarte2015, where additional comments about model parameters
and caveats are discussed. 

Are there similar programs? The Java program by @Reiter2013a offers
somewhat similar functionality to the previous version of
OncoSimulR, but it is restricted to at most four drivers (whereas
v.1 of OncoSimulR allowed for up to 64), you cannot use arbitrary
CBNs or OTs (or XORs or semimonotone graphs) to specify
restrictions, there is no allowance for passengers, and a single
type of model (a discrete time Galton-Watson process) is
implemented. The current functionality of OncoSimulR goes well
beyond the the previous version (and, thus, also the TPT of
[@Reiter2013a]). We now allow you to specify all types of fitness
effects in other general forward genetic simulators such as FFPopSim
[@Zanini2012], and some that, to our knowledge (e.g., order effects)
are not available from any genetics simulator. In addition, the
"lego approach" to flexibly combine different fitness specifications
is also unique.




<!-- These are some tables that might help to get an idea of the -->
<!-- functionality; they come from this -->
<!-- poster[http://dx.doi.org/10.7490/f1000research.1112860.1](http://dx.doi.org/10.7490/f1000research.1112860.1) -->
<!-- presented at ECCB 2016. -->

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## Steps in using OncoSimulR


Using this package will often involve the following steps:


1. Specify the fitness effects: sections \@ref(specfit) and \@ref(litex).

2. Simulate cancer progression: section \@ref(simul). You can simulate
  for a single subject or for a set of subjects. You will need to:
  
    - Decide on a model. This basically amounts to choosing a model with
    exponential growth ("Exp" or "Bozic") or a model with
    gompertz-like growth ("McFL"). If exponential growth, you can choose
    whether the the effects of mutations operate on the death rate
    ("Bozic") or the birth rate ("Exp")[^1]
  
    - Specify other parameters of the simulation. In particular, decide
    when to stop the simulation, mutation rates, etc.

     Of course, at least for initial playing around, you can use the
     defaults.
  
3. Sample from the simulated data and do something with those simulated
  data (e.g., fit an OT model to them). What you do with the data,
  however, is outside the scope of this package.

        

[^1]:It is of course possible to do this with the gompertz-like models,
      but there probably is little reason to do it. @McFarland2013 discuss
      this has little effect on their results, for example. In addition,
      decreasing the death rate will more easily lead to numerical
      problems as shown in section \@ref(ex-0-death).




Before anything else, let us load the package. We also explicitly load 
`r Biocpkg("graph")` and `r CRANpkg("igraph")` for the vignette to work (you
do not need that for your usual interactive work). And I set the default
color for vertices in igraph.

```{r, results="hide",message=FALSE, echo=TRUE, include=TRUE}
library(OncoSimulR)
library(graph)
library(igraph)
igraph_options(vertex.color = "SkyBlue2")
``` 

```{r, echo=FALSE, results='hide'}
options(width = 68)
``` 

To be explicit, what version are we running?
```{r}
packageVersion("OncoSimulR")
``` 



## Two quick examples {#quickexample}

Following the above we will run two examples. First a model with a few
genes and **epistasis**:

```{r, fig.width=6.5, fig.height=10}
## 1. Fitness effects: here we specify an 
##    epistatic model with modules.
sa <- 0.1
sb <- -0.2
sab <- 0.25
sac <- -0.1
sbc <- 0.25
sv2 <- allFitnessEffects(epistasis = c("-A : B" = sb,
                                       "A : -B" = sa,
                                       "A : C" = sac,
                                       "A:B" = sab,
                                       "-A:B:C" = sbc),
                         geneToModule = c(
                             "A" = "a1, a2",
                             "B" = "b",
                             "C" = "c"),
                         drvNames = c("a1", "a2", "b", "c"))
evalAllGenotypes(sv2, addwt = TRUE)

## 2. Simulate the data. Here we use the "McFL" model and set
##    explicitly parameters for mutation rate, initial size and size
##    of the population that will end the simulations, etc

RNGkind("Mersenne-Twister")
set.seed(983)
ep1 <- oncoSimulIndiv(sv2, model = "McFL",
                      mu = 5e-6,
                      sampleEvery = 0.02,
                      keepEvery = 0.5,
                      initSize = 2000,
                      finalTime = 3000,
                      onlyCancer = FALSE)
``` 



<!-- % set.seed(9) -->
<!-- % ep1 <- oncoSimulIndiv(sv2, model = "McFL", -->
<!-- %                      mu = 5e-6, -->
<!-- %                      sampleEvery = 0.02, -->
<!-- %                      keepEvery = 0.5, -->
<!-- %                      initSize = 2000, -->
<!-- %                      finalTime = 3000, -->
<!-- %                      onlyCancer = FALSE) -->

<!-- %% <<fig.width=6.5, fig.height=10>>= -->
<!-- %%  ## 1. Fitness effects: here we specify a  -->
<!-- %%  ##    epistatic model with modules. -->
<!-- %%  sa <- 0.1 -->
<!-- %%  sb <- -0.2 -->
<!-- %%  sab <- 0.25 -->
<!-- %%  sac <- -0.1 -->
<!-- %%  sbc <- 0.25 -->
<!-- %%  sv2 <- allFitnessEffects(epistasis = c("-A : B" = sb, -->
<!-- %%                                         "A : -B" = sa, -->
<!-- %%                                         "A : C" = sac, -->
<!-- %%                                         "A:B" = sab, -->
<!-- %%                                         "-A:B:C" = sbc), -->
<!-- %%                           geneToModule = c( -->
<!-- %%                               "Root" = "Root", -->
<!-- %%                               "A" = "a1, a2", -->
<!-- %%                               "B" = "b", -->
<!-- %%                               "C" = "c")) -->
<!-- %%  evalAllGenotypes(sv2, order = FALSE, addwt = TRUE) -->

<!-- %%  ## 2. Simulate the data. Here we use the "McFL" model and set explicitly -->
<!-- %%  ##    parameters for mutation rate, final and initial sizes, etc. -->
<!-- %%  RNGkind("Mersenne-Twister") -->
<!-- %%  set.seed(983) -->
<!-- %%  ep1 <- oncoSimulIndiv(sv2, model = "McFL", -->
<!-- %%                       mu = 5e-6, -->
<!-- %%                       sampleEvery = 0.02, -->
<!-- %%                       keepEvery = 0.5, -->
<!-- %%                       initSize = 2000, -->
<!-- %%                       finalTime = 3000, -->
<!-- %%                       onlyCancer = FALSE) -->
<!-- %% @  -->


```{r iep1x1,fig.width=6.5, fig.height=4.5}
## 3. We will not analyze those data any further. We will only plot
## them.  For the sake of a small plot, we thin the data.
plot(ep1, show = "drivers", xlim = c(0, 1500),
     thinData = TRUE, thinData.keep = 0.5)
``` 

<!-- ## Increase ylim and legend.ncols to avoid overlap of  -->
<!-- ## legend with rest of figure -->
<!-- plot(ep1, show = "genotypes", ylim = c(0, 4500),  -->
<!--      legend.ncols = 4, -->
<!--      xlim = c(0, 1500), -->
<!--      thinData = TRUE, thinData.keep = 0.5) -->



As a second example, we will use a model where we specify
**restrictions in the order of accumulation of mutations** using the
pancreatic cancer poset in @Gerstung2011 (see more
details in section \@ref(pancreas)):

```{r, fig.width=5}
## 1. Fitness effects: 
pancr <- allFitnessEffects(
    data.frame(parent = c("Root", rep("KRAS", 4), 
                   "SMAD4", "CDNK2A", 
                   "TP53", "TP53", "MLL3"),
               child = c("KRAS","SMAD4", "CDNK2A", 
                   "TP53", "MLL3",
                   rep("PXDN", 3), rep("TGFBR2", 2)),
               s = 0.1,
               sh = -0.9,
               typeDep = "MN"),
    drvNames = c("KRAS", "SMAD4", "CDNK2A", "TP53", 
	             "MLL3", "TGFBR2", "PXDN"))

## Plot the DAG of the fitnessEffects object
plot(pancr)
``` 
```{r}
## 2. Simulate from it. 

set.seed(4) ## Fix the seed, so we can repeat it
ep2 <- oncoSimulIndiv(pancr, model = "McFL",
                     mu = 1e-6,
                     sampleEvery = 0.02,
                     keepEvery = 1,
                     initSize = 1000,
                     finalTime = 10000,
                     onlyCancer = FALSE)
``` 

<!-- % set.seed(6) ## Fix the seed, so we can repeat it -->
<!-- % ep2 <- oncoSimulIndiv(pancr, model = "McFL", -->
<!-- %                      mu = 1e-6, -->
<!-- %                      sampleEvery = 0.02, -->
<!-- %                      keepEvery = 1, -->
<!-- %                      initSize = 2000, -->
<!-- %                      finalTime = 10000, -->
<!-- %                      onlyCancer = FALSE)
-->
```{r iep2x2,fig.width=6.5, fig.height=5}
## 3. What genotypes and drivers we get? And play with limits
##    to show only parts of the data. We also aggressively thin
##    the data.
par(cex = 0.7)
plot(ep2, show = "genotypes", xlim = c(1000, 8000), 
     ylim = c(0, 2400),
     thinData = TRUE, thinData.keep = 0.03)
``` 



## How long does it take? How fast is OncoSimulR? How much space do the return objects take? {#timings}


How long simulations take depend on several factors:


* Your hardware, of course.
* The evolutionary model: using the "McFL" model is often much
  slower (this model includes density dependence and is more complex).
* The granularity of how often you keep data (`keepEvery`
  argument). Note that the default, which is to keep as often as you
  sample (so that we preserve all history) can lead to very slow execution
  times.
* The mutation rate, because higher mutation rates lead to more
  clones, and more clones mean we need to iterate over, well, more clones,
  and keep larger data structures.

* The fitness specification (more complex fitness specifications tend
  to be slightly slower).
* Whether or not you keep the complete clone history (this affects
  mainly size of return object, not speed).
* The stopping conditions.



To give you an idea, we will use the above examples, with the
`detectionProb` stopping mechanism (see \@ref(detectprob)), two
different growth models (exponential and McFarland) and will obtain
100 simulations. The results I show are for a laptop with an 8-core
Intel Xeon E3-1505M CPU, running Debian GNU/Linux.

```{r, eval=FALSE}

system.time(
    ep1_exp <- oncoSimulPop(100, sv2, 
                            detectionProb = "default", 
                            detectionSize = NA,
                            detectionDrivers = NA,
                            finalTime = NA,
                            keepEvery = 5,
                            model = "Exp", 
                            sampleEvery = 0.02, 
                            initSize = 500,
                            mc.cores = detectCores()))

system.time(
    ep1_mc <- oncoSimulPop(100, sv2, 
                           detectionProb = "default", 
                           detectionSize = NA,
                           detectionDrivers = NA,
                           finalTime = NA,
                           keepEvery = 5,                                  
                           model = "McFL", 
                           sampleEvery = 0.02, 
                           initSize = 2000,
                           mc.cores = detectCores()))

system.time(
    ep2_exp <- oncoSimulPop(100, pancr, 
                            detectionProb = "default", 
                            detectionSize = NA,
                            detectionDrivers = NA,
                            finalTime = NA,
                            keepEvery = 5, 
                            model = "Exp", 
                            sampleEvery = 0.02, 
                            initSize = 500,
                            mc.cores = detectCores()))

system.time(
    ep2_mc <- oncoSimulPop(100, pancr, 
                           detectionProb = "default", 
                           detectionSize = NA,
                           detectionDrivers = NA,
                           finalTime = NA,
                           keepEvery = 5,
                           model = "McFL", 
                           sampleEvery = 0.02, 
                           initSize = 2000,
                           mc.cores = detectCores()))

``` 

And we look at the sizes of objects using:


``` {r, eval=FALSE}
print(object.size(ep1_exp), units = "MB")
```

<!-- ```{r, echo=FALSE, results='hide'} -->
<!-- dftm1 <- data.frame(Simulation = c("ep1_exp", "ep1_mc", "ep2_exp","ep2_mc"),  -->
<!--     ElapsedTime = c(0.8, 6.6, 1.1, 5.8), Size = c(1.6, 16.6, 1.6, 20.6)) -->

<!-- ``` -->

The above runs yield the following:

<!-- ```{r, results='show', echo=FALSE} -->
<!-- knitr::kable(dftm1, col.names = c("Simulation", "Elapsed Time (s)", "Object Size (MB)")) -->

<!-- ``` -->



<!-- |Simulation | Elapsed Time (s)| Object Size (MB)| -->
<!-- |:----------|----------------:|----------------:| -->
<!-- |ep1_exp    |              0.8|              1.6| -->
<!-- |ep1_mc     |              6.6|             16.6| -->
<!-- |ep2_exp    |              1.1|              1.6| -->
<!-- |ep2_mc     |              5.8|             20.6| -->

----------------------------------------------------------
Simulation    Elapsed Time (s)         Object Size (MB)
----------  ---------------------    ---------------------
ep1_exp                  0.8              1.6

ep1_mc                   6.6             16.6

ep2_exp                  1.1              1.6

ep2_mc                   5.8             20.6
----------  ---------------------    ---------------------






<!-- The above yields the following: -->

<!-- \begin{tabular}[h]{lll} -->
<!--   \hline -->
<!--   Simulation&Elapsed wall time (s) &Object size (MB)\\ -->
<!--   \hline -->
<!--   ep1\_exp & 0.8 & 1.6 \\ -->
<!--   ep1\_mc  & 6.6 & 16.8 \\ -->
<!--   ep2\_exp & 1.1 & 1.6 \\ -->
<!--   ep2\_mc  & 5.8 & 20.6 \\ -->
<!--   \hline -->
<!-- \end{tabular} -->


There are large differences in speed between models and sizes of objects
differ too: in these cases, the simulations using the "McFL" model run
for much longer (2000 to 2000 time units, vs. 100 to 1500 of the "Exp"
models) and also had a larger number of clones returned (5 to 16 vs. 1 to
3).



## Citing OncoSimulR and other documentation {#citing}

In R, you can do
```{r}
citation("OncoSimulR")
``` 
which will tell you how to cite the package.


This is the URL for the bioRxiv
paper: [http://biorxiv.org/content/early/2016/08/14/069500](http://biorxiv.org/content/early/2016/08/14/069500). You
can also take a look at this
poster, [http://dx.doi.org/10.7490/f1000research.1112860.1](http://dx.doi.org/10.7490/f1000research.1112860.1),
presented at ECCB 2016.


### HTML and PDF versions of the vignette {#pdfvignette}

A PDF version of this vignette is available from
<https://rdiaz02.github.io/OncoSimul/pdfs/OncoSimulR.pdf>.  And an
HTML version from
<https://rdiaz02.github.io/OncoSimul/OncoSimulR.html>. These files
correspond to the most recent, github version, of the package (i.e.,
they might include changes not yet available from the BioConudctor
package).



## Versions {#versions}

In this vignette and the documentation I often refer to version 1 (v.1)
and version 2 of OncoSimulR. Version 1 is the version available up to, and
including, BioConductor v. 3.1. Version 2 of OncoSimulR is available
starting from BioConductor 3.2 (and, of course, available too from
development versions of BioC). 
So, if you are using the current stable or development version of
BioConductor, or you grab the sources from github
(<https://github.com/rdiaz02/OncoSimul>) you are using what we call
version 2. 


**The functionality of version 1 will soon be removed.**




# Specifying fitness effects {#specfit}

## Introduction to the specification of fitness effects {#introfit}

With OncoSimulR you can specify different types of effects on fitness:



* A special type of epistatic effect that is particularly amenable
  to be represented as a graph. In this graph, having, say, "B" be a
  child of "A" means that B can only accumulate if A is already
  present.  This is what OT [@Desper1999JCB; @Szabo2008], CBN
  [@Beerenwinkel2007; @Gerstung2009; @Gerstung2011], progression
  networks [@Farahani2013], and other similar models
  [@Korsunsky2014] generally mean. Details are provided in section
  \@ref(posetslong). Note that this is not an order effect
  (discussed below): the fitness of a genotype from this DAGs is a
  function of whether or not the restrictions in the graph are
  satisfied, not the historical sequence of how they were satisfied.

* Effects where the order in which mutations are acquired matters, as
  illustrated in section \@ref(oe). There is, in fact, empirical evidence
  of these effects [@Ortmann2015]. For instance, the fitness of
  genotype "A, B" would differ depending on whether A or B was acquired
  first.

  
* General epistatic effects (e.g., section \@ref(epi)), including
  synthetic viability (e.g., section \@ref(sv)) and synthetic
  lethality/mortality (e.g., section \@ref(sl)).


* Genes that have independent effects on fitness (section \@ref(noint)).
  



Modules (see section \@ref(modules0)) allow you to specify any of the above
effects (except those for genes without interactions, as it would not make
sense there) in terms of modules (sets of genes), not individual genes. We
will introduce them right after \@ref(posetslong), and continue using them
thereafter.


A guiding design principle of OncoSimulR is to try to make the
specification of those effects as simple as possible but also as flexible
as possible. Thus, there are two main ways of specifying fitness effects:


* Combining different types of effects in a single specification. For
  instance, you can combine epistasis with order effects with no
  interaction genes with modules. What you would do here is specify the
  effects that different mutations (or their combinations) have on fitness
  (the fitness effects) and then have OncoSimulR take care of combining
  them as if each of these were lego pieces. We will refer to this as the
  **lego system of fitness effects**.
  
  
* Explicitly passing to OncoSimulR a mapping of genotypes to
  fitness. Here you specify the fitness of each genotype. We will refer to
  this as the **explicit mapping of genotypes to fitness**.



Both approaches have advantages and disadvantages. Here I emphasize some
relevant differences.

* With the lego system you can specify huge genomes with an enormous
  variety of interactions, since the possible genotypes are not
  constructed in advance. You would not be able to do this with the
  explicit mapping of genotypes to fitness if you wanted to, say,
  construct that mapping for a modest genotype of 500 genes (you'd have
  more genotypes than particles in the Universe).
  
* For many models/data you often intuitively start with the fitness of
  the genotypes, not the fitness consequences of the different
  mutations. In these cases, you'd need to do the math to specify the
  terms you want if you used the lego system.
  
* Sometimes you already have a moderate size genotype $\rightarrow$
  fitness mapping and you certainly do not want to do the math by 
  hand: here the lego system would be painful to use.
  
* But sometimes we do think in terms of "the effects on fitness of
  such and such mutations are" and that immediately calls for the lego
  system, where you focus on the effects, and let OncoSimulR take care of
  doing the math of combining.
  
* If you want to use order effects, you must use the lego system (at
  least for now).
    
* If you want to specify modules, you must use the lego system (the
  explicit mapping of genotypes is, by its very nature, ill-suited for
  this).
  
* The lego system might help you see what your model really means: in
  many cases, you can obtain fairly succinct specification of complex
  fitness models with just a few terms. Similarly, depending on what your
  emphasis is, you can often specify the same fitness landscape in several
  different ways.
  



Regardless of the route, you need to get that information into
  OncoSimulR's functions. The main function we will use is
  *`allFitnessEffects`*: this is the function in charge of reading
  the fitness specifications. We also need to discuss how, what, and where
  you have to pass to *`allFitnessEffects`*.
 

### Explicit mapping of genotypes to fitness {#explicitmap}

Conceptually, the simplest way to specify fitness is to specify the
mapping of all genotypes to fitness explicitly. An example will make
this clear. Let's suppose you have a simple two-gene scenario, so a
total of four genotypes, and you have a data frame with genotypes
and fitness, where genoytpes are specified as character vectors,
with mutated genes separated by commas:

```{r}
m4 <- data.frame(G = c("WT", "A", "B", "A, B"), F = c(1, 2, 3, 4))
``` 

Now, let's give that to the *`allFitnessEffects`* function:

```{r}
fem4 <- allFitnessEffects(genotFitness = m4)
``` 
(The message is just telling you what the program guessed you
wanted.)


That's it. You can plot that fitnessEffects object
```{r}
plot(fem4)
``` 

In this case, that plot is not very interesting (compare with the
`plot(pancr)` we saw in \@ref(quickexample) or the plots in
\@ref(posetslong)). 

You can also check what OncoSimulR thinks the fitnesses are, with the
*`evalAllGenotypes`* function that we will use repeatedly below
(of course, here we should see the same fitnesses we entered):

```{r}
evalAllGenotypes(fem4, addwt = TRUE)
``` 


And you can plot the fitness landscape:

```{r}
plotFitnessLandscape(evalAllGenotypes(fem4))
``` 


To specify the mapping you can also use a matrix (or data frame) with
$g + 1$ columns; each of the first $g$ columns contains a 1 or a 0
indicating that the gene of that column is mutated or not. Column $g+ 1$
contains the fitness values. And you do not even need to specify all the
genotypes (we will assume that the missing genotypes have fitness 1):

```{r}
m6 <- cbind(c(1, 1), c(1, 0), c(2, 3))
fem6 <- allFitnessEffects(genotFitness = m6)
evalAllGenotypes(fem6, addwt = TRUE)
plot(fem6)
```

```{r, fig.width=6.5, fig.height = 6.5}
plotFitnessLandscape(evalAllGenotypes(fem6))
``` 


This way of giving a fitness specification to OncoSimulR might be
ideal if you directly generate random mappings of genotypes to
fitness (or random fitness landscapes), as we will do in section
\@ref(gener-fit-land).


We will see an example of this way of passing fitness again in
\@ref(bauer), where will compare it with the lego system.

<!-- % Please see the documentation of *`allFitnessEffects`* for further -->
<!-- % details and examples. -->





<!-- % This can be done with OncoSimulR (e.g., see sections \@ref(e2), \@ref(e3) -->
<!-- % and \@ref(theminus) or the example in \@ref(weis1b)), but this only makes -->
<!-- % sense for subsets of the genes or for very small genotypes, as you -->
<!-- % probably do not want to be explicit about the mapping of $2^k$ genotypes -->
<!-- % to fitness when $k$ is larger than, say, four or five, and definitely not -->
<!-- % when $k$ is 10. -->


### How to specify fitness effects with the lego system {#howfit}

<!-- % A guiding design principle of OncoSimulR is to try to make the -->
<!-- % specification of those effects as simple as possible but also as flexible -->
<!-- % as possible.  -->


An alternative general approach followed in many genetic simulators
is to specify how particular combinations of alleles modify the
wildtype genotype or the genotype that contains the individual
effects of the interacting genes (e.g., see equation 1 in the
supplementary material for FFPopSim, @Zanini2012).  For example, if
we specify that a mutation in "A" contributes 0.04, a mutation in
"B" contributes 0.03, and the double mutation "A:B" contributes 0.1,
that means that the fitness of the "A, B" genotype (the genotype
with A and B mutated) is that of the wildtype (1, by default), plus
(actually, times ---see section \@ref(numfit)) the effects of having
A mutated, plus (times) the effects of having B mutated, plus
(times) the effects of "A:B" both being mutated.


We will see below that with the "lego system" it is possible to do
something very similar to the explicit mapping of section
\@ref(explicitmap).  But this will sometimes require a more cumbersome
notation (and sometimes also will require your doing some math). We will see
examples in sections \@ref(e2), \@ref(e3) and \@ref(theminus) or the example
in \@ref(weis1b). But then, if we can be explicit about (at least some of)
the mappings $genotype \rightarrow fitness$, how are these procedures
different? When you use the "lego system" you can combine both a partial
explicit mapping of genotypes to fitness with arbitrary fitness effects of
other genes/modules. In other words, with the "lego system" OncoSimulR
makes it simple to be explicit about the mapping of specific genotypes,
while also using the "how this specific effects modifies previous
effects" logic, leading to a flexible specification. This also means that
in many cases the same fitness effects can be specified in several
different ways.

Most of the rest of this section is devoted to explaining how to combine
those pieces. Before that, however, we need to discuss the fitness model
we use.



<!-- % As we will see in the examples (e.g., see sections \@ref(e2), \@ref(e3), -->
<!-- % \@ref(exlong)) OncoSimulR makes it simple to be explicit about the mapping -->
<!-- % of specific genotypes, while also using the ``how this specific effects -->
<!-- % modifies previous effects" logic, leading to a flexible -->
<!-- % specification. This also means that in many cases the same fitness -->
<!-- % effects can be specified in several different ways. -->


## Numeric values of fitness effects {#numfit}

We evaluate fitness using the usual  [@Zanini2012; @Gillespie1993;
  @Beerenwinkel2007; @Datta2013] multiplicative model: fitness is
$\prod (1 + s_i)$ where $s_i$ is the fitness effect of gene (or gene
interaction) $i$.  In all models except Bozic, this fitness refers to the
growth rate (the death rate being fixed to 1[^2]).
The original model of @McFarland2013 has a slightly different
parameterization, but you can go easily from one to the other (see section
\@ref(mcfl)).

For the Bozic model [@Bozic2010], however, the birth rate is set to
1, and the death rate then becomes $\prod (1 - s_i)$.

[^2]: You can change this if you really want to. 


### McFarland parameterization {#mcfl}

In the original model of @McFarland2013, the effects of drivers
contribute to the numerator of the birth rate, and those of the
(deleterious) passengers to the denominator as: $\frac{(1 +
s)^D}{(1 - s_p)^P}$, where $D$ and $P$ are, respectively, the total
number of drivers and passengers in a genotype, and here the fitness
effects of all drivers is the same ($s$) and that of all passengers
the same too ($s_p$). However, we can map from this ratio to the
usual product of terms by using a different value of $s_p$, that we
will call $s_{pp} = -s_p/(1 + s_p)$ (see @McFarland2014-phd, his
eq. 2.1 in p.9).  This reparameterization applies to v.2. In v.1 we
use the same parameterization as in the original one in
@McFarland2013.



### No viability of clones and types of models {#noviab}

For all models where fitness affects directly the birth rate (for now, all
except Bozic), if you specify that some event (say, mutating gene A) has
$s_A \le -1$, if that event happens then birth rate becomes zero which is
taken to indicate that the clone is not even viable and thus disappears
immediately without any chance for mutation[^3].

[^3]:This is a shortcut that we take because we think that it is
  what you mean. Note, however, that technically a clone with birth
  rate of 0 might have a non-zero probability of mutating before
  becoming extinct because in the continuous time model we use
  mutation is not linked to reproduction. In the present code, we
  are not allowing for any mutation when birth rate is 0. There are
  other options, but none which I find really better. An alternative
  implementation makes a clone immediately extinct if and only if
  any of the $s_i = -\infty$.  However, we still need to handle the
  case with $s_i < -1$ as a special case. We either make it
  identical to the case with any $s_i = -\infty$ or for any $s_i >
  -\infty$ we set $(1 + s_i) = \max(0, 1 + s_i)$ (i.e., if $s_i <
  -1$ then $(1 + s_i) = 0$), to avoid obtaining negative birth rates
  (that make no sense) and the problem of multiplying an even number
  of negative numbers. I think only the second would make sense as
  an alternative.

Models based on Bozic, however, have a birth rate of 1 and mutations
affect the death rate. In this case, a death rate larger than birth rate,
per se, does not signal immediate extinction and, moreover, even for death
rates that are a few times larger than birth rates, the clone could mutate
before becoming extinct[^4].

[^4]:We said "a few times". For a clone of population size 1 ---which is
the size at which all clones start from mutation---, if death rate is,
say, 90 but birth rate is 1, the probability of mutating before becoming
extinct is very, very close to zero for all reasonable values of mutation
rate}. How do we signal immediate extinction or no viability in this case?
You can set the value of $s = -\infty$.

<!-- %% Setting a value of -->
<!-- %% $s < -90$ has the same effect. -->

In general, if you want to identify some mutations or some
combinations of mutations as leading to immediate extinction (i.e.,
no viability), of the affected clone, set it to $-\infty$ as this
would work even if how birth rates of 0 are handled changes. Most
examples below evaluate fitness by its effects on the birth
rate. You can see one where we do it both ways in Section
\@ref(fit-neg-pos).



<!-- \footnote{In the C++ -->
<!-- code there is a different model, not directly callable from R for now, -->
<!-- called ``bozic2" that is slightly different. These comments apply to -->
<!-- the model that is right now callable from R -->


## Genes without interactions {#noint}

This is a imple scenario. Each gene $i$ has a fitness effect $s_i$ if
mutated. The $s_i$ can come from any distribution you want. As an example
let's use three genes. We know there are no order effects, but we will
also see what happens if we examine genotypes as ordered.

```{r}

ai1 <- evalAllGenotypes(allFitnessEffects(
    noIntGenes = c(0.05, -.2, .1)), order = FALSE)
``` 


We can easily verify the first results:

```{r}
ai1
``` 

```{r}
all(ai1[, "Fitness"]  == c( (1 + .05), (1 - .2), (1 + .1),
       (1 + .05) * (1 - .2),
       (1 + .05) * (1 + .1),
       (1 - .2) * (1 + .1),
       (1 + .05) * (1 - .2) * (1 + .1)))

``` 

And we can see that considering the order of mutations (see section
\@ref(oe)) makes no difference:

```{r}
(ai2 <- evalAllGenotypes(allFitnessEffects(
    noIntGenes = c(0.05, -.2, .1)), order = TRUE,
    addwt = TRUE))

``` 

(The meaning of the notation in the output table is as follows: "WT"
denotes the wild-type, or non-mutated clone. The notation $x > y$ means
that a mutation in "x" happened before a mutation in "y". A genotype
$x > y\ \_\ z$ means that a mutation in "x" happened before a
mutation in "y"; there is also a mutation in "z", but that is a gene
for which order does not matter).



And what if I want genes without interactions but I want modules (see
section \@ref(modules0))? Go to section \@ref(mod-no-epi).



## Using DAGs: Restrictions in the order of mutations as extended posets {#posetslong}


### AND, OR, XOR relationships {#andorxor}

The literature on oncogenetic trees, CBNs, etc, has used graphs as a way
of showing the restrictions in the order in which mutations can
accumulate. The meaning of "convergent arrows" in these graphs, however,
differs. In Figure 1 of @Korsunsky2014 we are shown a simple diagram
that illustrates the three basic different meanings of convergent arrows
using two parental nodes. We will illustrate it here with three. Suppose
we focus on node "g" in the following figure (we will create it shortly)

```{r, fig.height=4}
data(examplesFitnessEffects)
plot(examplesFitnessEffects[["cbn1"]])
``` 


* In relationships of the type used in **Conjunctive Bayesian
  Networks (CBN)** [e.g., @Gerstung2009], we are modeling an **AND**
  relationship, also called **CMPN** by @Korsunsky2014 or
  **monotone** relationship by @Farahani2013. If the relationship in
  the graph is fully respected, then "g" will only appear if all of
  "c", "d", and "e" are already mutated.
  
* **Semimonotone** relationships *sensu*
  @Farahani2013 or **DMPN** *sensu*
  @Korsunsky2014 are **OR** relationships: "g" will appear if
  one or more of "c", "d", or "e" are already mutated.

* **XMPN** relationships [@Korsunsky2014] are **XOR**
  relationships: "g" will be present only if exactly one of "c",
  "d", or "e" is present. 



Note that oncogenetic trees [@Desper1999JCB; @Szabo2008] need not
deal with the above distinctions, since the DAGs are trees: no node has
more than one incoming connection or more than one parent[^5].

[^5]: OTs and CBNs have some other technical differences about the
underlying model they assume, such as the exponential waiting time in
CBNs. We will not discuss them here.


To have a flexible way of specifying all of these restrictions, we will
want to be able to say what kind of dependency each child
node has on its parents.


### Fitness effects {#fitnessposets}

Those DAGs specify dependencies and, as explained in
@Diaz-Uriarte2015, it is simple to map them to a simple evolutionary
model: any set of mutations that does not conform to the restrictions
encoded in the graph will have a fitness of 0. However, we might not want
to require absolute compliance with the DAG. This means we might want to
allow deviations from the DAG with a corresponding penalization that is,
however, not identical to setting fitness to 0 [again, see
@Diaz-Uriarte2015]. This we can do by being explicit about the
fitness effects of the deviations from the restrictions encoded in the
DAG. We will use below a column of `s` for the fitness effect when
the restrictions are satisfied and a column of `sh` when they are
not. (See also \@ref(numfit) for the details about the meaning of the
fitness effects).


That way of specifying fitness effects makes it also trivial to use the
model in @Hjelm2006 where all mutations might be allowed to occur,
but the presence of some mutations increases the probability of occurrence
of other mutations. For example, the values of `sh` could be all
small positive ones (or for mildly deleterious effects, small negative
numbers), while the values of `s` are much larger positive numbers.


### Extended posets

In version 1 of this package we used posets in the sense of
@Beerenwinkel2007 and @Gerstung2009, as explained in section
\@ref(poset) and in the help for *`poset`*. Here, we continue using
two columns, that specify parents and children, but we add columns
for the specific values of fitness effects (both s and sh ---i.e.,
fitness effects for what happens when restrictions are and are not
satisfied) and for the type of dependency as explained in section
\@ref(andorxor).



We can now illustrate the specification of different fitness effects
using DAGs.

### DAGs: A first conjunction (AND) example {#cbn1}

```{r}

cs <-  data.frame(parent = c(rep("Root", 4), "a", "b", "d", "e", "c"),
                 child = c("a", "b", "d", "e", "c", "c", rep("g", 3)),
                 s = 0.1,
                 sh = -0.9,
                 typeDep = "MN")

cbn1 <- allFitnessEffects(cs)

``` 

(We skip one letter, just to show that names need not be consecutive or
have any particular order.)


We can get a graphical representation using the default "graphNEL"
```{r, fig.height=3}
plot(cbn1)
``` 

or one using "igraph":
```{r, fig.height=5}
plot(cbn1, "igraph")
``` 

<!-- %% The vignette crashes if I try to use the layout. -->

Since we have a parent and children, the reingold.tilford layout is
probably the best here, so you might want to use that:

```{r, fig.height=5}
library(igraph) ## to make the reingold.tilford layout available
plot(cbn1, "igraph", layout = layout.reingold.tilford)
``` 



And what is the fitness of all genotypes?

```{r}
gfs <- evalAllGenotypes(cbn1, order = FALSE, addwt = TRUE)

gfs[1:15, ]
```

You can verify that for each genotype, if a mutation is present without
all of its dependencies present, you get a $(1 - 0.9)$ multiplier, and you
get a $(1 + 0.1)$ multiplier for all the rest with its direct parents
satisfied. For example, genotypes "a", or "b", or "d", or "e" have
fitness $(1 + 0.1)$, genotype "a, b, c" has fitness $(1 + 0.1)^3$, but
genotype "a, c" has fitness $(1 + 0.1) (1 - 0.9) = 0.11$.



### DAGs: A second conjunction example {#cbn2}


Let's try a first attempt at a somewhat more complex example, where the
fitness consequences of different genes differ.
```{r}

c1 <- data.frame(parent = c(rep("Root", 4), "a", "b", "d", "e", "c"),
                 child = c("a", "b", "d", "e", "c", "c", rep("g", 3)),
                 s = c(0.01, 0.02, 0.03, 0.04, 0.1, 0.1, rep(0.2, 3)),
                 sh = c(rep(0, 4), c(-.1, -.2), c(-.05, -.06, -.07)),
                 typeDep = "MN")

try(fc1 <- allFitnessEffects(c1))

``` 
If you try this, you'll get an error. There is an error because the
"sh" varies within a child, and we do not allow that for a
poset-type specification, as it is ambiguous. If you need arbitrary
fitness values for arbitrary combinations of genotypes, you can
specify them using epistatic effects as in section \@ref(epi) and
order effects as in section \@ref(oe).

Why do we need to specify as many "s" and "sh" as there are rows (or a
single one, that gets expanded to those many) when the "s" and "sh"
are properties of the child node, not of the edges? Because, for ease, we
use a data.frame.

<!-- %% (By the way, yes, we convert all factors to strings in the parent, child, -->
<!-- %% and typeDep columns, so no need to specify `stringsAsFactor = TRUE`). -->



We fix the error in our specification. Notice that the "sh" is not set
to $-1$ in these examples. If you want strict compliance with the poset
restrictions, you should set $sh = -1$ or, better yet, $sh = -\infty$ (see
section \@ref(noviab)), but having an $sh > -1$ will lead to fitnesses that
are $> 0$ and, thus, is a way of modeling small deviations from the poset
[see discussion in @Diaz-Uriarte2015].

<!-- %% In these examples, the reason to set "sh" to values larger than $-1$ and -->
<!-- %% different among the genes is to allow us to easily see the actual, -->
<!-- %% different, terms that enter into the multiplication of the fitness effects -->
<!-- %% (and, also, to make it easier to catch bugs). -->


Note that for those nodes that depend only on "Root" the type of
dependency is irrelevant.

```{r}
c1 <- data.frame(parent = c(rep("Root", 4), "a", "b", "d", "e", "c"),
                 child = c("a", "b", "d", "e", "c", "c", rep("g", 3)),
                 s = c(0.01, 0.02, 0.03, 0.04, 0.1, 0.1, rep(0.2, 3)),
                 sh = c(rep(0, 4), c(-.9, -.9), rep(-.95, 3)),
                 typeDep = "MN")

cbn2 <- allFitnessEffects(c1)

``` 

<!-- %% We can get a graphical representation using the default "graphNEL" -->
<!-- %% <<fig.height=3>>= -->
<!-- %% plot(cbn2) -->
<!-- %% @  -->

<!-- %% or one using "igraph": -->
<!-- %% <<fig.height=5>>= -->
<!-- %%plot(cbn2, "igraph", layout = layout.reingold.tilford) -->
<!-- %% @  -->

<!-- %% (since this is a tree, the reingold.tilford layout is probably the best here). -->

We could get graphical representations but the figures would
be the same as in the example in section \@ref(cbn1), since the structure
has not changed, only the numeric values.

What is the fitness of all possible genotypes? Here, order of events
*per se* does not matter, beyond that considered in the poset. In
other words, the fitness of genotype "a, b, c" is the same no matter how
we got to "a, b, c". What matters is whether or not the genes on which
each of "a", "b", and "c" depend are present or not (I only show the first
10 genotypes)

```{r}
gcbn2 <- evalAllGenotypes(cbn2, order = FALSE)
gcbn2[1:10, ]
``` 


Of course, if we were to look at genotypes but taking into account order
of occurrence of mutations, we would see no differences

```{r}
gcbn2o <- evalAllGenotypes(cbn2, order = TRUE, max = 1956)
gcbn2o[1:10, ]
``` 

(The $max = 1956$ is there so that we show all the genotypes, even
if they are more than 256, the default.)

You can check the output and verify things are as they should. For instance:

```{r}
all.equal(
        gcbn2[c(1:21, 22, 28, 41, 44, 56, 63 ) , "Fitness"],
        c(1.01, 1.02, 0.1, 1.03, 1.04, 0.05,
          1.01 * c(1.02, 0.1, 1.03, 1.04, 0.05),
          1.02 * c(0.10, 1.03, 1.04, 0.05),
          0.1 * c(1.03, 1.04, 0.05),
          1.03 * c(1.04, 0.05),
          1.04 * 0.05,
          1.01 * 1.02 * 1.1,
          1.01 * 0.1 * 0.05,
          1.03 * 1.04 * 0.05,
          1.01 * 1.02 * 1.1 * 0.05,
          1.03 * 1.04 * 1.2 * 0.1, ## notice this
          1.01 * 1.02 * 1.03 * 1.04 * 1.1 * 1.2
          ))
``` 

A particular one that is important to understand is genotype with
mutated genes "c, d, e, g":

```{r}
gcbn2[56, ] 
all.equal(gcbn2[56, "Fitness"], 1.03 * 1.04 * 1.2 * 0.10)
``` 

where "g" is taken as if its dependencies are satisfied (as "c",
``d", and "e" are present) even when the dependencies of "c" are not
satisfied (and that is why the term for "c" is 0.9).


### DAGs: A semimonotone or "OR" example {#mn1}

We will reuse the above example, changing the type of relationship:
```{r}

s1 <- data.frame(parent = c(rep("Root", 4), "a", "b", "d", "e", "c"),
                 child = c("a", "b", "d", "e", "c", "c", rep("g", 3)),
                 s = c(0.01, 0.02, 0.03, 0.04, 0.1, 0.1, rep(0.2, 3)),
                 sh = c(rep(0, 4), c(-.9, -.9), rep(-.95, 3)),
                 typeDep = "SM")

smn1 <- allFitnessEffects(s1)

``` 

It looks like this (where edges are shown in blue to denote the
semimonotone relationship):
```{r, fig.height=3}
plot(smn1)
``` 


```{r}
gsmn1 <- evalAllGenotypes(smn1, order = FALSE)

``` 

Having just one parental dependency satisfied is now enough, in contrast
to what happened before. For instance:

```{r}
gcbn2[c(8, 12, 22), ]
gsmn1[c(8, 12, 22), ]

gcbn2[c(20:21, 28), ]
gsmn1[c(20:21, 28), ]
``` 


### An "XMPN" or "XOR" example {#xor1}

Again, we reuse the example above, changing the type of relationship:

```{r}

x1 <- data.frame(parent = c(rep("Root", 4), "a", "b", "d", "e", "c"),
                 child = c("a", "b", "d", "e", "c", "c", rep("g", 3)),
                 s = c(0.01, 0.02, 0.03, 0.04, 0.1, 0.1, rep(0.2, 3)),
                 sh = c(rep(0, 4), c(-.9, -.9), rep(-.95, 3)),
                 typeDep = "XMPN")

xor1 <- allFitnessEffects(x1)

``` 


It looks like this (edges in red to denote the "XOR" relationship):
```{r, fig.height=3}
plot(xor1)
``` 

```{r}

gxor1 <- evalAllGenotypes(xor1, order = FALSE)

``` 


Whenever "c" is present with both "a" and "b", the fitness component
for "c" will be $(1 - 0.1)$. Similarly for "g" (if more than one of
``d", "e", or "c" is present, it will show as $(1 - 0.05)$). For example:

```{r}
gxor1[c(22, 41), ] 
c(1.01 * 1.02 * 0.1, 1.03 * 1.04 * 0.05)
``` 

However, having just both "a" and "b" is identical to the case with
CBN and the monotone relationship (see sections \@ref(cbn2) and
\@ref(mn1)). If you want the joint presence of "a" and "b" to result in
different fitness than the product of the individual terms, without
considering the presence of "c", you can specify that using general
epistatic effects (section
\@ref(epi)).

<!-- %% ; XOR relationships of these kind are, actually, -->
<!-- %% examples of synthetic lethality, which are shown in section \@ref(sl). -->


We also see a very different pattern compared to CBN (section \@ref(cbn2))
here:
```{r}
gxor1[28, ] 
1.01 * 1.1 * 1.2
``` 

as exactly one of the dependencies for both "c" and "g" are satisfied.

But 
```{r}
gxor1[44, ] 
1.01 * 1.02 * 0.1 * 1.2
``` 
is the result of a $0.1$ for "c" (and a $1.2$ for "g" that has exactly
one of its dependencies satisfied).


### Posets: the three types of relationships {#p3}

```{r}

p3 <- data.frame(
    parent = c(rep("Root", 4), "a", "b", "d", "e", "c", "f"),
    child = c("a", "b", "d", "e", "c", "c", "f", "f", "g", "g"),
    s = c(0.01, 0.02, 0.03, 0.04, 0.1, 0.1, 0.2, 0.2, 0.3, 0.3),
    sh = c(rep(0, 4), c(-.9, -.9), c(-.95, -.95), c(-.99, -.99)),
    typeDep = c(rep("--", 4), 
                "XMPN", "XMPN", "MN", "MN", "SM", "SM"))
fp3 <- allFitnessEffects(p3)
``` 

This is how it looks like:
```{r, fig.height=3}
plot(fp3)
``` 

We can also use "igraph":

```{r, fig.height=6}
plot(fp3, "igraph", layout.reingold.tilford)
``` 


```{r}

gfp3 <- evalAllGenotypes(fp3, order = FALSE)

``` 



Let's look at a few:

```{r}
gfp3[c(9, 24, 29, 59, 60, 66, 119, 120, 126, 127), ]

c(1.01 * 1.1, 1.03 * .05, 1.01 * 1.02 * 0.1, 0.1 * 0.05 * 1.3,
  1.03 * 1.04 * 1.2, 1.01 * 1.02 * 0.1 * 0.05,
  0.1 * 1.03 * 1.04 * 1.2 * 1.3,
  1.01 * 1.02 * 0.1 * 1.03 * 1.04 * 1.2,
  1.02 * 1.1 * 1.03 * 1.04 * 1.2 * 1.3,
  1.01 * 1.02 * 1.03 * 1.04 * 0.1 * 1.2 * 1.3)

``` 

As before, looking at the order of mutations makes no difference (look at
the test directory to see a test that verifies this assertion).



## Modules {#modules0}
As already mentioned, we can think in all the effects of fitness in terms
not of individual genes but, rather, modules. This idea is discussed in,
for example, @Raphael2014a, @Gerstung2011: the restrictions encoded
in, say, the DAGs can be considered to apply not to genes, but to
modules, where each module is a set of genes (and the intersection between
modules is the empty set). Modules, then, play the role of a "union
operation" over sets of genes. Of course, if we can use modules for the
restrictions in the DAGs we should also be able to use them for epistasis
and order effects, as we will see later (e.g., \@ref(oemod)).







### What does a module provide {#module-what-for}

Modules can provide very compact ways of specifying relationships when you
want to, well, model the existence of modules. For simplicity suppose
there is a module, "A", made of genes "a1" and "a2", and a module
"B", made of a single gene "b1". Module "B" can mutate if module
"A" is mutated, but mutating both "a1" and "a2" provides no
additional fitness advantage compared to mutating only a single one of
them.  We can specify this as:

```{r}
s <- 0.2
sboth <- (1/(1 + s)) - 1
m0 <- allFitnessEffects(data.frame(
    parent = c("Root", "Root", "a1", "a2"),
    child = c("a1", "a2", "b", "b"),
    s = s,
    sh = -1,
    typeDep = "OR"),
                        epistasis = c("a1:a2" = sboth))
evalAllGenotypes(m0, order = FALSE, addwt = TRUE)
``` 

Note that we need to add an epistasis term, with value "sboth"
to capture the idea of "mutating both "a1" and "a2"
provides no additional fitness advantage compared to mutating only a
single one of them"; see details in section \@ref(epi).



Now, specify it using modules:

```{r}
s <- 0.2
m1 <- allFitnessEffects(data.frame(
    parent = c("Root", "A"),
    child = c("A", "B"),
    s = s,
    sh = -1,
    typeDep = "OR"),
                        geneToModule = c("Root" = "Root",
                                         "A" = "a1, a2",
                                         "B" = "b1"))
evalAllGenotypes(m1, order = FALSE, addwt = TRUE)
``` 

This captures the ideas directly. The typing savings here are small, but
they can be large with modules with many genes.


<!-- %% %% \begin{tabular} {c c c} -->
<!-- %% %%   A & B & Fitness \\ -->
<!-- %% %%   \hline -->
<!-- %% %%   wt&wt& 1 \\ -->
<!-- %% %%   wt&M& sb \\ -->
<!-- %% %%   M&wt& sa\\ -->
<!-- %% %%   M&M& sab)\\ -->
<!-- %% %%   \hline -->
<!-- %% %% \end{tabular} -->

<!-- %% with A being 1, 2, and B 3, 4. -->

<!-- %% and having in a tree A depends on Root and B depends on A -->



<!-- %% \begin{tabular} {c c c} -->
<!-- %%   model & Fitness satisfied & fitness not satisf\\ -->
<!-- %%   \hline -->
<!-- %%   0 , 1 & s \\ -->
<!-- %%   0 , 2 & s \\ -->

<!-- %%   1 , 3 & s3 & sm \\ -->
<!-- %%   2 , 3 & s3 & sm \\ -->

<!-- %%   1 , 4 & s3 & sm \\ -->
<!-- %%   2 , 4 & s3 & sm \\ -->
  
<!-- %%   1 : 2 & s12 \\ -->
<!-- %%   3:  4 & s34 \\ -->
  

<!-- %%   \hline -->
<!-- %% \end{tabular} -->

<!-- %% just give the specification, the full one. -->


<!-- %% and write equivalendes of s12 as a function of Sa, S34 as a function of -->
<!-- %% Sb, etc. -->

### Specifying modules {#modules}

How do you specify modules? The general procedure is simple: you pass a
vector that makes explicit the mapping from modules to sets of genes. We
just saw an example. There are several additional examples such as
\@ref(pm3), \@ref(oemod), \@ref(epimod).

<!-- %% Why do we force you to specify "Root" = "Root"? We could check for it, -->
<!-- %% and add it if it is not present. But we want you to be explicit (and we -->
<!-- %% want to avoid you shooting yourself in the foot having a gene that is not -->
<!-- %% the root of the tree but is called "Root", etc). -->


It is important to note that, once you specify modules, we expect all of
the relationships (except those that involve the non interacting genes) to
be specified as modules. Thus, all elements of the epistasis, posets (the
DAGs) and order effects components should be specified in terms of
modules. But you can, of course, specify a module as containing a single
gene (and a single gene with the same name as the module).


What about the "Root" node? If you use a "restriction table", that
restriction table (that DAG) must have a node named "Root" and in the
mapping of genes to module there **must** be a first entry that has a
module and gene named "Root", as we saw above with 
`geneToModule  = c("Root" = "Root", ...`. 
We force you to do this to be explicit about
the "Root" node. This is not needed (thought it does not hurt) with
other fitness specifications. For instance, if we have a model with two
modules, one of them with two genes (see details in section
\@ref(mod-no-epi)) we do not need to pass a "Root" as in


```{r}
fnme <- allFitnessEffects(epistasis = c("A" = 0.1,
                                        "B" = 0.2),
                          geneToModule = c("A" = "a1, a2",
                                           "B" = "b1"))
evalAllGenotypes(fnme, order = FALSE, addwt = TRUE)
``` 

but it is also OK to have a "Root" in the `geneToModule`:

```{r}
fnme2 <- allFitnessEffects(epistasis = c("A" = 0.1,
                                        "B" = 0.2),
                          geneToModule = c(
                              "Root" = "Root",
                              "A" = "a1, a2",
                              "B" = "b1"))
evalAllGenotypes(fnme, order = FALSE, addwt = TRUE)
``` 


### Modules and posets again: the three types of relationships and modules {#pm3}


We use the same specification of poset, but add modules. To keep it
manageable, we only add a few genes for some modules, and have some
modules with a single gene. Beware that the number of genotypes is
starting to grow quite fast, though.  We capitalize to differentiate
modules (capital letters) from genes (lowercase with a number), but this
is not needed.


```{r}
p4 <- data.frame(
    parent = c(rep("Root", 4), "A", "B", "D", "E", "C", "F"),
    child = c("A", "B", "D", "E", "C", "C", "F", "F", "G", "G"),
    s = c(0.01, 0.02, 0.03, 0.04, 0.1, 0.1, 0.2, 0.2, 0.3, 0.3),
    sh = c(rep(0, 4), c(-.9, -.9), c(-.95, -.95), c(-.99, -.99)),
    typeDep = c(rep("--", 4), 
                "XMPN", "XMPN", "MN", "MN", "SM", "SM"))

fp4m <- allFitnessEffects(
    p4,
    geneToModule = c("Root" = "Root", "A" = "a1",
                     "B" = "b1, b2", "C" = "c1",
                     "D" = "d1, d2", "E" = "e1",
                     "F" = "f1, f2", "G" = "g1"))
``` 

By default, plotting shows the modules:

```{r, fig.height=3}
plot(fp4m)
``` 

but we can show the gene names instead of the module names:

```{r, fig.height=3}
plot(fp4m, expandModules = TRUE)
``` 

or

```{r, fig.height=6}
plot(fp4m, "igraph", layout = layout.reingold.tilford, 
     expandModules = TRUE)

``` 

We obtain the fitness of all genotypes in the usual way:

```{r}
gfp4 <- evalAllGenotypes(fp4m, order = FALSE, max = 1024)
``` 

Let's look at a few of those:

```{r}
gfp4[c(12, 20, 21, 40, 41, 46, 50, 55, 64, 92,
       155, 157, 163, 372, 632, 828), ]

c(1.01 * 1.02, 1.02, 1.02 * 1.1, 0.1 * 1.3, 1.03, 
  1.03 * 1.04, 1.04 * 0.05, 0.05 * 1.3,  
  1.01 * 1.02 * 0.1, 1.02 * 1.1, 0.1 * 0.05 * 1.3,
  1.03 * 0.05, 1.03 * 0.05, 1.03 * 1.04 * 1.2, 1.03 * 1.04 * 1.2, 
  1.02 * 1.1 * 1.03 * 1.04 * 1.2 * 1.3)

``` 



## Order effects {#oe}

As explained in the introduction (\@ref(intro)), by order effects we
mean a phenomenon such as the one shown empirically by @Ortmann2015:
the fitness of a double mutant "A", "B" is different depending on
whether "A" was acquired before "B" or "B" before "A". This, of
course, can be generalized to more than two genes.

Note that these order effects are different from the order
restrictions discussed in section \@ref(posetslong). In there we
might say that acquiring "B" depends or is facilitated by having "A"
mutated (and, unless we allowed for multiple mutations, having "A"
mutated means having "A" mutated before "B"). However, once you have
the genotype "A, B", its fitness does not depend on the order in
which "A" and "B" appeared.



### Order effects: three-gene orders

Consider this case, where three specific three-gene orders and two
two-gene orders (one of them a subset of one of the three) lead to
different fitness compared to the wild-type. We add also modules, to show
its usage (but just limit ourselves to using one gene per module here). 

Order effects are specified using a $x > y$, that means that that order
effect is satisfied when module $x$ is mutated before module $y$.

```{r}
o3 <- allFitnessEffects(orderEffects = c(
                            "F > D > M" = -0.3,
                            "D > F > M" = 0.4,
                            "D > M > F" = 0.2,
                            "D > M"     = 0.1,
                            "M > D"     = 0.5),
                        geneToModule =
                            c("M" = "m",
                              "F" = "f",
                              "D" = "d") )


(ag <- evalAllGenotypes(o3, addwt = TRUE, order = TRUE))
``` 


<!-- %% <<>>= -->
<!-- %% o3 <- allFitnessEffects(orderEffects = c( -->
<!-- %%                             "F > D > M" = -0.3, -->
<!-- %%                             "D > F > M" = 0.4, -->
<!-- %%                             "D > M > F" = 0.2, -->
<!-- %%                             "D > M"     = 0.1, -->
<!-- %%                             "M > D"     = 0.5), -->
<!-- %%                         geneToModule = -->
<!-- %%                             c("Root" = "Root", -->
<!-- %%                               "M" = "m", -->
<!-- %%                               "F" = "f", -->
<!-- %%                               "D" = "d") ) -->
<!-- %% (ag <- evalAllGenotypes(o3, addwt = TRUE)) -->
<!-- %% @  -->

(The meaning of the notation in the output table is as follows: "WT"
denotes the wild-type, or non-mutated clone. The notation $x > y$ means
that a mutation in "x" happened before a mutation in "y". A genotype
$x > y\ \_\ z$ means that a mutation in "x" happened before a
mutation in "y"; there is also a mutation in "z", but that is a gene
for which order does not matter).


The values for the first nine genotypes come directly from the fitness
specifications. The 10th genotype matches $D > F > M$ ($= (1 + 0.4)$)
but also $D > M$ ($(1 + 0.1)$). The 11th matches $D > M > F$ and $D >
M$. The 12th matches $F > D > M$ but also $D > M$. Etc.




### Order effects and modules with multiple genes {#oemod}

Consider the following case:

```{r}

ofe1 <- allFitnessEffects(
    orderEffects = c("F > D" = -0.3, "D > F" = 0.4),
    geneToModule =
        c("F" = "f1, f2",
          "D" = "d1, d2") )

ag <- evalAllGenotypes(ofe1, order = TRUE)

``` 

There are four genes, $d1, d2, f1, f2$, where each $d$ belongs to module
$D$ and each $f$ belongs to module $F$.

What to expect for cases such as $d1 > f1$ or $f1 > d1$ is clear, as shown in

```{r}
ag[5:16,]
``` 

Likewise, cases such as $d1 > d2 > f1$ or $f2 > f1 > d1$ are clear,
because in terms of modules they map to $ D > F$ or $F > D$: the observed
order of mutation $d1 > d2 > f1$ means that module $D$ was mutated first
and module $F$ was mutated second. Similar for $d1 > f1 > f2$ or
$f1 > d1 > d2$: those map to $D > F$ and $F > D$. We can see the fitness
of those four case in:

```{r}
ag[c(17, 39, 19, 29), ]
``` 

and they correspond to the values of those order effects, where $F > D =
(1 - 0.3)$ and $D > F = (1 + 0.4)$:

```{r}
ag[c(17, 39, 19, 29), "Fitness"] == c(1.4, 0.7, 1.4, 0.7)
``` 

What if we match several patterns? For example, $d1 > f1 > d2 > f2$ and
$d1 > f1 > f2 > d2$? The first maps to $D > F > D > F$ and the second to
$D > F > D$. But since we are concerned with which one happened first and
which happened second we should expect those two to correspond to the same
fitness, that of pattern $D > F$, as is the case:

```{r}
ag[c(43, 44),]
ag[c(43, 44), "Fitness"] == c(1.4, 1.4)
``` 
More generally, that applies to all the patterns that start with one of
the "d" genes:

```{r}
all(ag[41:52, "Fitness"] == 1.4)
``` 

Similar arguments apply to the opposite pattern, $F > D$, which apply to
all the possible gene mutation orders that start with one of the "f"
genes. For example:

```{r}
all(ag[53:64, "Fitness"] == 0.7)
``` 



### Order and modules with 325 genotypes

We can of course have more than two genes per module. This just repeats
the above, with five genes (there are 325 genotypes, and that is why we
pass the "max" argument to *`evalAllGenotypes`*, to allow for
more than the default 256).

```{r}

ofe2 <- allFitnessEffects(
    orderEffects = c("F > D" = -0.3, "D > F" = 0.4),
    geneToModule =
        c("F" = "f1, f2, f3",
          "D" = "d1, d2") )
ag2 <- evalAllGenotypes(ofe2, max = 325, order = TRUE)

``` 

We can verify that any combination that starts with a "d" gene and then
contains at least one "f" gene will have  a fitness of $1+0.4$.  And any
combination that starts with an "f" gene and contains at least one "d"
genes will have a fitness of $1 - 0.3$.  All other genotypes have a
fitness of 1:

```{r}
all(ag2[grep("^d.*f.*", ag2[, 1]), "Fitness"] == 1.4)
all(ag2[grep("^f.*d.*", ag2[, 1]), "Fitness"] == 0.7)
oe <- c(grep("^f.*d.*", ag2[, 1]), grep("^d.*f.*", ag2[, 1]))
all(ag2[-oe, "Fitness"] == 1)
``` 



### Order effects and genes without interactions

We will now look at both order effects and interactions. To make things
more interesting, we name genes so that the ordered names do split nicely
between those with and those without order effects (this, thus, also
serves as a test of messy orders of names).

```{r}

foi1 <- allFitnessEffects(
    orderEffects = c("D>B" = -0.2, "B > D" = 0.3),
    noIntGenes = c("A" = 0.05, "C" = -.2, "E" = .1))

``` 

You can get a verbose view of what the gene names and modules are (and
their automatically created numeric codes) by:

```{r}
foi1[c("geneModule", "long.geneNoInt")]
``` 

We can get the fitness of all genotypes (we set $max = 325$ because that
is the number of possible genotypes):

```{r}
agoi1 <- evalAllGenotypes(foi1,  max = 325, order = TRUE)
head(agoi1)
``` 



Now:
```{r}
rn <- 1:nrow(agoi1)
names(rn) <- agoi1[, 1]

agoi1[rn[LETTERS[1:5]], "Fitness"] == c(1.05, 1, 0.8, 1, 1.1)

``` 

According to the fitness effects we have specified, we also know that any
genotype with only two mutations, one of which is either "A", "C" "E" and
the other is "B" or "D" will have the fitness corresponding to "A", "C" or
"E", respectively:

```{r}
agoi1[grep("^A > [BD]$", names(rn)), "Fitness"] == 1.05
agoi1[grep("^C > [BD]$", names(rn)), "Fitness"] == 0.8
agoi1[grep("^E > [BD]$", names(rn)), "Fitness"] == 1.1
agoi1[grep("^[BD] > A$", names(rn)), "Fitness"] == 1.05
agoi1[grep("^[BD] > C$", names(rn)), "Fitness"] == 0.8
agoi1[grep("^[BD] > E$", names(rn)), "Fitness"] == 1.1
``` 


We will not be playing many additional games with regular expressions, but
let us check those that start with "D" and have all the other mutations,
which occupy rows 230 to 253; fitness should be equal (within numerical
error, because of floating point arithmetic) to the order effect of "D"
before "B" times the other effects $(1 - 0.3) * 1.05 * 0.8 * 1.1 = 0.7392$

```{r}
all.equal(agoi1[230:253, "Fitness"] ,
          rep((1 - 0.2) * 1.05 * 0.8 * 1.1, 24))
``` 
and that will also be the value of any genotype with the five mutations
where "D" comes before "B" such as those in rows 260 to 265, 277, or
322 and 323, but it will be equal to $(1 + 0.3) * 1.05 * 0.8 * 1.1 =
1.2012$ in those where "B" comes before "D". Analogous arguments apply
to four, three, and two mutation genotypes.





## Synthetic viability {#sv}

Synthetic viability and synthetic lethality
  [e.g., @Ashworth2011; @Hartman2001] are just special cases of epistasis
  (section \@ref(epi)) but we deal with them here separately.


### A simple synthetic viability example
A simple and extreme example of synthetic viability is shown in the
following table, where the joint mutant has fitness larger than the wild
type, but each single mutant is lethal.



---------------
A  B   Fitness
-- -- ----------
wt wt  1

wt M   0

M  wt  0

M  M   (1 + s)
-- -- --------


where "wt" denotes wild type and "M" denotes mutant.


We can specify this (setting $s = 0.2$) as (I play around with spaces, to
show there is a certain flexibility with them):

```{r}
s <- 0.2
sv <- allFitnessEffects(epistasis = c("-A : B" = -1,
                                      "A : -B" = -1,
                                      "A:B" = s))
``` 

Now, let's look at all the genotypes (we use "addwt" to also get the wt,
which by decree has fitness of 1), and disregard order:

```{r}
(asv <- evalAllGenotypes(sv, order = FALSE, addwt = TRUE))
``` 

Asking the program to consider the order of mutations of course makes no
difference:

```{r}
evalAllGenotypes(sv, order = TRUE, addwt = TRUE)
``` 

Another example of synthetic viability is shown in section \@ref(misra1b).

Of course, if multiple simultaneous mutations are not possible in the
simulations, it is not possible to go from the wildtype to the double
mutant in this model where the single mutants are not viable.




### Synthetic viability using Bozic model {#fit-neg-pos}

If we were to use the above specification with Bozic's models, we might
not get what we think we should get:

```{r}
evalAllGenotypes(sv, order = FALSE, addwt = TRUE, model = "Bozic")
```

What gives here? The simulation code would alert you of this (see section
\@ref(fit-neg-pos)) in this particular case because there are ``-1",
which might indicate that this is not what you want. The problem is that
you probably want the Death rate to be infinity (the birth rate was 0, so
no clone viability, when we used birth rates ---section \@ref(noviab)).

Let us say so explicitly:

```{r}
s <- 0.2
svB <- allFitnessEffects(epistasis = c("-A : B" = -Inf,
                                      "A : -B" = -Inf,
                                      "A:B" = s))
evalAllGenotypes(svB, order = FALSE, addwt = TRUE, model = "Bozic")
```


Likewise, values of $s$ larger than one have no effect beyond setting $s =
1$ (a single term of $(1 - 1)$ will drive the product to 0, and as we
cannot allow negative death rates negative values are set to 0):


```{r}

s <- 1
svB1 <- allFitnessEffects(epistasis = c("-A : B" = -Inf,
                                       "A : -B" = -Inf,
                                       "A:B" = s))

evalAllGenotypes(svB1, order = FALSE, addwt = TRUE, model = "Bozic")


s <- 3
svB3 <- allFitnessEffects(epistasis = c("-A : B" = -Inf,
                                       "A : -B" = -Inf,
                                       "A:B" = s))

evalAllGenotypes(svB3, order = FALSE, addwt = TRUE, model = "Bozic")


```

Of course, death rates of 0.0 are likely to lead to trouble down the road,
when we actually conduct simulations (see section \@ref(ex-0-death)).



### Synthetic viability, non-zero fitness, and modules

This is a slightly more elaborate case, where there is one module and the
single mutants have different fitness between themselves, which is
non-zero. Without the modules, this is the same as in Misra et
al. @Misra2014, Figure 1b, which we go over in section \@ref(misra).


---------------------
A  B       Fitness 
-- --   -------------
wt wt     1 

wt M     $1 + s_b$ 

M  wt     $1 + s_a$

M  M     $1 + s_{ab}$
-- -- ----------------


where $s_a, s_b < 0$ but $s_{ab} > 0$. 



```{r}
sa <- -0.1
sb <- -0.2
sab <- 0.25
sv2 <- allFitnessEffects(epistasis = c("-A : B" = sb,
                             "A : -B" = sa,
                             "A:B" = sab),
                         geneToModule = c(
                             "A" = "a1, a2",
                             "B" = "b"))
evalAllGenotypes(sv2, order = FALSE, addwt = TRUE)
``` 

And if we look at order, of course it makes no difference:

```{r}
evalAllGenotypes(sv2, order = TRUE, addwt = TRUE)
``` 

<!-- %% And it looks like: -->
<!-- %% <<>>= -->
<!-- %% plot(sv2) -->
<!-- %% @  -->
<!-- %% a fairly simple plot. -->


## Synthetic mortality or synthetic lethality {#sl}

In contrast to section \@ref(sv), here the joint mutant has decreased viability:

-------------------------
A    B        Fitness 
--- ---   -------------
wt  wt                1 

wt  M         $1 + s_b$ 

M   wt        $1 + s_a$

M   M      $1 + s_{ab}$
--  --  ----------------

where $s_a, s_b > 0$ but $s_{ab} < 0$. 



```{r}
sa <- 0.1
sb <- 0.2
sab <- -0.8
sm1 <- allFitnessEffects(epistasis = c("-A : B" = sb,
                             "A : -B" = sa,
                             "A:B" = sab))
evalAllGenotypes(sm1, order = FALSE, addwt = TRUE)

``` 

And if we look at order, of course it makes no difference:

```{r}
evalAllGenotypes(sm1, order = TRUE, addwt = TRUE)
``` 

## Epistasis {#epi}

### Epistasis: two alternative specifications {#e2}

We want the following mapping of genotypes to fitness:

------------------------
A    B       Fitness 
--   --   --------------
wt   wt    1 

wt   M     $1 + s_b$ 

M    wt    $1 + s_a$

M    M     $1 + s_{ab}$
--  --    --------------- 
 
Suppose that the actual numerical values are $s_a = 0.2, s_b = 0.3, s_{ab}
= 0.7$.

We specify the above as follows: 
```{r}
sa <- 0.2
sb <- 0.3
sab <- 0.7

e2 <- allFitnessEffects(epistasis =
                            c("A: -B" = sa,
                              "-A:B" = sb,
                              "A : B" = sab))
evalAllGenotypes(e2, order = FALSE, addwt = TRUE)

``` 

That uses the "-" specification, so we explicitly exclude some patterns:
with "A:-B" we say "A when there is no B".

But we can also use a specification where we do not use the "-". That
requires a different numerical value of the interaction, because now, as
we are rewriting the interaction term as genotype "A is mutant, B is
mutant" the double mutant will incorporate the effects of "A mutant",
``B mutant" and "both A and B mutants". We can define a new $s_2$ that
satisfies $(1 + s_{ab}) = (1 + s_a) (1 + s_b) (1 + s_2)$ so
$(1 + s_2) = (1 + s_{ab})/((1 + s_a) (1 + s_b))$ and therefore specify as:


```{r}
s2 <- ((1 + sab)/((1 + sa) * (1 + sb))) - 1

e3 <- allFitnessEffects(epistasis =
                            c("A" = sa,
                              "B" = sb,
                              "A : B" = s2))
evalAllGenotypes(e3, order = FALSE, addwt = TRUE)

``` 

Note that this is the way you would specify effects with FFPopsim
@Zanini2012. Whether this specification or the previous one with
"-" is simpler will depend on the model. For synthetic mortality and
viability, I think the one using "-" is simpler to map genotype tables
to fitness effects. See also section \@ref(e3) and \@ref(theminus) and the
example in section \@ref(weis1b).


Finally, note that we can also specify some of these effects by combining
the graph and the epistasis, as shown in section \@ref(misra1a) or
\@ref(weis1b).

### Epistasis with three genes and two alternative specifications {#e3}

Suppose we have 

-------------------------------------
A  B   C     Fitness 
-- --  --  --------------------------
M  wt  wt   $1 + s_a$ 

wt M   wt   $1 + s_b$ 

wt wt  M    $1 + s_c$ 

M  M   wt   $1 + s_{ab}$ 

wt M   M    $1 + s_{bc}$ 

M  wt  M    $(1 + s_a) (1 + s_c)$ 

M  M   M    $1 + s_{abc}$ 
-- --  --  -------------------------- 

where missing rows have a fitness of 1 (they have been deleted for
conciseness). Note that the mutant for exactly A and C has a fitness that
is the product of the individual terms (so there is no epistasis in that case).


```{r}
sa <- 0.1
sb <- 0.15
sc <- 0.2
sab <- 0.3
sbc <- -0.25
sabc <- 0.4

sac <- (1 + sa) * (1 + sc) - 1

E3A <- allFitnessEffects(epistasis =
                            c("A:-B:-C" = sa,
                              "-A:B:-C" = sb,
                              "-A:-B:C" = sc,
                              "A:B:-C" = sab,
                              "-A:B:C" = sbc,
                              "A:-B:C" = sac,
                              "A : B : C" = sabc)
                                                )

evalAllGenotypes(E3A, order = FALSE, addwt = FALSE)

``` 

We needed to pass the $s_{ac}$ coefficient explicitly, even if it that
term was just the product. We can try to avoid using the "-", however
(but we will need to do other calculations). For simplicity, I use capital
``S" in what follows where the letters differ from the previous
specification:


```{r}

sa <- 0.1
sb <- 0.15
sc <- 0.2
sab <- 0.3
Sab <- ( (1 + sab)/((1 + sa) * (1 + sb))) - 1
Sbc <- ( (1 + sbc)/((1 + sb) * (1 + sc))) - 1
Sabc <- ( (1 + sabc)/
          ( (1 + sa) * (1 + sb) * (1 + sc) *
            (1 + Sab) * (1 + Sbc) ) ) - 1

E3B <- allFitnessEffects(epistasis =
                             c("A" = sa,
                               "B" = sb,
                               "C" = sc,
                               "A:B" = Sab,
                               "B:C" = Sbc,
                               ## "A:C" = sac, ## not needed now
                               "A : B : C" = Sabc)
                                                )
evalAllGenotypes(E3B, order = FALSE, addwt = FALSE)

``` 

The above two are, of course, identical:

```{r}
all(evalAllGenotypes(E3A, order = FALSE, addwt = FALSE) == 
    evalAllGenotypes(E3B, order = FALSE, addwt = FALSE))
``` 

We avoid specifying the "A:C", as it just follows from the individual
"A" and "C" terms, but given a specified genotype table, we need to do
a little bit of addition and multiplication to get the coefficients. 


### Why can we specify some effects with a "-"? {#theminus}

Let's suppose we want to specify the synthetic viability example seen
before:

-----------------
A  B   Fitness
-- -- ----------
wt wt  1

wt M   0

M  wt  0

M  M   (1 + s)
-- -- --------



where "wt" denotes wild type and "M" denotes mutant.

If you want to directly map the above table to the fitness table for the
program, to specify the genotype "A is wt, B is a mutant" you can
specify it as "-A,B", not just as "B". Why? Because
just the presence of a "B" is also compatible with genotype "A is
mutant and B is mutant".  If you use "-" you are explicitly saying what
should not be there so that "-A,B" is NOT compatible with
"A, B". Otherwise, you need to carefully add coefficients.
Depending on what you are trying to model, different specifications might
be simpler. See the examples in section \@ref(e2) and \@ref(e3). You have
both options.


### Epistasis: modules {#epimod}
There is nothing conceptually new, but we will show an example here:

```{r}

sa <- 0.2
sb <- 0.3
sab <- 0.7

em <- allFitnessEffects(epistasis =
                            c("A: -B" = sa,
                              "-A:B" = sb,
                              "A : B" = sab),
                        geneToModule = c("A" = "a1, a2",
                                         "B" = "b1, b2"))
evalAllGenotypes(em, order = FALSE, addwt = TRUE)
``` 


Of course, we can do the same thing without using the "-", as in section \@ref(e2):

```{r}
s2 <- ((1 + sab)/((1 + sa) * (1 + sb))) - 1

em2 <- allFitnessEffects(epistasis =
                            c("A" = sa,
                              "B" = sb,
                              "A : B" = s2),
                         geneToModule = c("A" = "a1, a2",
                                         "B" = "b1, b2")
                         )
evalAllGenotypes(em2, order = FALSE, addwt = TRUE)

``` 


## I do not want epistasis, but I want modules! {#mod-no-epi}

Sometimes you might want something like having several modules, say "A"
and "B", each with a number of genes, but with "A" and "B" showing
no interaction. 

It is a terminological issue whether we should allow `noIntGenes`
(no interaction genes), as explained in section \@ref(noint) to actually be
modules. The reasoning for not allowing them is that the situation
depicted above (several genes in module A, for example) actually is one of
interaction: the members of "A" are combined using an "OR" operator
(i.e., the fitness consequences of having one or more genes of A mutated
are the same), not just simply multiplying their fitness; similarly for
``B". This is why no interaction genes also mean no modules allowed.

So how do you get what you want in this case?  Enter the names of
the modules in the `epistasis` component but have no term for ":"
(the colon). Let's see an example:


```{r}

fnme <- allFitnessEffects(epistasis = c("A" = 0.1,
                                        "B" = 0.2),
                          geneToModule = c("A" = "a1, a2",
                                           "B" = "b1, b2, b3"))

evalAllGenotypes(fnme, order = FALSE, addwt = TRUE)

``` 

In previous versions these was possible using the longer, still accepted
way of specifying a `:` with a value of 0, but this is no longer
needed:

```{r}
fnme <- allFitnessEffects(epistasis = c("A" = 0.1,
                                        "B" = 0.2,
                                        "A : B" = 0.0),
                          geneToModule = c("A" = "a1, a2",
                                           "B" = "b1, b2, b3"))

evalAllGenotypes(fnme, order = FALSE, addwt = TRUE)

``` 

This can, of course, be extended to more modules.


## A longer example: Poset, epistasis, synthetic mortality and viability, order effects and genes without interactions, with some modules {#exlong}

We will now put together a complex example. We will use the poset from
section \@ref(pm3) but will also add:

* Order effects that involve genes in the poset. In this case, if C
  happens before F, fitness decreases by $1 - 0.1$. If it happens the
  other way around, there is no effect on fitness beyond their individual
  contributions.
  <!-- but if it happens the   other way around it increases by $1 + 0.13$. -->
* Order effects that involve two new modules, "H" and "I" (with
  genes "h1, h2" and "i1", respectively), so that if H happens before
  I fitness increases by $1 + 0.12$.
* Synthetic mortality between modules "I" (already present in the
  epistatic interaction) and "J" (with genes "j1" and "j2"): the
  joint presence of these modules leads to cell death (fitness of 0).
* Synthetic viability between modules "K" and "M" (with genes
  "k1", "k2" and "m1", respectively), so that their joint presence
  is viable but adds nothing to fitness (i.e., mutation of both has
  fitness $1$), whereas each single mutant has a fitness of $1 - 0.5$.
* A set of 5 driver genes ($n1, \ldots, n5$) with fitness that comes
  from an exponential distribution with rate of 10.




As we are specifying many different things, we will start by writing each
set of effects separately:

```{r}
p4 <- data.frame(
    parent = c(rep("Root", 4), "A", "B", "D", "E", "C", "F"),
    child = c("A", "B", "D", "E", "C", "C", "F", "F", "G", "G"),
    s = c(0.01, 0.02, 0.03, 0.04, 0.1, 0.1, 0.2, 0.2, 0.3, 0.3),
    sh = c(rep(0, 4), c(-.9, -.9), c(-.95, -.95), c(-.99, -.99)),
    typeDep = c(rep("--", 4), 
                "XMPN", "XMPN", "MN", "MN", "SM", "SM"))

oe <- c("C > F" = -0.1, "H > I" = 0.12)
sm <- c("I:J"  = -1)
sv <- c("-K:M" = -.5, "K:-M" = -.5)
epist <- c(sm, sv)

modules <- c("Root" = "Root", "A" = "a1",
             "B" = "b1, b2", "C" = "c1",
             "D" = "d1, d2", "E" = "e1",
             "F" = "f1, f2", "G" = "g1",
             "H" = "h1, h2", "I" = "i1",
             "J" = "j1, j2", "K" = "k1, k2", "M" = "m1")

set.seed(1) ## for repeatability
noint <- rexp(5, 10)
names(noint) <- paste0("n", 1:5)

fea <- allFitnessEffects(rT = p4, epistasis = epist,
                         orderEffects = oe,
                         noIntGenes = noint,
                         geneToModule = modules)
``` 


How does it look?

```{r, fig.height=5.5}
plot(fea)
``` 

or

```{r, fig.height=5.5}
plot(fea, "igraph")
``` 


We can, if we want, expand the modules using a "graphNEL" graph
```{r, fig.height=5.5}
plot(fea, expandModules = TRUE)
``` 

or an "igraph" one
```{r, fig.height=6.5}
plot(fea, "igraph", expandModules = TRUE)
``` 


We will not evaluate the fitness of all genotypes, since the number of all
ordered genotypes is $> 7*10^{22}$. We will look at some specific genotypes:


```{r}

evalGenotype("k1 > i1 > h2", fea) ## 0.5
evalGenotype("k1 > h1 > i1", fea) ## 0.5 * 1.12

evalGenotype("k2 > m1 > h1 > i1", fea) ## 1.12

evalGenotype("k2 > m1 > h1 > i1 > c1 > n3 > f2", fea) 
## 1.12 * 0.1 * (1 + noint[3]) * 0.05 * 0.9

``` 

Finally, let's generate some ordered genotypes randomly:

```{r}

randomGenotype <- function(fe, ns = NULL) {
    gn <- setdiff(c(fe$geneModule$Gene,
                    fe$long.geneNoInt$Gene), "Root")
    if(is.null(ns)) ns <- sample(length(gn), 1)
    return(paste(sample(gn, ns), collapse = " > "))
}

set.seed(2) ## for reproducibility

evalGenotype(randomGenotype(fea), fea, echo = TRUE, verbose = TRUE)
## Genotype:  k2 > i1 > c1 > n1 > m1
##  Individual s terms are : 0.0755182 -0.9
##  Fitness:  0.107552 
evalGenotype(randomGenotype(fea), fea, echo = TRUE, verbose = TRUE)
## Genotype:  n2 > h1 > h2
##  Individual s terms are : 0.118164
##  Fitness:  1.11816 
evalGenotype(randomGenotype(fea), fea, echo = TRUE, verbose = TRUE)
## Genotype:  d2 > k2 > c1 > f2 > n4 > m1 > n3 > f1 > b1 > g1 > n5 > h1 > j2
##  Individual s terms are : 0.0145707 0.0139795 0.0436069 0.02 0.1 0.03 -0.95 0.3 -0.1
##  Fitness:  0.0725829 
evalGenotype(randomGenotype(fea), fea, echo = TRUE, verbose = TRUE)
## Genotype:  h2 > c1 > f1 > n2 > b2 > a1 > n1 > i1
##  Individual s terms are : 0.0755182 0.118164 0.01 0.02 -0.9 -0.95 -0.1 0.12
##  Fitness:  0.00624418 
evalGenotype(randomGenotype(fea), fea, echo = TRUE, verbose = TRUE)
## Genotype:  h2 > j1 > m1 > d2 > i1 > b2 > k2 > d1 > b1 > n3 > n1 > g1 > h1 > c1 > k1 > e1 > a1 > f1 > n5 > f2
##  Individual s terms are : 0.0755182 0.0145707 0.0436069 0.01 0.02 -0.9 0.03 0.04 0.2 0.3 -1 -0.1 0.12
##  Fitness:  0 
evalGenotype(randomGenotype(fea), fea, echo = TRUE, verbose = TRUE)
## Genotype:  n1 > m1 > n3 > i1 > j1 > n5 > k1
##  Individual s terms are : 0.0755182 0.0145707 0.0436069 -1
##  Fitness:  0 
evalGenotype(randomGenotype(fea), fea, echo = TRUE, verbose = TRUE)
## Genotype:  d2 > n1 > g1 > f1 > f2 > c1 > b1 > d1 > k1 > a1 > b2 > i1 > n4 > h2 > n2
##  Individual s terms are : 0.0755182 0.118164 0.0139795 0.01 0.02 -0.9 0.03 -0.95 0.3 -0.5
##  Fitness:  0.00420528 
evalGenotype(randomGenotype(fea), fea, echo = TRUE, verbose = TRUE)
## Genotype:  j1 > f1 > j2 > a1 > n4 > c1 > n3 > k1 > d1 > h1
##  Individual s terms are : 0.0145707 0.0139795 0.01 0.1 0.03 -0.95 -0.5
##  Fitness:  0.0294308 
evalGenotype(randomGenotype(fea), fea, echo = TRUE, verbose = TRUE)
## Genotype:  n5 > f2 > f1 > h2 > n4 > c1 > n3 > b1
##  Individual s terms are : 0.0145707 0.0139795 0.0436069 0.02 0.1 -0.95
##  Fitness:  0.0602298 
evalGenotype(randomGenotype(fea), fea, echo = TRUE, verbose = TRUE)
## Genotype:  h1 > d1 > f2
##  Individual s terms are : 0.03 -0.95
##  Fitness:  0.0515 


``` 

## Homozygosity, heterozygosity, oncogenes, tumor suppressors {#oncog}

We are using what is conceptually a single linear chromosome. However, you
can use it to model scenarios where the numbers of copies affected matter,
by properly duplicating the genes. 

Suppose we have a tumor suppressor gene, G, with two copies, one from Mom
and one from Dad. We can have a table like:

----------------------------
$O_M$  $O_D$     Fitness 
-----  -----  -------------- 
wt      wt       1 

wt      M        1

M       wt       1

M       M        $(1 + s)$
----   -----  ---------------


where $s > 0$, meaning that you need two hits, one in each copy, to
trigger the clonal expansion.


What about oncogenes? A simple model is that one single hit leads to
clonal expansion and additional hits lead to no additional changes, as in
this table for gene O, where again the M or D subscript denotes the copy
from Mom or from Dad:

----------------------------
$O_M$  $O_D$     Fitness 
-----  -----  -------------- 
wt      wt        1 

wt      M        $(1 + s)$

M       wt       $(1 + s)$

M       M        $(1 + s)$
----  -----   --------------


If you have multiple copies you can proceed similarly. As you can see,
these are nothing but special cases of synthetic mortality (\@ref(sl)),
synthetic viability (\@ref(sv)) and epistasis (\@ref(epi)).


## Gene-specific mutation rates {#per-gene-mutation}

You can specify gene-specific mutation rates. Instead of passing a scalar
value for `mu`, you pass a named vector. (This does not work with
the old v. 1 format, though; yet another reason to stop using that
format). This is a simple example (many more are available in the tests,
see file `./tests/testthat/test.per-gene-mutation-rates.R`).

```{r}

muvar2 <- c("U" = 1e-6, "z" = 5e-5, "e" = 5e-4, "m" = 5e-3,
            "D" = 1e-4)
ni1 <- rep(0, 5)
names(ni1) <- names(muvar2) ## We use the same names, of course
fe1 <- allFitnessEffects(noIntGenes = ni1)
bb <- oncoSimulIndiv(fe1, 
                     mu = muvar2, onlyCancer = FALSE,
                     initSize = 1e5,
                     finalTime = 25,
                     seed =NULL)

``` 

## Mutator genes {#mutator}

You can specify mutator/antimutator genes
  [e.g. @gerrish_complete_2007; @tomlinson_mutation_1996]. These are genes
  that, when mutated, lead to an increase/decrease in the mutation rate
  all over the genome (similar to what happens with, say, mutations in
  mismatch-repair genes or microsatellite instability in cancer).

The specification is very similar to that for fitness effects, except we
do not (at least for now) the use of DAGs for poset-like structures nor
allow for order effects (we have seen no reference in the literature to
suggest any of these would be relevant). You can, however, specify
epistasis and use modules. Note that the mutator genes must be a subset of
the genes in the fitness effects; if you want to have mutator genes that
have no direct fitness effects, give them a fitness effect of 0.


This first is a very simple example with simple fitness effects and
modules for mutators. We will specify the fitness and mutator effects and
evaluate the fitness and mutator effects:

```{r}
fe2 <- allFitnessEffects(noIntGenes =
                         c(a1 = 0.1, a2 = 0.2,
                           b1 = 0.01, b2 = 0.3, b3 = 0.2,
                           c1 = 0.3, c2 = -0.2))

fm2 <- allMutatorEffects(epistasis = c("A" = 5,
                                       "B" = 10,
                                       "C" = 3),
                         geneToModule = c("A" = "a1, a2",
                                          "B" = "b1, b2, b3",
                                          "C" = "c1, c2"))

## Show the fitness effect of a specific genotype
evalGenotype("a1, c2", fe2, verbose = TRUE)

## Show the mutator effect of a specific genotype
evalGenotypeMut("a1, c2", fm2, verbose = TRUE)

## Fitness and mutator of a specific genotype
evalGenotypeFitAndMut("a1, c2", fe2, fm2, verbose = TRUE)
``` 

You can also use the `evalAll` functions. We do not show the output
here to avoid cluttering the vignette:

```{r, eval=FALSE}
## Show only all the fitness effects
evalAllGenotypes(fe2, order = FALSE)

## Show only all mutator effects
evalAllGenotypesMut(fm2)

## Show all fitness and mutator
evalAllGenotypesFitAndMut(fe2, fm2, order = FALSE)
``` 


Building upon the above, the next is an example where we have a bunch of
no interaction genes that affect fitness, and a small set of genes that
affect the mutation rate (but have no fitness effects).


```{r}

set.seed(1) ## for reproducibility
## 17 genes, 7 with no direct fitness effects
ni <- c(rep(0, 7), runif(10, min = -0.01, max = 0.1))
names(ni) <- c("a1", "a2", "b1", "b2", "b3", "c1", "c2",
               paste0("g", 1:10))

fe3 <- allFitnessEffects(noIntGenes = ni)

fm3 <- allMutatorEffects(epistasis = c("A" = 5,
                                       "B" = 10,
                                       "C" = 3,
                                       "A:C" = 70),
                         geneToModule = c("A" = "a1, a2",
                                          "B" = "b1, b2, b3",
                                          "C" = "c1, c2"))
``` 

Let us check what the effects are of a few genotypes:

```{r}
## These only affect mutation, not fitness
evalGenotypeFitAndMut("a1, a2", fe3, fm3, verbose = TRUE)
evalGenotypeFitAndMut("a1, b3", fe3, fm3, verbose = TRUE)

## These only affect fitness: the mutator multiplier is 1
evalGenotypeFitAndMut("g1", fe3, fm3, verbose = TRUE)                      
evalGenotypeFitAndMut("g3, g9", fe3, fm3, verbose = TRUE)

## These affect both
evalGenotypeFitAndMut("g3, g9, a2, b3", fe3, fm3, verbose = TRUE)
``` 


Finally, we will do a simulation with those data

```{r}
set.seed(1) ## so that it is easy to reproduce
mue1 <- oncoSimulIndiv(fe3, muEF = fm3, 
                       mu = 1e-6,
                       initSize = 1e5,
                       model = "McFL",
                       detectionSize = 5e6,
                       finalTime = 500,
                       onlyCancer = FALSE)
``` 

```{r, eval=FALSE}
## We do not show this in the vignette to avoid cluttering it
## with output
mue1
``` 


Of course, it is up to you to keep things reasonable: mutator effects are
multiplicative, so if you specify, say, 20 genes (without modules), or 
20 modules, each with a mutator effect of 50, the overall mutation rate
can be increased by a factor of $50^{20}$ and that is unlikely to be what
you really want.

You can play with the following case (an extension of the example above),
where a clone with a mutator phenotype and some fitness enhancing
mutations starts giving rise to many other clones, some with additional
mutator effects, and thus leading to the number of clones blowing up (as
some also accumulate additional fitness-enhancing mutations). Things start
getting out of hand shortly after time 250. The code below takes a
few minutes and is commented, but you can run it to get an idea of the
increase in the number of clones and their relationships (the usage of
*`plotClonePhylog`* is explained in section \@ref(phylog)).

```{r, eval=FALSE}

set.seed(1) ## for reproducibility
## 17 genes, 7 with no direct fitness effects
ni <- c(rep(0, 7), runif(10, min = -0.01, max = 0.1))
names(ni) <- c("a1", "a2", "b1", "b2", "b3", "c1", "c2",
               paste0("g", 1:10))

## Next is for nicer figure labeling.
## consider drivers those with s >0
gp <- which(ni > 0) 

fe3 <- allFitnessEffects(noIntGenes = ni,
                         drvNames = names(ni)[gp])


set.seed(12)
mue1 <- oncoSimulIndiv(fe3, muEF = fm3, 
                       mu = 1e-6,
                       initSize = 1e5,
                       model = "McFL",
                       detectionSize = 5e6,
                       finalTime = 270,
                       keepPhylog = TRUE,
                       onlyCancer = FALSE)
mue1
## If you decrease N even further it gets even more cluttered
op <- par(ask = TRUE)
plotClonePhylog(mue1, N = 10, timeEvents = TRUE) 
plot(mue1, plotDrivers = TRUE, addtot = TRUE,
     plotDiversity = TRUE)
## The stacked plot is slow; be patient
## Most clones have tiny population sizes, and their lines
## are piled on top of each other
plot(mue1, addtot = TRUE,
     plotDiversity = TRUE, type = "stacked")
par(op)
``` 


# Plotting fitness landscapes {#plot-fit-land}


The *`evalAllGenotypes`* and related functions allow you to obtain
tables of the genotype to fitness mappings. It might be more convenient to
actually plot that, allowing us to quickly identify local minima and
maxima and get an idea of how the fitness landscape looks.

In *`plotFitnessLandscape`* I have blatantly and shamelessly copied most
of the looks of the plots of MAGELLAN [@brouillet_magellan:_2015] (see
also <http://wwwabi.snv.jussieu.fr/public/Magellan/>), a very nice
web-based tool for fitness landscape plotting and analysis (MAGELLAN
provides some other extra functionality and epistasis statistics not
provided here).

As an example, let us show the previous example of Weissman et al. we saw
in \@ref(weissmanex):

```{r}

d1 <- -0.05 ## single mutant fitness 0.95
d2 <- -0.08 ## double mutant fitness 0.92
d3 <- 0.2   ## triple mutant fitness 1.2
s2 <- ((1 + d2)/(1 + d1)^2) - 1
s3 <- ( (1 + d3)/((1 + d1)^3 * (1 + s2)^3) ) - 1

wb <- allFitnessEffects(
    epistasis = c(
        "A" = d1,
        "B" = d1,
        "C" = d1,
        "A:B" = s2,
        "A:C" = s2,
        "B:C" = s2,
        "A:B:C" = s3))
``` 

<!-- \clearpage -->

```{r, fig.width=6.5, fig.height=5}
plotFitnessLandscape(wb, use_ggrepel = TRUE) 
``` 

We have set `use_ggrepel = TRUE` to avoid overlap of labels.

<!-- \clearpage -->

For some types of objects, directly invoking *`plot`* will give
you the fitness plot

```{r, fig.width=6.5, fig.height=5}
(ewb <- evalAllGenotypes(wb, order = FALSE))
plot(ewb, use_ggrepel = TRUE) 

``` 

<!-- \clearpage -->
This is another example we saw before (\@ref(pancreas)), that will give a
very busy plot:

```{r wasthis111, fig.width=9.5, fig.height=9.5}
par(cex = 0.7)
pancr <- allFitnessEffects(
    data.frame(parent = c("Root", rep("KRAS", 4), 
                   "SMAD4", "CDNK2A", 
                   "TP53", "TP53", "MLL3"),
               child = c("KRAS","SMAD4", "CDNK2A", 
                   "TP53", "MLL3",
                   rep("PXDN", 3), rep("TGFBR2", 2)),
               s = 0.1,
               sh = -0.9,
               typeDep = "MN"))
plot(evalAllGenotypes(pancr, order = FALSE), use_ggrepel = TRUE)

``` 


<!-- \clearpage -->

# Specifying fitness effects: some examples from the literature {#litex}

## Bauer et al., 2014 {#bauer}

In the model of Bauer and collaborators [@Bauer2014, pp. 54] we have
"For cells without the primary driver mutation, each secondary
driver mutation leads to a change in the cell's fitness by
$s_P$. For cells with the primary driver mutation, the fitness
advantage obtained with each secondary driver mutation is $s_{DP}$."

The proliferation probability is given as:


* $\frac{1}{2}(1 + s_p)^k$ when there are $k$ secondary drivers mutated and no primary diver;
* $\frac{1}{2}\frac{1+S_D^+}{1+S_D^-} (1 + S_{DP})^k$ when the primary driver is mutated;


apoptosis is one minus the proliferation rate.

### Using a DAG

We cannot find a simple mapping from their expressions to our fitness
parameterization, but we can get fairly close by using a DAG; in this one,
note the unusual feature of having one of the "s" terms (that for the
driver dependency on root) be negative. Using the parameters given in the
legend of their Figure 3 for $s_p, S_D^+, S_D^-, S_{DP}$ and obtaining
that negative value for the dependency of the driver on root we can do:


```{r}
K <- 4
sp <- 1e-5
sdp <- 0.015
sdplus <- 0.05
sdminus <- 0.1
cnt <- (1 + sdplus)/(1 + sdminus)
prod_cnt <- cnt - 1
bauer <- data.frame(parent = c("Root", rep("p", K)),
                    child = c("p", paste0("s", 1:K)),
                    s = c(prod_cnt, rep(sdp, K)),
                    sh = c(0, rep(sp, K)),
                    typeDep = "MN")
fbauer <- allFitnessEffects(bauer)
(b1 <- evalAllGenotypes(fbauer, order = FALSE, addwt = TRUE))

``` 

Note that what we specify as "typeDep" is irrelevant (MN, SMN, or XMPN
make no difference).

This is the DAG:
```{r, fig.height=3}
plot(fbauer)
``` 


And if you compare the tabular output of *`evalAllGenotypes`* you can
see that the values of fitness reproduces the fitness landscape that they
show in their Figure 1. We can also use our plot for fitness landscapes:

```{r, fig.width=6, fig.height=6}
plot(b1, use_ggrepel = TRUE)
``` 


### Specifying fitness of genotypes directly

An alternative approach to specify the fitness, if the number of
genotypes is reasonably small, is to directly evaluate fitness as
given by their expressions. Then, use the `genotFitness` argument to
*`allFitnessEffects`*. 

We will create all possible genotypes; then we will write a function
that gives the fitness of each genotype according to their
expression; finally, we will call this function on the data frame of
genotypes, and pass this data frame to *`allFitnessEffects`*.


```{r}
m1 <- expand.grid(p = c(1, 0), s1 = c(1, 0), s2 = c(1, 0),
                  s3 = c(1, 0), s4 = c(1, 0))

fitness_bauer <- function(p, s1, s2, s3, s4, 
                          sp = 1e-5, sdp = 0.015, sdplus = 0.05,
                          sdminus = 0.1) {
    if(!p) {
        b <- 0.5 * ( (1 + sp)^(sum(c(s1, s2, s3, s4))))
    } else {
        b <- 0.5 * 
            (((1 + sdplus)/(1 + sdminus)  *
              (1 + sdp)^(sum(c(s1, s2, s3, s4)))))
    }
    fitness <- b - (1 - b)
    our_fitness <- 1 + fitness ## prevent negative fitness and
    ## make wt fitness = 1
    return(our_fitness)
}

m1$Fitness <- 
    apply(m1, 1, function(x) do.call(fitness_bauer, as.list(x)))

bauer2 <- allFitnessEffects(genotFitness = m1)
``` 

Now, show the fitness of all genotypes:

```{r}
evalAllGenotypes(bauer2, order = FALSE, addwt = TRUE)
``` 



<!-- % If the primary driver is -->
<!-- % mutated, then the expression is $\frac{1+S_D^+}{1+S_D^-} (1 + S_{DP})^k$. -->
<!-- % They set apoptosis as $1 - proliferation$.  So, ignoring constants such as -->
<!-- % $1/2$, and setting $ P = \frac{1+S_D^+}{1+S_D^-}$ we can prepare a table -->
<!-- % as (for a largest $k$ of 5 in this example, but can make it arbitrarily -->
<!-- % large): -->

<!-- % <<>>= -->

<!-- % K <- 5 -->
<!-- % sd <- 0.1 -->
<!-- % sdp <- 0.15 -->
<!-- % sp <- 0.05 -->
<!-- % bauer <- data.frame(parent = c("Root", rep("p", K)), -->
<!-- %                     child = c("p", paste0("s", 1:K)), -->
<!-- %                     s = c(sd, rep(sdp, K)), -->
<!-- %                     sh = c(0, rep(sp, K)), -->
<!-- %                     typeDep = "MN") -->
<!-- % fbauer <- allFitnessEffects(bauer) -->


<!-- % @  -->




<!-- % <<>>= -->
<!-- % (b1 <- evalAllGenotypes(fbauer, order = FALSE))[1:10, ] -->
<!-- % @  -->

<!-- % Order makes no difference -->

<!-- % <<>>= -->
<!-- % (b2 <- evalAllGenotypes(fbauer, order = TRUE, max = 2000))[1:15, ] -->
<!-- % @  -->

<!-- % And the number of levels is the right one: 11 -->
<!-- % <<>>= -->
<!-- % length(table(b1$Fitness)) -->
<!-- % length(table(b2$Fitness)) -->
<!-- % @  -->


<!-- %% ### Bauer et al.\ specified only via epistatic interactions} -->
<!-- %% Yes, do it: as -p,s1, and -p,s2, etc. But much more of a mess. -->

<!-- %% ### Adding modules to Bauer et al.} -->

Can we use modules in this example, if we use the "lego system"? Sure,
as in any other case.

<!-- \clearpage -->

## Misra et al., 2014 {#misra}

Figure 1 of @Misra2014 presents three scenarios which
are different types of epistasis. 

<!-- %% (I show the fitness scenarios without -->
<!-- %% axis, to replicate as close as possible what they show in their -->
<!-- paper) -->


### Example 1.a {#misra1a}
```{r, echo=FALSE, fig.height=4, fig.width=4}

df1 <- data.frame(x = c(1, 1.2, 1.4), f = c(1, 1.2, 1.2),
                 names = c("wt", "A", "B"))
plot(df1[, 2] ~ df1[, 1], axes = TRUE, xlab= "", 
     ylab = "Fitness", xaxt = "n", yaxt = "n", ylim = c(1, 1.21))
segments(1, 1, 1.2, 1.2)
segments(1, 1, 1.4, 1.2)
text(1, 1, "wt", pos = 4)
text(1.2, 1.2, "A", pos = 2)
text(1.4, 1.2, "B", pos = 2)
## axis(1,  tick = FALSE, labels = FALSE)
## axis(2,  tick = FALSE, labels = FALSE)
``` 


In that figure it is evident that the fitness effect of "A" and "B"
are the same. There are two different models depending on whether "AB"
is just the product of both, or there is epistasis. In the first case
probably the simplest is:

```{r}
s <- 0.1 ## or whatever number
m1a1 <- allFitnessEffects(data.frame(parent = c("Root", "Root"),
                                     child = c("A", "B"),
                                     s = s,
                                     sh = 0,
                                     typeDep = "MN"))
evalAllGenotypes(m1a1, order = FALSE, addwt = TRUE)
``` 


If the double mutant shows epistasis, as we saw before (section \@ref(e2))
we have a range of options. For example:

```{r}
s <- 0.1
sab <- 0.3
m1a2 <- allFitnessEffects(epistasis = c("A:-B" = s,
                                        "-A:B" = s,
                                        "A:B" = sab))
evalAllGenotypes(m1a2, order = FALSE, addwt = TRUE)
``` 

But we could also modify the graph dependency structure, and we have to
change the value of the coefficient, since that is what multiplies each of
the terms for "A" and "B": $(1 + s_{AB}) = (1 + s)^2(1 + s_{AB3}) $

```{r}
sab3 <- ((1 + sab)/((1 + s)^2)) - 1
m1a3 <- allFitnessEffects(data.frame(parent = c("Root", "Root"),
                                     child = c("A", "B"),
                                     s = s,
                                     sh = 0,
                                     typeDep = "MN"),
                          epistasis = c("A:B" = sab3))
evalAllGenotypes(m1a3, order = FALSE, addwt = TRUE)
``` 

And, obviously
```{r}
all.equal(evalAllGenotypes(m1a2, order = FALSE, addwt = TRUE),
          evalAllGenotypes(m1a3, order = FALSE, addwt = TRUE))
``` 


### Example 1.b {#misra1b}

This is a specific case of synthetic viability (see also section \@ref(sv)):

```{r, echo=FALSE, fig.width=4, fig.height=4}

df1 <- data.frame(x = c(1, 1.2, 1.2, 1.4), f = c(1, 0.4, 0.3, 1.3),
                 names = c("wt", "A", "B", "AB"))
plot(df1[, 2] ~ df1[, 1], axes = TRUE, xlab= "", ylab = "Fitness",
     xaxt = "n", yaxt = "n", ylim = c(0.29, 1.32))
segments(1, 1, 1.2, 0.4)
segments(1, 1, 1.2, 0.3)
segments(1.2, 0.4, 1.4, 1.3)
segments(1.2, 0.3, 1.4, 1.3)
text(x = df1[, 1], y = df1[, 2], labels = df1[, "names"], pos = c(4, 2, 2, 2))
## text(1, 1, "wt", pos = 4)
## text(1.2, 1.2, "A", pos = 2)
## text(1.4, 1.2, "B", pos = 2)
``` 


Here, $S_A, S_B < 0$, $S_B < 0$, $S_{AB} > 0$ and $(1 + S_{AB}) (1 + S_A) (1 +
S_B) > 1$.

As before, we can specify this in several different ways. The simplest is
to specify all genotypes:
```{r}
sa <- -0.6
sb <- -0.7
sab <- 0.3
m1b1 <- allFitnessEffects(epistasis = c("A:-B" = sa,
                                        "-A:B" = sb,
                                        "A:B" = sab))
evalAllGenotypes(m1b1, order = FALSE, addwt = TRUE)
``` 

We could also use a tree and modify the "sab" for the epistasis, as
before (\@ref(misra1a)).



### Example 1.c {#misra1c}

The final case, in figure 1.c of Misra et al., is just epistasis, where a
mutation in one of the genes is deleterious (possibly only mildly), in the
other is beneficial, and the double mutation has fitness larger than any
of the other two.


```{r, echo=FALSE, fig.width=4, fig.height=4}

df1 <- data.frame(x = c(1, 1.2, 1.2, 1.4), f = c(1, 1.2, 0.7, 1.5),
                 names = c("wt", "A", "B", "AB"))
plot(df1[, 2] ~ df1[, 1], axes = TRUE, xlab = "", ylab = "Fitness",
     xaxt = "n", yaxt = "n", ylim = c(0.69, 1.53))
segments(1, 1, 1.2, 1.2)
segments(1, 1, 1.2, 0.7)
segments(1.2, 1.2, 1.4, 1.5)
segments(1.2, 0.7, 1.4, 1.5)
text(x = df1[, 1], y = df1[, 2], labels = df1[, "names"], pos = c(3, 3, 3, 2))
## text(1, 1, "wt", pos = 4)
## text(1.2, 1.2, "A", pos = 2)
## text(1.4, 1.2, "B", pos = 2)

``` 

Here we have that $s_A > 0$, $s_B < 0$, $(1 + s_{AB}) (1 + s_A) (1 +
s_B) > (1 + s_{AB})$ so $s_{AB} > \frac{-s_B}{1 + s_B}$


As before, we can specify this in several different ways. The simplest is
to specify all genotypes:
```{r}
sa <- 0.2
sb <- -0.3
sab <- 0.5
m1c1 <- allFitnessEffects(epistasis = c("A:-B" = sa,
                                        "-A:B" = sb,
                                        "A:B" = sab))
evalAllGenotypes(m1c1, order = FALSE, addwt = TRUE)
``` 

We could also use a tree and modify the "sab" for the epistasis, as
before (\@ref(misra1a)).


<!-- \clearpage -->
## Ochs and Desai, 2015 {#ochsdesai}

In @Ochs2015 the authors present a model shown graphically as (the
actual numerical values are arbitrarily set by me):


```{r, echo=FALSE, fig.width=4.5, fig.height=3.5}

df1 <- data.frame(x = c(1, 2, 3, 4), f = c(1.1, 1, 0.95, 1.2),
                 names = c("u", "wt", "i", "v"))
plot(df1[, 2] ~ df1[, 1], axes = FALSE, xlab = "", ylab = "")
par(las = 1)
axis(2)
axis(1, at = c(1, 2, 3, 4), labels = df1[, "names"], ylab = "")
box()
arrows(c(2, 2, 3), c(1, 1, 0.95),
       c(1, 3, 4), c(1.1, 0.95, 1.2))
## text(1, 1, "wt", pos = 4)
## text(1.2, 1.2, "A", pos = 2)
## text(1.4, 1.2, "B", pos = 2)
```

In their model, $s_u > 0$, $s_v > s_u$, $s_i < 0$, we can only arrive at
$v$ from $i$, and the mutants "ui" and "uv" can never appear as their
fitness is 0, or $-\infty$, so $s_{ui} = s_{uv} = -1$ (or $-\infty$).

We can specify this combining a graph and epistasis specifications:

```{r}
su <- 0.1
si <- -0.05
fvi <- 1.2 ## the fitnes of the vi mutant
sv <- (fvi/(1 + si)) - 1
sui <- suv <- -1
od <- allFitnessEffects(
    data.frame(parent = c("Root", "Root", "i"),
               child = c("u", "i", "v"),
               s = c(su, si, sv),
               sh = -1,
               typeDep = "MN"),
    epistasis = c(
        "u:i" = sui,
        "u:v" = suv))
``` 

A figure showing that model is
```{r, fig.width=3, fig.height=3}
plot(od)
``` 

And the fitness of all genotype is
```{r}
evalAllGenotypes(od, order = FALSE, addwt = TRUE)
``` 


## Weissman et al., 2009 {#weissmanex}
In their figure 1a, @Weissman2009 present this model
(actual numeric values are set arbitrarily)

### Figure 1.a}

```{r, echo=FALSE, fig.width=4, fig.height=3}

df1 <- data.frame(x = c(1, 2, 3), f = c(1, 0.95, 1.2),
                 names = c("wt", "1", "2"))
plot(df1[, 2] ~ df1[, 1], axes = FALSE, xlab = "", ylab = "")
par(las = 1)
axis(2)
axis(1, at = c(1, 2, 3), labels = df1[, "names"], ylab = "")
box()
segments(c(1, 2), c(1, 0.95),
       c(2, 3), c(0.95, 1.2))
## text(1, 1, "wt", pos = 4)
## text(1.2, 1.2, "A", pos = 2)
## text(1.4, 1.2, "B", pos = 2)
```

where the ``1" and ``2" refer to the total number of mutations in two
different loci. This is, therefore, very similar to the example in section
\@ref(misra1b). Here we have, in their notation, $\delta_1 < 0$, fitness of
single "A" or single "B" = $1 + \delta_1$, $S_{AB} > 0$,
$(1 + S_{AB})(1 + \delta_1)^2 > 1$.


### Figure 1.b {#weis1b}

In their figure 1b they show

```{r, echo=FALSE, fig.width=4, fig.height=3}

df1 <- data.frame(x = c(1, 2, 3, 4), f = c(1, 0.95, 0.92, 1.2),
                 names = c("wt", "1", "2", "3"))
plot(df1[, 2] ~ df1[, 1], axes = FALSE, xlab = "", ylab = "")
par(las = 1)
axis(2)
axis(1, at = c(1, 2, 3, 4), labels = df1[, "names"], ylab = "")
box()
segments(c(1, 2, 3), c(1, 0.95, 0.92),
       c(2, 3, 4), c(0.95, 0.92, 1.2))
## text(1, 1, "wt", pos = 4)
## text(1.2, 1.2, "A", pos = 2)
## text(1.4, 1.2, "B", pos = 2)
```

Where, as before, 1, 2, 3, denote the total number of mutations over three
different loci and $\delta_1 < 0$, $\delta_2 < 0$, fitness of single
mutant is $(1 + \delta_1)$, of double mutant is $(1 + \delta_2)$ so that
$(1 + \delta_2) = (1 + \delta_1)^2 (1 + s_2)$ and of triple mutant is
$(1 + \delta_3)$, so that
$(1 + \delta_3) = (1 + \delta_1)^3 (1 + s_2)^3 (1 + s_3)$.


We can specify this combining a graph with epistasis:

```{r}

d1 <- -0.05 ## single mutant fitness 0.95
d2 <- -0.08 ## double mutant fitness 0.92
d3 <- 0.2   ## triple mutant fitness 1.2

s2 <- ((1 + d2)/(1 + d1)^2) - 1
s3 <- ( (1 + d3)/((1 + d1)^3 * (1 + s2)^3) ) - 1

w <- allFitnessEffects(
    data.frame(parent = c("Root", "Root", "Root"),
               child = c("A", "B", "C"),
               s = d1,
               sh = -1,
               typeDep = "MN"),
    epistasis = c(
        "A:B" = s2,
        "A:C" = s2,
        "B:C" = s2,
        "A:B:C" = s3))
``` 

The model can be shown graphically as:
```{r, fig.width=4, fig.height=4}
plot(w)
``` 

And fitness of all genotypes is:

```{r}
evalAllGenotypes(w, order = FALSE, addwt = TRUE)
``` 



Alternatively, we can directly specify what each genotype adds to the
fitness, given the included genotype. This is basically replacing the
graph by giving each of "A", "B", and "C" directly:

```{r}
wb <- allFitnessEffects(
    epistasis = c(
        "A" = d1,
        "B" = d1,
        "C" = d1,
        "A:B" = s2,
        "A:C" = s2,
        "B:C" = s2,
        "A:B:C" = s3))

evalAllGenotypes(wb, order = FALSE, addwt = TRUE)
``` 

The plot, of course, is not very revealing and we cannot show that there
is a three-way interaction (only all three two-way interactions):

```{r, , fig.width=3, fig.height=3}
plot(wb)
``` 

As we have seen several times already (sections \@ref(e2), \@ref(e3),
\@ref(theminus)) we can also give the genotypes directly and, consequently,
the fitness of each genotype (not the added contribution):

```{r}
wc <- allFitnessEffects(
    epistasis = c(
        "A:-B:-C" = d1,
        "B:-C:-A" = d1,
        "C:-A:-B" = d1,
        "A:B:-C" = d2,
        "A:C:-B" = d2,
        "B:C:-A" = d2,
        "A:B:C" = d3))
evalAllGenotypes(wc, order = FALSE, addwt = TRUE)
``` 


## Gerstung et al., 2011, pancreatic cancer poset {#pancreas}

Similar to what we did in v.1 (see section \@ref(poset)) we can specify the
pancreatic cancer poset in @Gerstung2011 (their
figure 2B, left). We use directly the names of the genes, since that is
immediately supported by the new version.

```{r, fig.width=4}

pancr <- allFitnessEffects(
    data.frame(parent = c("Root", rep("KRAS", 4), 
                   "SMAD4", "CDNK2A", 
                   "TP53", "TP53", "MLL3"),
               child = c("KRAS","SMAD4", "CDNK2A", 
                   "TP53", "MLL3",
                   rep("PXDN", 3), rep("TGFBR2", 2)),
               s = 0.1,
               sh = -0.9,
               typeDep = "MN"))

plot(pancr)
``` 

Of course the "s" and "sh" are set arbitrarily here.



## Raphael and Vandin's 2014 modules {#raphael-ex}

In @Raphael2014a, the authors show several progression models
in terms of modules. We can code the extended poset for the colorectal
cancer model in their Figure 4.a is (s and sh are arbitrary):


```{r, fig.height = 4}
rv1 <- allFitnessEffects(data.frame(parent = c("Root", "A", "KRAS"),
                                    child = c("A", "KRAS", "FBXW7"),
                                    s = 0.1,
                                    sh = -0.01,
                                    typeDep = "MN"),
                         geneToModule = c("Root" = "Root",
                             "A" = "EVC2, PIK3CA, TP53",
                             "KRAS" = "KRAS",
                             "FBXW7" = "FBXW7"))

plot(rv1, expandModules = TRUE, autofit = TRUE)

``` 

We have used the (experimental) `autofit` option to fit the labels to the
edges. Note how we can use the same name for genes and modules, but we
need to specify all the modules. 

<!-- \clearpage -->
Their Figure 5b is

```{r, fig.height=6}
rv2 <- allFitnessEffects(
    data.frame(parent = c("Root", "1", "2", "3", "4"),
               child = c("1", "2", "3", "4", "ELF3"),
               s = 0.1,
               sh = -0.01,
               typeDep = "MN"),
    geneToModule = c("Root" = "Root",
                     "1" = "APC, FBXW7",
                     "2" = "ATM, FAM123B, PIK3CA, TP53",
                     "3" = "BRAF, KRAS, NRAS",
                     "4" = "SMAD2, SMAD4, SOX9",
                     "ELF3" = "ELF3"))

plot(rv2, expandModules = TRUE,   autofit = TRUE)
``` 

<!-- %%very poor rendering in the PDF, in separate page, et c. -->
<!-- %% plot(rv2, "igraph", expandModules = TRUE,  -->
<!-- %%       layout = layout.reingold.tilford, -->
<!-- %%       autofit = TRUE, -->
<!-- %%       scale_char = 8) -->



# Running and plotting the simulations: starting, ending, and examples {#simul}

## Starting and ending {#starting-ending}


After you have decided the specifics of the fitness effects and the model,
you need to decide:


* Where will you start your simulation from. This involves deciding
  the initial population size (argument `initSize`) and, possibly,
  the genotype of the initial population; the later is covered in section
  \@ref(initmut).

* When will you stop it: how long to run it, and whether or not to
  require simulations to reach cancer (under some definition of what it
  means to reach cancer). This is covered in \@ref(endsimul).



## Can I start the simulation from a specific mutant? {#initmut}

You bet. In v.1 you can only give the initial mutant as one with a single
mutated gene. In version 2, however, you can specify the genotype for the
initial mutant with the same flexibility as in
*`evalGenotype`*. Here we show a couple of examples (we use the
representation of the parent-child relationships ---discussed in section
\@ref(phylog)--- of the clones so that you can see which clones appear, and
from which, and check that we are not making mistakes).

<!-- %% o3init <- allFitnessEffects(orderEffects = c( -->
<!-- %%                             "M > D > F" = 0.99, -->
<!-- %%                             "D > M > F" = 0.2, -->
<!-- %%                             "D > M"     = 0.1, -->
<!-- %%                             "M > D"     = 0.9), -->
<!-- %%                         noIntGenes = c("u" = 0.01,  -->
<!-- %%                                        "v" = 0.01, -->
<!-- %%                                        "w" = 0.001, -->
<!-- %%                                        "x" = 0.0001, -->
<!-- %%                                        "y" = -0.0001, -->
<!-- %%                                        "z" = -0.001), -->
<!-- %%                         geneToModule = -->
<!-- %%                             c("Root" = "Root", -->
<!-- %%                               "M" = "m", -->
<!-- %%                               "F" = "f", -->
<!-- %%                               "D" = "d") ) -->

```{r prbau003, fig.height=6}

o3init <- allFitnessEffects(orderEffects = c(
                            "M > D > F" = 0.99,
                            "D > M > F" = 0.2,
                            "D > M"     = 0.1,
                            "M > D"     = 0.9),
                        noIntGenes = c("u" = 0.01, 
                                       "v" = 0.01,
                                       "w" = 0.001,
                                       "x" = 0.0001,
                                       "y" = -0.0001,
                                       "z" = -0.001),
                        geneToModule =
                            c("M" = "m",
                              "F" = "f",
                              "D" = "d") )

oneI <- oncoSimulIndiv(o3init, model = "McFL",
                       mu = 5e-5, finalTime = 500,
                       detectionDrivers = 3,
                       onlyCancer = FALSE,
                       initSize = 1000,
                       keepPhylog = TRUE,
                       initMutant = c("m > u > d")
                       )
plotClonePhylog(oneI, N = 0)
```


```{r prbau003bb, fig.height=6}
## Note we also disable the stopping stochastically as a function of size
## to allow the population to grow large and generate may different
## clones.
ospI <- oncoSimulPop(2, 
                    o3init, model = "Exp",
                    mu = 5e-5, finalTime = 500,
                    detectionDrivers = 3,
                    onlyCancer = TRUE,
                    initSize = 10,
                    keepPhylog = TRUE,
                    initMutant = c("d > m > z"),
                    mc.cores = 2
                    )
op <- par(mar = rep(0, 4), mfrow = c(1, 2))
plotClonePhylog(ospI[[1]])
plotClonePhylog(ospI[[2]])
par(op)

ossI <- oncoSimulSample(2, 
                        o3init, model = "Exp",
                        mu = 5e-5, finalTime = 500,
                        detectionDrivers = 2,
                        onlyCancer = TRUE,
                        initSize = 10,
                        initMutant = c("z > d"),
                        ## check presence of initMutant:
                        thresholdWhole = 1 
                    )

## No phylogeny is kept with oncoSimulSample, but look at the 
## OcurringDrivers and the sample
ossI$popSample
ossI$popSummary[, "OccurringDrivers", drop = FALSE]
``` 

## Ending the simulations {#endsimul}

OncoSimulR provides very flexible ways to decide when to stop a
simulation. Here we focus on a single simulation; see further options with
multiple simulations in \@ref(sample).



* **`onlyCancer = TRUE`**. A simulation will be repeated until any
  one of the "reach cancer" conditions is met, if this happens before
  the simulation reaches `finalTime`[^6]. These conditions are:

    [^6]: Of course, the "reach cancer" idea and the `onlyCancer` argument
    are generic names; this could have been labeled "reach whatever
    interests me".
  
    + Total population size becomes larger than `detectionSize`.
    + The number of drivers in any one genotype or clone becomes equal
    to, or larger than, `detectionDrivers`; note that this allows you
    to stop the simulation as soon as a **specific genotype** is
    found, by using exactly and only the genes that make that genotype as
    the drivers.
    + The tumor is detected according to a stochastic detection
    mechanism, where the probability of "detecting the tumor" increases
    with population size; this is explained below (\@ref(detectprob)) and
    is controlled by argument `detectionProb`.
  
  
    As we exit as soon as any of the exiting conditions is reached,
    if you only care about one condition, set the other to `NA`.

* **`onlyCancer = FALSE`**. A simulation will run only once, and
  will exit as soon as any of the above conditions are met or as soon as
  the total population size becomes zero or we reach `finalTime`.



As an example of `onlyCancer = TRUE`, focusing on the first two
mechanisms, suppose you give `detectionSize = 1e4` and `detectionDrivers
=3` (and you have `detectionProb = NA`).  A simulation will exit as soon
as it reaches a total population size of $1e4$ or any clone has four
drivers, whichever comes first (if any of these happen before
`finalTime`).

In the `onlyCancer = TRUE` case, what happens if we reach
`finalTime` (or the population size becomes zero) before any of the
``reach cancer" conditions have been fulfilled?  The simulation will be
repeated again, within the following limits:


* `max.wall.time`: the total wall time we allow an individual
  simulation to run;
* `max.num.tries`: the maximum number of times we allow a
  simulation to be repeated to reach cancer;
* `max.wall.time.total` and `max.num.tries.total`,
  similar to the above but over a set of simulations in function
  *`oncoSimulSample`*.



Incidentally, we keep track of the number of attempts used (the component
`other$attemptsUsed$`) before we reach cancer, so you can estimate
(as from a negative binomial sampling) the probability of reaching your
desired end point under different scenarios.


The `onlyCancer = FALSE` case might be what you want to do when you
examine general population genetics scenarios without focusing on possible
sampling issues. To do this, set `finalTime` to the value you want
and set `onlyCancer = FALSE`; in addition, set
`detectionProb` to "NA" and `detectionDrivers` and
`detectionSize` to "NA" or to huge numbers^[Setting
  `detectionDrivers` and `detectionSize` to "NA" is in
  fact equivalent to setting them to the largest possible numbers for
  these variables: $2^{32} -1$ and $\infty$, respectively.]. In this
scenario you simply collect the simulation output at the end of the run,
regardless of what happened with the population (it became extinct, it did
not reach a large size, it did not accumulate drivers, etc).





<!-- % The simplest procedure is to run the simulation for a fixed number of time -->
<!-- % periods (as specified by argument `finalTime`) or until the -->
<!-- % population goes extinct, whichever happens first. This might be what you -->
<!-- % want to do when you examine general population genetics scenarios without -->
<!-- % focusing on possible sampling issues. To do this, set `finalTime` -->
<!-- % to the value you want and set `onlyCancer = FALSE`; in addition, -->
<!-- % set `detectionProb` to "NA" and `detectionDrivers` and -->
<!-- % `detectionSize` to "NA" or to impossibly large -->
<!-- % numbers\footnote{Setting `detectionDrivers` and -->
<!-- %   `detectionSize` to "NA" is in fact equivalent to setting them -->
<!-- %   to the largest possible numbers: $2^32 -1$ and $\infty$, -->
<!-- %   respectively.}. This scenario is the `onlyCancer = FALSE` because -->
<!-- % you simply collect the simulation output, regardless of what happened with -->
<!-- % the population (it became extinct, it did not reach a large size, it did -->
<!-- % not accumulate drivers, etc). -->


<!-- % If we set `onlyCancer = TRUE`. Here a simulation will be repeated -->
<!-- % until the first one of the "reach cancer" conditions is met\footnote{Of -->
<!-- %   course, the "reach cancer" idea and the `onlyCancer` argument -->
<!-- %   are generic names; this could have been labeled "reach cardiovascular -->
<!-- %   disease" or "reach whatever interests me".}. These conditions are: -->

<!-- % \begin{itemize} -->

<!-- % \item total population size, given by `detectionSize`; -->

<!-- % \item number of drivers in any one genotype or clone, given by -->
<!-- %   `detectionDrivers`; note that this allows you to stop the -->
<!-- %   simulation as soon as a **specific genotype** is found, by using -->
<!-- %   exactly and only the genes that make that genotype as the drivers; -->

<!-- % \item a stochastic detection mechanism, where "detecting cancer" is a -->
<!-- %   function of total population size, with arguments as given in -->
<!-- %   `detectionProb`; this is explained below: \@ref(detectprob). -->

<!-- % \end{itemize} -->



<!-- % The simplest procedure is to run the simulation for a fixed number of time -->
<!-- % periods (as specified by argument `finalTime`) or until the -->
<!-- % population goes extinct, whichever happens first. This might be what you -->
<!-- % want to do when you examine general population genetics scenarios without -->
<!-- % focusing on possible sampling issues. To do this, set `finalTime` -->
<!-- % to the value you want and set `onlyCancer = FALSE`; in addition, -->
<!-- % set `detectionProb` to "NA" and `detectionDrivers` and -->
<!-- % `detectionSize` to "NA" or to impossibly large -->
<!-- % numbers\footnote{Setting `detectionDrivers` and -->
<!-- %   `detectionSize` to "NA" is in fact equivalent to setting them -->
<!-- %   to the largest possible numbers: $2^32 -1$ and $\infty$, -->
<!-- %   respectively.}. This scenario is the `onlyCancer = FALSE` because -->
<!-- % you simply collect the simulation output, regardless of what happened with -->
<!-- % the population (it became extinct, it did not reach a large size, it did -->
<!-- % not accumulate drivers, etc). -->



### Stochastic detection mechanism: "detectionProb"  {#detectprob}

This is the process that is controlled by the argument
`detectionProb`. Here the probability of tumor detection increases
with the total population size. This is biologically a reasonable
assumption: the larger the tumor, the more likely it is it will be
detected.

<!-- % The third mechanism for stopping the simulation assumes that the -->
<!-- % probability of tumor detection increases with the total population -->
<!-- % size. This is biologically a reasonable assumption: the larger the tumor, -->
<!-- % the more likely it is it will be detected.  -->

At regularly spaced times during the simulation, we compute the
probability of detection as a function of size and determine (by comparing
against a random uniform number) if the simulation should finish. For
simplicity, and to make sure the probability is bounded between 0 and 1,
we use the function

<!-- % \begin{equation} -->
<!-- %   \label{eq:2} -->
<!-- %   P(N) = 1 - e^{-cPDetect (N - PDBaseline)}, N > PDBaseline \\ -->
<!-- %   P(N) = 0, N \leq PDBaseline -->
<!-- % \end{equation} -->


<!-- $$ -->
<!--   P(N) =  -->
<!--   \begin{cases} -->
<!--   1 - e^{ -cPDetect (N - PDBaseline)} & \text{if } N > PDBaseline \\ -->
<!--   0 & \text{if } N \leq PDBaseline -->
<!--   \end{cases} -->
<!-- $$ {#eq:2} -->


\begin{equation}
  P(N) = 
  \begin{cases}
  1 - e^{ -cPDetect (N - PDBaseline)} & \text{if } N > PDBaseline \\
  0 & \text{if } N \leq PDBaseline
  \end{cases}
  \label{eq:2}
\end{equation}


where $P(N)$ is the probability that a tumor with a population size $N$
will be detected, and $cPDetect$ controls the increase in $P(N)$ with
population size; with $PDBaseline$ we both control the minimal population
size at which this mechanism stats operating (because we will rarely want
detection unless there is some meaningful increase of population size over
`initSize`) and we model the increase in $P(N)$ as a function of
differences with respect to $PDBaseline$.


The $P(N)$ refers to the probability of detection at each one of the
occasions when we assess the probability of exiting. When, or how often,
do we do that? When we assess probability of exiting is controlled by
`checkSizePEvery`, which will often be much larger than
`sampleEvery`^[We assess probability of exiting at every
  sampling time, as given by `sampleEvery`, that is the smallest
  possible sampling time that is separated from the previous time of
  assessment by at least `checkSizePEvery`. In other words, the
  interval between successive assessments will be the smallest multiple
  integer of `sampleEvery` that is larger than
  `checkSizePEvery`. For example, suppose `sampleEvery = 2`
  and `checkSizePEvery = 3`: we will assess exiting at times
  $4, 8, 12, 16, \ldots$. If `sampleEvery = 3` and
  `checkSizePEvery = 3`: we will assess exiting at times
  $6, 12, 18, \ldots$.]. Biologically, a way to think of
`checkSizePEvery` is "time between doctor appointments".


Finally, you can specify $cPDetect$ directly (you will need to set
`n2` and `p2` to NA). However, it might be more intuitive to
specify the pair `n2`, `p2`, such that $P(n2) = p2$ (and
from that pair we solve for the value of `cPDetect`).


You can get a feeling for the effects of these arguments by playing with
the following code, that we do not execute here for the sake of
speed. Here no mutation has any effect, but there is a non-zero
probability of exiting as soon as the total population size becomes larger
than the initial population size. So, eventually, all simulations will
exit and, as we are using the McFarland model, population size will vary
slightly around the initial population size.


```{r prbaux002, eval=FALSE}
gi2 <- rep(0, 5)
names(gi2) <- letters[1:5]
oi2 <- allFitnessEffects(noIntGenes = gi2)
s5 <- oncoSimulPop(200,
                   oi2,
                   model = "McFL",
                   initSize = 1000,
                   detectionProb = c(p2 = 0.1, 
                                     n2 = 2000, 
                                     PDBaseline = 1000,
                                     checkSizePEvery = 2), 
                   detectionSize = NA,
                   finalTime = NA, 
                   keepEvery = NA,
                   detectionDrivers = NA)
s5
hist(unlist(lapply(s5, function(x) x$FinalTime)))
``` 

As you decrease `checkSizePEvery` the distribution of "FinalTime"
will resemble more and more an exponential distribution.


In this vignette, there are some further examples of using this mechanism
in \@ref(s-cbn1) and \@ref(mcf5070), with the default arguments.


<!-- % Further comments about this procedure and its relation to sampling -->
<!-- % multiple simulations are provided in \@ref(popss-osp). -->
<!-- % ### So does `finalTime` matter much?} -->
<!-- % \label{meaning-final-time} -->
<!-- % This should be implicit from the above discussion, but `finalTime` -->
<!-- % basically works as a stopping point for the simulations and, in contrast -->
<!-- % to the other mechanisms for exiting a simulation, has rarely any special -->
<!-- % meaning.  -->


## Bauer's example again {#bauer2} 

<!-- Cannot write the correct Bauer's example, because conversion fails -->

We will use the model of @Bauer2014 that we saw in section \@ref(bauer).


```{r prbaux001}
K <- 5
sd <- 0.1
sdp <- 0.15
sp <- 0.05
bauer <- data.frame(parent = c("Root", rep("p", K)),
                    child = c("p", paste0("s", 1:K)),
                    s = c(sd, rep(sdp, K)),
                    sh = c(0, rep(sp, K)),
                    typeDep = "MN")
fbauer <- allFitnessEffects(bauer, drvNames = "p")
set.seed(1)
## Use fairly large mutation rate
b1 <- oncoSimulIndiv(fbauer, mu = 5e-5, initSize = 1000,
                     finalTime = NA,
                     onlyCancer = TRUE,
                     detectionProb = "default")

``` 


We will now use a variety of plots

```{r baux1,fig.width=6.5, fig.height=10}
par(mfrow = c(3, 1))
## First, drivers
plot(b1, type = "line", addtot = TRUE)
plot(b1, type = "stacked")
plot(b1, type = "stream")
``` 

```{r baux2,fig.width=6.5, fig.height=10}
par(mfrow = c(3, 1))
## Next, genotypes
plot(b1, show = "genotypes", type = "line")
plot(b1, show = "genotypes", type = "stacked")
plot(b1, show = "genotypes", type = "stream")
``` 


<!-- % %% For poster -->
<!-- % <<>>= -->

<!-- % pdf(file = "b1-traj.pdf", width = 8, height = 8) -->
<!-- % par(cex = 1.55) -->
<!-- % par(cex.axis= 0.9) -->
<!-- % par(las = 1) -->
<!-- % plot(b1, show = "genotypes", type = "stacked",  -->
<!-- %      plotDiversity = TRUE, legend.ncols = 3) -->
<!-- % dev.off() -->

<!-- % @  -->

In this case, probably the stream plots are most helpful. Note, however,
that (in contrast to some figures in the literature showing models of
clonal expansion) the stream plot (or the stacked plot) does not try to
explicitly show parent-descendant relationships, which would hardly be
realistically possible in these plots (although the plots of phylogenies
in section \@ref(phylog) could be of help).

## McFarland model with 5000 passengers and 70 drivers {#mcf5070}

```{r, fig.width=6}

set.seed(678)
nd <- 70  
np <- 5000 
s <- 0.1  
sp <- 1e-3 
spp <- -sp/(1 + sp)
mcf1 <- allFitnessEffects(noIntGenes = c(rep(s, nd), rep(spp, np)),
                          drvNames = seq.int(nd))
mcf1s <-  oncoSimulIndiv(mcf1,
                         model = "McFL", 
                         mu = 1e-7,
                         detectionProb = "default",
                         detectionSize = 1e20, 
                         detectionDrivers = 9999,
                         sampleEvery = 0.02,
                         keepEvery = 8,
                         initSize = 2000,
                         finalTime = 4000,
                         onlyCancer = FALSE)
summary(mcf1s)

``` 

<!-- %% -->
<!-- %% set.seed(456) -->

```{r mcf1sx1,fig.width=6.5, fig.height=10}
par(mfrow  = c(2, 1))
## I use thinData to make figures smaller and faster
plot(mcf1s, addtot = TRUE, lwdClone = 0.9, log = "", 
     thinData = TRUE, thinData.keep = 0.5)
plot(mcf1s, show = "drivers", type = "stacked",
     thinData = TRUE, thinData.keep = 0.3,
     legend.ncols = 2)
``` 


With the above output (where we see there are over 500 different
genotypes) trying to represent the genotypes makes no sense. 



## McFarland model with 50000 passengers and 70 drivers: clonal competition {#mcf50070}

The next is too slow (takes a couple of minutes in an i5 laptop) and too
big to run in a vignette, because we keep track of over 4000 different
clones (which leads to a result object of over 800 MB):

```{r, eval=FALSE}

set.seed(123)
nd <- 70  
np <- 50000 
s <- 0.1  
sp <- 1e-4 ## as we have many more passengers
spp <- -sp/(1 + sp)
mcfL <- allFitnessEffects(noIntGenes = c(rep(s, nd), rep(spp, np)),
                          drvNames = seq.int(nd))
mcfLs <-  oncoSimulIndiv(mcfL,
                         model = "McFL", 
                         mu = 1e-7,
                         detectionSize = 1e8, 
                         detectionDrivers = 100,
                         sampleEvery = 0.02,
                         keepEvery = 2,
                         initSize = 1000,
                         finalTime = 2000,
                         onlyCancer = FALSE)
``` 

But you can access the pre-stored results and plot them (beware: this
object has been trimmed by removing empty passenger rows in the Genotype matrix)

```{r, mcflsx2,fig.width=6}
data(mcfLs)
plot(mcfLs, addtot = TRUE, lwdClone = 0.9, log = "",
     thinData = TRUE, thinData.keep = 0.3,
     plotDiversity = TRUE)
``` 


The argument `plotDiversity = TRUE` asks to show a small plot on top
with Shannon's diversity index.


```{r}
summary(mcfLs)
## number of passengers per clone
summary(colSums(mcfLs$Genotypes[-(1:70), ]))
``` 


Note that we see clonal competition between clones with the same number of
drivers (and with different drivers, of course). We will return to this
(section \@ref(clonalint)).

A stacked plot might be better to show the extent of clonal
competition (plotting takes some time ---a stream plot reveals
similar patterns and is also slower than the line plot). I will
aggressively thin the data for this plot so it is faster and smaller
(but we miss some of the fine grain, of course):


```{r mcflsx3}
plot(mcfLs, type = "stacked", thinData = TRUE, 
     thinData.keep = 0.2,
     plotDiversity = TRUE,
     xlim = c(0, 1000))
``` 


<!-- %% %% The problem is the Genotype matrix. We remove empty passenger rows. -->
<!-- %% <<>>= -->
<!-- %% g1 <- mcfLs$Genotypes[1:nd, ] -->
<!-- %% g2 <- mcfLs$Genotypes[(nd+1):(nd+np), ] -->
<!-- %% rs <- rowSums(g2) -->
<!-- %% g3 <- g2[which(rs == 0), ] -->
<!-- %% g4 <- rbind(g1, g3) -->
<!-- %% @  -->




## Loading fitnessEffects data for simulation examples {#fedata}
We will use several of the previous examples. Most of them are in file
`examplesFitnessEffects`, where they are stored inside a list,
with named components (names the same as in the examples above):

```{r}
data(examplesFitnessEffects)
names(examplesFitnessEffects)
``` 





## Simulation with a conjunction example {#s-cbn1}

We will simulate using the simple CBN-like restrictions of
section \@ref(cbn1) with two different models. 

```{r smmcfls}
data(examplesFitnessEffects)
evalAllGenotypes(examplesFitnessEffects$cbn1, order = FALSE)[1:10, ]
sm <-  oncoSimulIndiv(examplesFitnessEffects$cbn1,
                      model = "McFL", 
                      mu = 5e-7,
                      detectionSize = 1e8, 
                      detectionDrivers = 2,
                      detectionProb = "default",
                      sampleEvery = 0.025,
                      keepEvery = 5,
                      initSize = 2000,
                      onlyCancer = TRUE)
summary(sm)
``` 

<!-- %% We will use several plots here. -->

<!-- %% <<>>= -->
<!-- %% ## Show drivers, line plot -->
<!-- %% plot(sm, show = "drivers", type = "line", addtot = TRUE) -->
<!-- %% ## drivers, stacked -->
<!-- %% plot(sm, show = "drivers", type = "stacked") -->

<!-- %% ## Genotypes, line plot -->
<!-- %% plot(sm, show = "genotypes", type = "line") -->
<!-- %% ## genotypes, stacked -->
<!-- %% plot(sm, show = "genotypes", type = "stacked") -->
<!-- %% @  -->


```{r smbosb1}
set.seed(1234)
evalAllGenotypes(examplesFitnessEffects$cbn1, order = FALSE, 
                 model = "Bozic")[1:10, ]
sb <-  oncoSimulIndiv(examplesFitnessEffects$cbn1,
                       model = "Bozic", 
                       mu = 5e-6,
                      detectionProb = "default",
                       detectionSize = 1e8, 
                       detectionDrivers = 4,
                       sampleEvery = 2,
                       initSize = 2000,
                       onlyCancer = TRUE)
summary(sb)
``` 

As usual, we will use several plots here.
<!-- \clearpage -->

```{r sbx1,fig.width=6.5, fig.height=3.3}
## Show drivers, line plot
par(cex = 0.75, las = 1)
plot(sb,show = "drivers", type = "line", addtot = TRUE,
     plotDiversity = TRUE)
``` 
```{r sbx2,fig.width=6.5, fig.height=3.3}
## Drivers, stacked
par(cex = 0.75, las = 1)
plot(sb,show = "drivers", type = "stacked", plotDiversity = TRUE)
``` 
```{r sbx3,fig.width=6.5, fig.height=3.3}
## Drivers, stream
par(cex = 0.75, las = 1)
plot(sb,show = "drivers", type = "stream", plotDiversity = TRUE)
``` 
<!-- \clearpage -->
```{r sbx4,fig.width=6.5, fig.height=3.3}
## Genotypes, line plot
par(cex = 0.75, las = 1)
plot(sb,show = "genotypes", type = "line", plotDiversity = TRUE)
``` 
```{r sbx5,fig.width=6.5, fig.height=3.3}
## Genotypes, stacked
par(cex = 0.75, las = 1)
plot(sb,show = "genotypes", type = "stacked", plotDiversity = TRUE)
``` 
```{r sbx6,fig.width=6.5, fig.height=3.3}
## Genotypes, stream
par(cex = 0.75, las = 1)
plot(sb,show = "genotypes", type = "stream", plotDiversity = TRUE)
``` 

The above illustrates again that different types of plots can be useful to
reveal different patterns in the data. For instance, here, because of the
huge relative frequency of one of the clones/genotypes, the stacked and
stream plots do not reveal the other clones/genotypes as we cannot use a
log-transformed y-axis, even if there are other clones/genotypes present.




## Simulation with order effects and McFL model {#clonalint}

<!-- %% Interesting to show effects of order: o3 -->

<!-- %% Increase mutation rate, so does not take forever -->
<!-- %% <<>>= -->

<!-- %% tmp <-  oncoSimulIndiv(examplesFitnessEffects[["o3"]], -->
<!-- %%                        model = "McFL",  -->
<!-- %%                        mu = 5e-5, -->
<!-- %%                        detectionSize = 1e8,  -->
<!-- %%                        detectionDrivers = 3, -->
<!-- %%                        sampleEvery = 0.025, -->
<!-- %%                        max.num.tries = 10, -->
<!-- %%                        keepEvery = -9, -->
<!-- %%                        initSize = 2000, -->
<!-- %%                        finalTime = 8000, -->
<!-- %%                        onlyCancer = TRUE);  -->

<!-- %% tmp -->

<!-- %% tmp <-  oncoSimulIndiv(examplesFitnessEffects[["o3"]], -->
<!-- %%                        model = "Bozic",  -->
<!-- %%                        mu = 5e-5, -->
<!-- %%                        detectionSize = 1e6,  -->
<!-- %%                        detectionDrivers = 4, -->
<!-- %%                        sampleEvery = 2, -->
<!-- %%                        max.num.tries = 100, -->
<!-- %%                        keepEvery = -9, -->
<!-- %%                        initSize = 2000, -->
<!-- %%                        onlyCancer = TRUE) -->
<!-- %% tmp -->

<!-- %% @  -->

(We use a somewhat large mutation rate than usual, so that the simulation
runs quickly.)


```{r, fig.width=6}

set.seed(4321)
tmp <-  oncoSimulIndiv(examplesFitnessEffects[["o3"]],
                       model = "McFL", 
                       mu = 5e-5,
                       detectionSize = 1e8, 
                       detectionDrivers = 3,
                       sampleEvery = 0.025,
                       max.num.tries = 10,
                       keepEvery = 5,
                       initSize = 2000,
                       finalTime = 6000,
                       onlyCancer = FALSE) 
``` 

We show a stacked and a line plot of the drivers:

<!-- \clearpage -->

```{r tmpmx1,fig.width=6.5, fig.height=4.1}
par(las = 1, cex = 0.85)
plot(tmp, addtot = TRUE, log = "", plotDiversity = TRUE,
     thinData = TRUE, thinData.keep = 0.2)
``` 
```{r tmpmx2,fig.width=6.5, fig.height=4.1}
par(las = 1, cex = 0.85)
plot(tmp, type = "stacked", plotDiversity = TRUE, 
     ylim = c(0, 5500), legend.ncols = 4,
     thinData = TRUE, thinData.keep = 0.2)
``` 

In this example (and at least under Linux, with both GCC and clang), we
can see that the mutants with three drivers do not get established when we
stop the simulation at time 6000. This is one case where the summary
statistics about number of drivers says little of value, as fitness is
very different for genotypes with the same number of mutations, and does
not increase in a simple way with drivers:

```{r}
evalAllGenotypes(examplesFitnessEffects[["o3"]], addwt = TRUE,
                 order = TRUE)
``` 

A few figures could help:

```{r tmpmx3,fig.width=6.5, fig.height=5.5}
plot(tmp, show = "genotypes", ylim = c(0, 5500), legend.ncols = 3,
     thinData = TRUE, thinData.keep = 0.5)
``` 

(When reading the figure legends, recall that genotype  $x > y\ \_\ z$ is
one where a mutation in "x" happened before a mutation in "y", and
there is also a mutation in "z" for which order does not matter. Here,
there are no genes for which order does not matter and thus there is
nothing after the "_").


In this case, the clones with three drivers end up displacing those with
two by the time we stop; moreover, notice how those with one driver never
really grow to a large population size, so we basically go from a
population with clones with zero drivers to a population made of clones
with two or three drivers:

<!-- %%<<fig.width=6} -->

```{r}
set.seed(15)
tmp <-  oncoSimulIndiv(examplesFitnessEffects[["o3"]],
                       model = "McFL", 
                       mu = 5e-5,
                       detectionSize = 1e8, 
                       detectionDrivers = 3,
                       sampleEvery = 0.015,
                       max.num.tries = 10,
                       keepEvery = 5,
                       initSize = 2000,
                       finalTime = 20000,
                       onlyCancer = FALSE,
                       extraTime = 1500)
tmp
``` 

<!-- \clearpage -->

use a drivers plot:
```{r tmpmdx5,fig.width=6.5, fig.height=4}
par(las = 1, cex = 0.85)
plot(tmp, addtot = TRUE, log = "", plotDiversity = TRUE,
     thinData = TRUE, thinData.keep = 0.5)
``` 
```{r tmpmdx6,fig.width=6.5, fig.height=4}
par(las = 1, cex = 0.85)
plot(tmp, type = "stacked", plotDiversity = TRUE,
     legend.ncols = 4, ylim = c(0, 5200), xlim = c(0, 1500),
     thinData = TRUE, thinData.keep = 0.5)
``` 

<!-- \clearpage -->

Now show the genotypes explicitly:
```{r tmpmdx7,fig.width=6.5, fig.height=5.3}
## Improve telling appart the most abundant 
## genotypes by sorting colors
## differently via breakSortColors
## Modify ncols of legend, so it is legible by not overlapping
## with plot
par(las = 1, cex = 0.85)
plot(tmp, show = "genotypes", breakSortColors = "distave",
     plotDiversity = TRUE, legend.ncols = 4,
     ylim = c(0, 5300), xlim = c(0, 1500),
     thinData = TRUE, thinData.keep = 0.5)
```



As before, the argument `plotDiversity = TRUE` asks to show a small
plot on top with Shannon's diversity index. Here, as before, the quick
clonal expansion of the clone with two drivers leads to a sudden drop in
diversity (for a while, the population is made virtually of a single
clone). Note, however, that compared to section \@ref(mcf50070), we are
modeling here a scenario with very few genes, and correspondingly very few
possible genotypes, and thus it is not strange that we observe very little
diversity.

<!-- %% These patterns, however, are not always present -->

<!-- %% <<fig.width=6>>= -->

<!-- %% set.seed(7654)  -->
<!-- %% tmp <-  oncoSimulIndiv(examplesFitnessEffects[["o3"]], -->
<!-- %%                        model = "McFL",  -->
<!-- %%                        mu = 5e-5, -->
<!-- %%                        detectionSize = 1e8,  -->
<!-- %%                        detectionDrivers = 3, -->
<!-- %%                        sampleEvery = 0.015, -->
<!-- %%                        max.num.tries = 10, -->
<!-- %%                        keepEvery = 5, -->
<!-- %%                        initSize = 2000, -->
<!-- %%                        finalTime = 10000, -->
<!-- %%                        onlyCancer = FALSE, -->
<!-- %%                        extraTime = 10) -->
<!-- %% tmp -->
<!-- %% plot(tmp, addtot = TRUE, log = "") -->

<!-- %% @  -->


<!-- %% Although in other runs we do not reach the three gene mutant and continue -->
<!-- %% with clone competition for a long time: -->


(We have used `extraTime` to continue the simulation well past the
point of detection, here specified as three drivers. Instead of specifying
`extraTime` we can set the `detectionDrivers` value to a
number larger than the number of existing possible drivers, and the
simulation will run until `finalTime` if `onlyCancer = FALSE`.)





<!-- \clearpage -->

## Numerical issues with death rates of 0 in Bozic model {#ex-0-death}

As we mentioned above (section \@ref(fit-neg-pos)) death rates of 0 can
lead to trouble when using Bozic's model:

<!-- %% <<>>= -->

<!-- %% set.seed(987) -->
<!-- %% ie3 <- allFitnessEffects(noIntGenes = rexp(3)) -->
<!-- %% evalAllGenotypes(ie3, order = FALSE, addwt = TRUE,  -->
<!-- %%                  model = "Bozic") -->

<!-- %% ie3_b <- oncoSimulIndiv(ie3, model = "Bozic") -->

<!-- %% evalAllGenotypes(ie3, order = FALSE, addwt = TRUE) -->

<!-- %% ie3_e <- oncoSimulIndiv(ie3, model = "Exp") -->

<!-- %% @  -->

<!-- %% Even simpler -->

<!-- %% ## set.seed(987) -->

```{r}
i1 <- allFitnessEffects(noIntGenes = c(1, 0.5))
evalAllGenotypes(i1, order = FALSE, addwt = TRUE, 
                 model = "Bozic")
i1_b <- oncoSimulIndiv(i1, model = "Bozic")

``` 


Of course, there is no problem in using the above with other models:

```{r}
evalAllGenotypes(i1, order = FALSE, addwt = TRUE, 
                 model = "Exp")
i1_e <- oncoSimulIndiv(i1, model = "Exp")
summary(i1_e)
``` 




## Interactive graphics {#interactive}

It is possible to create interactive stacked area and stream plots using
the `r Githubpkg("hrbrmstr/streamgraph")` package, available from
<https://github.com/hrbrmstr/streamgraph>.  However, that package is
not available as a CRAN or BioConductor package, and thus we cannot depend
on it for this vignette (or this package). You can, however, paste the
code below and make it run locally.

Before calling the *`streamgraph`* function, though, we need to
convert the data from the original format in which it is stored into
"long format". A simple convenience function is provided as
*`OncoSimulWide2Long`* in `r Biocpkg("OncoSimulR")`.


As an example, we will use the data we generated above for section
\@ref(bauer2).


```{r, eval=FALSE}
## Convert the data
lb1 <- OncoSimulWide2Long(b1)

## Install the streamgraph package from github and load
library(devtools)
devtools::install_github("hrbrmstr/streamgraph")
library(streamgraph)

## Stream plot for Genotypes
sg_legend(streamgraph(lb1, Genotype, Y, Time, scale = "continuous"),
              show=TRUE, label="Genotype: ")

## Staked area plot and we use the pipe
streamgraph(lb1, Genotype, Y, Time, scale = "continuous", 
            offset = "zero") %>%
    sg_legend(show=TRUE, label="Genotype: ")
``` 


<!-- %% (Note: the idiomatic way of doing the above with `r CRANpkg("tidyr")` is using  -->
<!-- %% \verb= %>% =, the pipe operator. Something like  -->
<!-- %% \begin{verbatim} -->
<!-- %% streamgraph(lb1, Genotype, Y, Time, scale = "continuous",   -->
<!-- %%            offset = "zero") \%>\%                                                                                                                                sg_legend(show=TRUE, label=``Genotype: ")  -->
<!-- %% \end{verbatim} -->

<!-- %% but it gives me problems with knitr, etc). -->



# Sampling multiple simulations {#sample}

Often, you will want to simulate multiple runs of the same scenario, and
then obtain the matrix of runs by mutations (a matrix of
individuals/samples by genes or, equivalently, a vector of "genotypes"),
and do something with them.  OncoSimulR offers several ways of doing this.

The key function here is *`samplePop`*, either called explicitly
after *`oncoSimulPop`* (or *`oncoSimulIndiv`*), or
implicitly as part of a call to *`oncoSimulSample`*. With
*`samplePop`* you can use **single cell** or **whole  tumor** sampling (for details see the help of
*`samplePop`*). Depending on how the simulations were conducted,
you might also sample at different times, or as a function of population
sizes. A major difference between procedures has to do with whether or not
you want to keep the complete history of the simulations.

**You want to keep the complete history of simulations**. You will
simulate using:


* `oncoSimulIndiv` repeatedly (maybe within
  *`mclapply`*), to parallelize the run).
* `oncoSimulPop`. `oncoSimulPop` is basically a
  thin wrapper around `oncoSimulIndiv` that uses
  *`mclapply`*.

   In both cases, you specify the conditions for ending the simulations (as
   explained in \@ref(endsimul)).

   Then, you will use function `oncoSimulSample` to obtain the matrix
   of samples by mutations.

  
**You do not want to keep the complete history of the
  simulations**. You will simulate using:


* `oncoSimulIndiv` repeatedly,  with argument `keepEvery = NA`. 
* `oncoSimulPop`, with argument `keepEvery = NA`. 

   In both cases you specify the conditions for ending the simulations (as
   explained in \@ref(endsimul)).  Then, you will use function
   `oncoSimulSample`.


  
* `oncoSimulSample`, specifying the conditions for ending the
  simulations (as explained in \@ref(endsimul)). In this case, you will
  not use `oncoSimulSample`, as that is implicitly called by
  `oncoSimulSample`.  The output is directly the matrix (and a
  little bit of summary from each run), and during the simulation it
  only stores one time point.
  


<!-- % In this case, you will not use `oncoSimulSample`, as that is -->
<!-- % implicitly called by `oncoSimulSample`. -->
  



Why the difference between the above cases? If you keep the complete
history, you can take samples at any of the times between the beginning
and the end of the simulations. If you do not keep the history, you can
only sample at the time the simulation exited.  Why would you want to use
the second route? If we are only interested in the final matrix of
individuals by mutations, keeping the complete history the above is
wasteful, because we store fully all of the simulations (for example in
the call to *`oncoSimulPop`*) and then sample (in the call to
*`samplePop`*). Other reasons for choosing one over the other
might have to do with flexibility (e.g., if you use
*`oncoSimulPop`* the arguments for `detectionSize`,
`detectionDrivers` must be the same for all simulations but this is
not the case for *`oncoSimulSample`*) and parallelized
execution. 


Further criteria to use when choosing between sampling procedures is
to realize that if you use *`oncoSimulPop`* the arguments for
`detectionSize` and `detectionDrivers` must be the same for all
simulations. This is not the case for *`oncoSimulSample`*. See
further comments in \@ref(diffsample).



The following are a few examples. First we run `oncoSimulPop` to
obtain 4 simulations and in the last line we sample from them:
```{r}

pancrPop <- oncoSimulPop(4, pancr,
                         detectionSize = 1e7,
                         keepEvery = 10,
                         mc.cores = 2)

summary(pancrPop)
samplePop(pancrPop)

``` 
  

Now a simple multiple call to `oncoSimulIndiv` wrapped inside
*`mclapply`*; this is basically the same we just did above. We set
the class of the object to allow direct usage of
*`samplePop`*. (Note: in Windows `mc.cores > 1` is not
supported, so for the vignette to run in Windows, Linux, and Mac we
explicitly set it here in the call to *`mclapply`*. For regular
usage, you will not need to do this; just use whatever is appropriate for
your operating system and number of cores. As well, we do not need any of
this with *`oncoSimulPop`* because the code inside
*`oncoSimulPop`* already takes care of setting `mc.cores`
to 1 in Windows).

```{r}
library(parallel)

if(.Platform$OS.type == "windows") {
    mc.cores <- 1
} else {
    mc.cores <- 2
}

p2 <- mclapply(1:4, function(x) oncoSimulIndiv(pancr,
                                               detectionSize = 1e7,
                                               keepEvery = 10),
                                               mc.cores = mc.cores)
class(p2) <- "oncosimulpop"
samplePop(p2)
``` 
  

Above, we have kept the complete history of the simulations as you can
check by doing, for instance

```{r}
tail(pancrPop[[1]]$pops.by.time)
``` 


If we were not interested in the complete history of simulations we could
have done instead (note the argument `keepEvery = NA`)

```{r}
pancrPopNH <- oncoSimulPop(4, pancr,
                           detectionSize = 1e7,
                           keepEvery = NA,
                           mc.cores = 2)

summary(pancrPopNH)
samplePop(pancrPopNH)
``` 

which only keeps the very last sample:
```{r}
pancrPopNH[[1]]$pops.by.time
``` 

Or we could have used *`oncoSimulSample`*:

```{r}
pancrSamp <- oncoSimulSample(4, pancr)
pancrSamp$popSamp

``` 


Again, why the above differences? If we are only interested in the
final matrix of populations by mutations, keeping the complete
history the above is wasteful, because we store fully all of the
simulations (in the call to *`oncoSimulPop`*) and then sample (in
the call to *`samplePop`*).


<!-- % We will use the "pancreas" example, above section \@ref(pancreas). -->
<!-- % <<>>= -->

<!-- % pancrPop <- oncoSimulPop(10, pancr, -->
<!-- %                          detectionSize = 1e7, -->
<!-- %                          keepEvery = 10, -->
<!-- %                          mc.cores = 2) -->

<!-- % summary(pancrPop) -->

<!-- % @  -->

<!-- % The above runs the simulation process 10 times, and stores the -->
<!-- % results. We can then sample from them: -->

<!-- % <<>>= -->
<!-- % pancrSPop <- samplePop(pancrPop) -->
<!-- % pancrSPop -->
<!-- % @  -->



<!-- % But if we are only interested in the final matrix of populations by -->
<!-- % mutations, the above is wasteful, because we store fully all of the -->
<!-- % simulations (in the call to *`oncoSimulPop`*) and then sample (in -->
<!-- % the call to *`samplePop`*). In particular, data from every -->
<!-- % sampling time (as given by `sampleEvery`) is preserved. It is in the -->
<!-- % call to *`samplePop`* when we actually sample the data. -->


<!-- % An alternative approach is to use the function -->
<!-- % *`oncoSimulSample`*. The output is directly the matrix (and a -->
<!-- % little bit of summary from each run), and during the simulation it only -->
<!-- % stores one time point.  -->


<!-- % <<>>= -->

<!-- % pancrSamp <- oncoSimulSample(10, pancr) -->
<!-- % pancrSamp -->

<!-- % @  -->

<!-- % %% FIXME: or oncoSimulPop with keepEvery = NULL. of mclapply of oncoSimulIndiv -->




<!-- FIXME -->
<!-- make this longer or restructure or whatever -->

<!-- ## Further criteria for choosing between sampling procedures {#choose-proc} -->

<!-- Further criteria to use when choosing between sampling procedures is -->
<!-- to realize that if you use *`oncoSimulPop`* the arguments for -->
<!-- `detectionSize` and `detectionDrivers` must be the same for all -->
<!-- simulations. This is not the case for *`oncoSimulSample`*. -->


<!-- samplePop can only sample with the arguments you give -->
<!-- (especially ) -->

## Differences between "samplePop" and "oncoSimulSample" {#diffsample}


*`samplePop`* provides two sampling times: "last" and
"uniform". It also allows you to sample at the first sample time(s) at
which the population(s) reaches a given size, which can be either the same
or different for each simulation (with argument `popSizeSample`).
"last" means to sample each individual in the very last time period of the
simulation. "uniform" means sampling each individual at a time choosen
uniformly from all the times recorded in the simulation between the time
when the first driver appeared and the final time period. "unif" means
that it is almost sure that different individuals will be sampled at
different times. "last" does not guarantee that different individuals will
be sampled at the same time unit, only that all will be sampled in the
last time unit of their simulation.



With *`oncoSimulSample`* we obtain samples that correspond to
`timeSample = "last"` in *`samplePop`* by specifying a
unique value for *`detectionSize`* and
*`detectionDrivers`*. The data from each simulation will
correspond to the time point at which those are reached (analogous to
`timeSample = "last"`). How about uniform sampling? We pass a
vector of *`detectionSize`* and *`detectionDrivers`*,
where each value of the vector comes from a uniform distribution. This is
not identical to the "uniform" sampling of  *`oncoSimulSample`*,
as we are not sampling uniformly over all time periods, but are stopping
at uniformly distributed values over the stopping conditions. Arguably,
however, the procedure in *`samplePop`* might be closer to what we
mean with "uniformly sampled over the course of the disease" if that
course is measured in terms of drivers or size of tumor.


<!-- % As an example, if you look at the output above, the object "pancrSamp" -->
<!-- % contains some simulations that have only a few drivers because those -->
<!-- % simulations were set to run only until they had just a small number of -->
<!-- % cells. -->

An advantage of *`oncoSimulSample`* is that we can specify
arbitrary sampling schemes, just by passing the appropriate vector
*`detectionSize`* and *`detectionDrivers`*. A disadvantage
is that if we change the stopping conditions we can not just resample the
data, but we need to run it again.

There is no difference between *`oncoSimulSample`* and
*`oncoSimulPop`* + *`samplePop`* in terms of the
`typeSample` argument (whole tumor or single cell).


Finally, there are some additional differences between the two
functions. *`oncoSimulPop`* can run parallelized (it uses
*`mclapply`*). This is not done with *`oncoSimulSample`*
because this function is designed for simulation experiments where you
want to examine many different scenarios simultaneously. Thus, we provide
additional stopping criteria (`max.wall.time.total` and
`max.num.tries.total`) to determine whether to continue running the
simulations, that bounds the total running time of all the simulations in
a call to *`oncoSimulSample`*. And, if you are running multiple
different scenarios, you might want to make multiple, separate,
independent calls (e.g., from different R processes) to
*`oncoSimulSample`*, instead of relying in *`mclapply`*,
since this is likely to lead to better usage of multiple cores/CPUs if you
are examining a large number of different scenarios.






<!-- % ### `popSizeSample` and *`oncoSimulPop`*} -->
<!-- % \label{popss-osp} -->


<!-- % Suppose you run a set of simulations with a large `finalTime` with -->
<!-- % *`oncoSimulPop`*. Since you can pass to *`samplePop`* a -->
<!-- % vector for `popSizeSample` this might seem to resemble a -->
<!-- % deterministic version of the stochastic detection mechanism -->
<!-- % (\@ref(detectprob)): for each simulation, you would take a sample at the -->
<!-- % first time a given population size is reached. You should notice, however, -->
<!-- % that for any simulation you are not sampling with a probability of -->
<!-- % detection that increases with size. Moreover, you can end up with "NA" -->
<!-- % in your sample. Suppose you have a set of fitness such that a given -->
<!-- % simulation, say number 1, never went beyond total population size -->
<!-- % 1000. Now, if you pass a vector of `popSizeSample` that has a value -->
<!-- % larger than a 1000 for the first position, you will get an "NA": there -->
<!-- % never is a value where for population size where that size is reached.  -->




<!-- % ## Dealing with errors in -->
<!-- %   *`oncoSimulPop`* {#errorosp} -->

<!-- % Suppose you did something like -->

<!-- % <<>>= -->
<!-- % pancrError <- oncoSimulPop(10, pancr, -->
<!-- %                            initSize = 1e-5, -->
<!-- %                            detectionSize = 1e7, -->
<!-- %                            keepEvery = 10, -->
<!-- %                            mc.cores = 2) -->
<!-- % @  -->

<!-- % The warning you are seeing tells you there was an error in the functions -->
<!-- % called by *`mclapply`*. If you check the help for -->
<!-- % *`mclpapply`* you'll see that it returns a try-error object, so we -->
<!-- % can inspect it. For instance, we can do: -->

<!-- % <<>>= -->
<!-- % pancrError[[1]] -->
<!-- % @  -->

<!-- % But that output is hard to read. This is better: -->

<!-- % <<>>= -->
<!-- % pancrError[[1]][1] -->
<!-- % @  -->
 
<!-- % And from here you can clearly see the error that was returned by -->
<!-- % *`oncoSimulIndiv`*: `initSize < 1` (which is indeed true: -->
<!-- % we pass `initSize = 1e-5`). -->
<!-- %% FIXME: use cases of each. -->

# Runing simulations: odds and ends 

## Dealing with errors in "oncoSimulPop" {#errorosp}

When running OncoSimulR under Windows *`mclapply`* does not use
multiple cores, and errors from *`oncoSimulPop`* are reported
directly. For example:

```{r}
## This code will only be evaluated under Windows
if(.Platform$OS.type == "windows")
    try(pancrError <- oncoSimulPop(10, pancr,
                               initSize = 1e-5,
                               detectionSize = 1e7,
                               keepEvery = 10,
                               mc.cores = 2))
``` 


Under POSIX operating systems (e.g., GNU/Linux or Mac OSX)
*`oncoSimulPop`* can ran parallelized by calling
*`mclapply`*. Now, suppose you did something like

```{r}
## Do not run under Windows
if(.Platform$OS.type != "windows")
    pancrError <- oncoSimulPop(10, pancr,
                               initSize = 1e-5,
                               detectionSize = 1e7,
                               keepEvery = 10,
                               mc.cores = 2)
``` 

The warning you are seeing tells you there was an error in the functions
called by *`mclapply`*. If you check the help for
*`mclpapply`* you'll see that it returns a try-error object, so we
can inspect it. For instance, we could do:

```{r, eval=FALSE}
pancrError[[1]]
``` 

But the output of this call might be easier to read:

```{r, eval=FALSE}
pancrError[[1]][1]
``` 
 
And from here you could see the error that was returned by
*`oncoSimulIndiv`*: `initSize < 1` (which is indeed true:
we pass `initSize = 1e-5`).


## What can you do with the simulations?

This is up to you. Later (section \@ref(sample-1)) we show an example where
we infer an oncogenetic tree from simulated data.


<!-- %% As an example, we can try to infer an oncogenetic tree -->
<!-- %% (and plot it) using the `r CRANpkg("Oncotree")` package @Oncotree after -->
<!-- %% getting a quick look at the marginal frequencies of events: -->

<!-- %% <<fig.width=4, fig.height=4>>= -->
<!-- %% colSums(pancrSamp)/nrow(pancrSamp) -->

<!-- %% require(Oncotree) -->
<!-- %% otp <- oncotree.fit(pancrSamp) -->
<!-- %% plot(otp) -->
<!-- %% @  -->


## Whole tumor sampling, genotypes, and allele counts: what  gives? {#wtsampl}

You are obtaining genotypes, regardless of order.  When we use "whole
tumor sampling", it is the frequency of the mutations in each gene that
counts, not the order. So, for instance, "c, d" and "c, d" both
contribute to the counts of "c" and "d". Similarly, when we use single
cell sampling, we obtain a genotype defined in terms of mutations, but
there might be multiple orders that give this genotype. For example, $d >
c$ and $c > d$ both  give you a genotype with "c" and "d" mutated, and
thus in the output you can have two columns with both genes mutated.



<!-- %% in an attempt to explain it, this just makes it too confusing. The -->
<!-- %% above is enough. -->
<!-- %% ## What if there is order? {#sim-order} -->

<!-- %% Consider the following example (I fix the seed and use a single core, so -->
<!-- %% no parallelization, to make sure we can reproduce the results) -->

<!-- %% <<>>= -->

<!-- %% oe8 <- allFitnessEffects(orderEffects = c( -->
<!-- %%                              "M > F > M" = 0, -->
<!-- %%                              "D > F > M" = 0.1, -->
<!-- %%                              "F > D > M" = 0.2 -->
<!-- %% ), -->
<!-- %%                       epistasis = c("D" = 0.02, "M" = 0.02, "F" = 0.02), -->
<!-- %%                         geneToModule = -->
<!-- %%                             c("Root" = "Root", -->
<!-- %%                               "M" = "m", -->
<!-- %%                               "F" = "f", -->
<!-- %%                               "D" = "d") ) -->

<!-- %% evalAllGenotypes(oe8) -->

<!-- %% set.seed(678)  -->
<!-- %% oe8P1 <- oncoSimulPop(8, oe8, -->
<!-- %%                      model = "Exp",  -->
<!-- %%                       detectionSize = 1e8, keepEvery = 10, mc.cores = 1) -->
<!-- %% lapply(oe8P1, print) -->




<!-- %% set.seed(678)  -->
<!-- %% oe8P1 <- oncoSimulPop(1, oe8, -->
<!-- %%                      model = "McFL",  -->
<!-- %%                       detectionDrivers = 2,  -->
<!-- %%                       keepEvery = 10, mc.cores = 1) -->
<!-- %% lapply(oe8P1, print) -->

<!-- %% @  -->




<!-- %% <<>>= -->

<!-- %% o8 <- allFitnessEffects(orderEffects = c( -->
<!-- %%                             "F > D" = 0, -->
<!-- %%                             "D > F" = 0.14, -->
<!-- %%                             "D > M" = 0.13, -->
<!-- %%                             "F > M" = 0.12, -->
<!-- %%                             "M > D" = 0.15), -->
<!-- %%                       epistasis = c("D" = 0.01, "M" = 0.01, "F" = 0.02), -->
<!-- %%                         geneToModule = -->
<!-- %%                             c("Root" = "Root", -->
<!-- %%                               "M" = "m", -->
<!-- %%                               "F" = "f", -->
<!-- %%                               "D" = "d") ) -->

<!-- %% evalAllGenotypes(o8) -->

<!-- %% set.seed(678)  -->
<!-- %% o8P1 <- oncoSimulPop(8, o8, -->
<!-- %%                      model = "Exp", keepEvery = 10, mc.cores = 1) -->
<!-- %% ## lapply(o8P1, print) -->
<!-- %% @  -->

<!-- %% Now, if we look at the sixth population we see -->

<!-- %% <<>>= -->
<!-- %% o8P1[[6]] -->
<!-- %% @  -->

<!-- %% Obviously, in terms of the genes that are mutated, both "d, f, m" and -->
<!-- %% "d, m, f" have the same genes mutated so if we sample, for instance doing -->

<!-- %% <<>>= -->

<!-- %% @  -->





<!-- %% o9 <- allFitnessEffects(orderEffects = c( -->
<!-- %%                             "F > D > M" = 0, -->
<!-- %%                             "D > F > M" = 0.14, -->
<!-- %%                             "D > M > F" = 0.13, -->
<!-- %%                             "D > M"     = 0.12, -->
<!-- %%                             "M > D"     = 0.15), -->
<!-- %%                       epistasis = c("D:-M" = 0.05, "M:-D" = 0.04), -->
<!-- %%                         geneToModule = -->
<!-- %%                             c("Root" = "Root", -->
<!-- %%                               "M" = "m", -->
<!-- %%                               "F" = "f", -->
<!-- %%                               "D" = "d") ) -->


<!-- %% set.seed(11) -->
<!-- %% o9P1 <- oncoSimulPop(8, o9, -->
<!-- %%                      model = "Exp", keepEvery = 10, mc.cores = 1) -->
<!-- %% lapply(o9P1, print) -->


<!-- %% @  -->



<!-- %% ## Testing of mappings} -->

<!-- %% The mapping of restriction tables, epistasis, and order effects to -->
<!-- %% fitness, especially when there are modules, is a delicate part of the -->
<!-- %% code: reasonable cases are straightforward to deal with, but there are -->
<!-- %% many ways to shoot oneself in the foot. That is why we have placed lots of -->
<!-- %% pre- and post-condition checks in the code (both R and C++), and we have a -->
<!-- %% comprehensive set of tests in file zz. You are welcome to suggest more -->
<!-- %% tricky scenarios (and tests for them). -->


<!-- %% # Introduction} -->

<!-- %% This vignette presents the OncoSimulR package. OncoSimulR allows you to -->
<!-- %% simulate tumor progression using several models of tumor progression. In -->
<!-- %% these simulations you can restrict the order in which mutations can -->
<!-- %% accumulate. For instance, you can restrict the allowed order as specified, -->
<!-- %% for instance, in Oncogenetic Tree (OT; @Desper1999JCB, Szabo2008) or -->
<!-- %% Conjunctive Bayesian Network (CBN; @Beerenwinkel2007, Gerstung2009, -->
<!-- %%   Gerstung2011}) models. Moreover, you can add passenger mutations to the -->
<!-- %% simulations. The models so far implemented are all continuous time models, -->
<!-- %% which are simulated using the BNB algorithm of Mather et -->
<!-- %% al.\ @Mather2012. This is a summary of some of the key features: -->


<!-- %% \begin{itemize} -->
<!-- %% \item You can pass arbitrary restrictions as specified by OTs or CBNs. -->
  
<!-- %% \item You can add passenger mutations. -->
  
<!-- %% \item You can allow for deviations from the OT and CBN models, specifying -->
<!-- %%   a penalty for such deviations (the $s_h$ parameter). -->
  
<!-- %% \item Right now, three different models are available, two that lead to -->
<!-- %%   exponential growth, one of them loosely based on Bozic et al.\ -->
<!-- %%   \cite{Bozic2010}, and another that leads to logistic-like growth, based -->
<!-- %%   on McFarland et al.\ \cite{McFarland2013}. -->
<!-- %% \item Simulations are generally very fast as I use the BNB algorithm -->
<!-- %%   implemented in C++. -->
<!-- %% \end{itemize} -->


<!-- %% Further details about the motivation for wanting to -->
<!-- %% simulate data this way can be found in \cite{ot-biorxiv}, where additional -->
<!-- %% comments about model parameters and caveats are discussed. The Java -->
<!-- %% program by \cite{Reiter2013a} offers somewhat similar functionality, but -->
<!-- %% they are restricted to at most four drivers, you cannot use arbitrary CBNs -->
<!-- %% or OTs to specify order restrictions, there is no allowance for -->
<!-- %% passengers, and a single type of model (a discrete time Galton-Watson -->
<!-- %% process) is implemented. -->





<!-- %% Using this package will often involve the following steps: -->

<!-- %% \begin{enumerate} -->
<!-- %% \item Specify the restrictions in the order of mutations: section \@ref(poset). -->
<!-- %% \item Simulate cancer progression: section \@ref(simul). You can simulate -->
<!-- %%   for a single subject or for a set of subjects. You will need to -->
<!-- %%   \begin{itemize} -->
<!-- %%   \item Decide on a model (e.g., Bozic or McFarland). -->
<!-- %%   \item Specify the parameters of the model. -->
<!-- %%   \end{itemize} -->
<!-- %%   Of course, at least for initial playing around, you can use the defaults. -->
  
<!-- %% \item Sample from the simulated data: section \@ref(sample), and do -->
<!-- %%   something with those simulated data (e.g., fit an OT model to -->
<!-- %%   them). What you do with the data, however, is outside the scope of this -->
<!-- %%   package.    -->
<!-- %% \end{enumerate} -->


<!-- %% Before anything else, let us load the package. We also explicitly load -->
<!-- %% `r Biocpkg("graph")` for the vignette to work (you do not need that for your -->
<!-- %% usual interactive work). -->

<!-- %% <<>>= -->
<!-- %% library(OncoSimulR) -->
<!-- %% library(graph) -->
<!-- %% @  -->


<!-- %% # Specifying restrictions: posets {#poset} -->

<!-- %% How to specify the restrictions is shown in the help for -->
<!-- %% *`poset`*. It is often useful, to make sure you did not make any -->
<!-- %% mistakes, to plot the poset. This is from the examples (we use an "L" -->
<!-- %% after a number so that the numbers are integers, not doubles; we could -->
<!-- %% alternatively have modified `storage.mode`). -->

<!-- %% <<fig.height=3>>= -->
<!-- %% ## Node 2 and 3 depend on 1, and 4 depends on no one -->
<!-- %% p1 <- cbind(c(1L, 1L, 0L), c(2L, 3L, 4L)) -->
<!-- %% plotPoset(p1, addroot = TRUE) -->
<!-- %% @  -->

<!-- %% <<fig.height=3>>= -->
<!-- %% ## A simple way to create a poset where no gene (in a set of 15) depends -->
<!-- %% ## on any other. -->
<!-- %% p4 <- cbind(0L, 15L) -->
<!-- %% plotPoset(p4, addroot = TRUE) -->
<!-- %% @  -->



<!-- %% Specifying posets is actually straightforward. For instance, we can -->
<!-- %% specify the pancreatic cancer poset in Gerstung et al.\ -->
<!-- %% \cite{Gerstung2011} (their figure 2B, left). We specify the poset using -->
<!-- %% numbers, but for nicer plotting we will use names (KRAS is 1, SMAD4 is 2, -->
<!-- %% etc). This example is also in the help for *`poset`*: -->

<!-- %% <<fig.height=3>>= -->
<!-- %% pancreaticCancerPoset <- cbind(c(1, 1, 1, 1, 2, 3, 4, 4, 5), -->
<!-- %%                                c(2, 3, 4, 5, 6, 6, 6, 7, 7)) -->
<!-- %% storage.mode(pancreaticCancerPoset) <- "integer" -->
<!-- %% plotPoset(pancreaticCancerPoset, -->
<!-- %%           names = c("KRAS", "SMAD4", "CDNK2A", "TP53", -->
<!-- %%                     "MLL3","PXDN", "TGFBR2")) -->
<!-- %% @ -->
<!-- %% # Simulating cancer progression {#simul} -->


<!-- %% We can simulate the progression in a single subject. Using an example -->
<!-- %% very similar to the one in the help: -->


<!-- %% <<echo=FALSE,results='hide',error=FALSE>>= -->
<!-- %% options(width=60) -->
<!-- %% @  -->

<!-- %% <<>>= -->
<!-- %% ## use poset p1101 -->
<!-- %% data(examplePosets) -->
<!-- %% p1101 <- examplePosets[["p1101"]] -->

<!-- %% ## Bozic Model -->
<!-- %% b1 <- oncoSimulIndiv(p1101, keepEvery = 15) -->
<!-- %% summary(b1) -->
<!-- %% @  -->


<!-- %% The first thing we do is make it simpler (for future examples) to use a -->
<!-- %% set of restrictions. In this case, those encoded in poset p1101. Then, we -->
<!-- %% run the simulations and look at a simple summary and a plot. %% We explicitly -->
<!-- %% %% set `silent = TRUE` to prevent the vignette from filling up with -->
<!-- %% %% intermediate output. -->

<!-- %% If you want to plot the trajectories, it is better to keep more frequent -->
<!-- %% samples,  so you can see when clones appear: -->

<!-- %% <<fig.height=5, fig.width=5>>= -->
<!-- %% b2 <- oncoSimulIndiv(p1101, keepEvery = 1) -->
                    
<!-- %% summary(b2) -->
<!-- %% plot(b2) -->
<!-- %% @  -->


<!-- %% The following is an example where we do not care about passengers, but we -->
<!-- %% want to use a different graph, and we want a few more drivers before -->
<!-- %% considering cancer has been reached. And we allow it to run for longer. -->
<!-- %% Note that in the McF model `detectionSize` really plays no -->
<!-- %% role. Note also how we pass the poset: it is the same as before, but now -->
<!-- %% we directly access the poset in the list of posets. -->

<!-- %% <<>>= -->

<!-- %% m2 <- oncoSimulIndiv(examplePosets[["p1101"]], model = "McFL",  -->
<!-- %%                      numPassengers = 0, detectionDrivers = 8,  -->
<!-- %%                      mu = 5e-7, initSize = 4000,  -->
<!-- %%                      sampleEvery = 0.025, -->
<!-- %%                      finalTime = 25000, keepEvery = 5,  -->
<!-- %%                      detectionSize = 1e6)  -->
<!-- %% plot(m2, addtot = TRUE, log = "") -->

<!-- %% @  -->


<!-- %% The default is to simulate progression until a simulation reaches cancer -->
<!-- %% (i.e., only simulations that satisfy the detectionDrivers or the -->
<!-- %% detectionSize will be returned). If you use the McF model with large -->
<!-- %% enough `initSize` this will often be the case but not if you use -->
<!-- %% very small `initSize`. Likewise, most of the Bozic runs do not -->
<!-- %% reach cancer. Lets try a few: -->

<!-- %% <<>>= -->
<!-- %% b3 <- oncoSimulIndiv(p1101, onlyCancer = FALSE) -->
<!-- %% summary(b3) -->

<!-- %% b4 <- oncoSimulIndiv(p1101, onlyCancer = FALSE) -->
<!-- %% summary(b4) -->
<!-- %% @  -->

<!-- %% Plot those runs: -->

<!-- %% <<fig.width=8, fig.height=4>>= -->
<!-- %% par(mfrow = c(1, 2)) -->
<!-- %% par(cex = 0.8) ## smaller font -->
<!-- %% plot(b3) -->
<!-- %% plot(b4) -->
<!-- %% @  -->


<!-- %% ## Simulating progression in several subjects} -->

<!-- %% To simulate the progression in a bunch of subjects (we will use only -->
<!-- %% four, so as not to fill the vignette with plots) we can do, with the same -->
<!-- %% settings as above: -->

<!-- %% <<>>= -->
<!-- %% p1 <- oncoSimulPop(4, p1101) -->
<!-- %% par(mfrow = c(2, 2)) -->
<!-- %% plot(p1) -->
<!-- %% @  -->
<!-- %% # Sampling from a set of simulated subjects {#sample} -->
<!-- %% \label{sec:sampling-from-set} -->
<!-- %% You will often want to do something with the simulated data. For instance, -->
<!-- %% sample the simulated data. Here we will obtain the trajectories for 100 -->
<!-- %% subjects in a scenario without passengers. Then we will sample with the -->
<!-- %% default options and store that as a vector of genotypes (or a matrix of -->
<!-- %% subjects by genes): -->
<!-- %% <<>>= -->
<!-- %% m1 <- oncoSimulPop(100, examplePosets[["p1101"]],  -->
<!-- %%                    numPassengers = 0) -->
<!-- %% @  -->
<!-- %% The function *`samplePop`* samples that object, and also gives you -->
<!-- %% some information about the output: -->
<!-- %% <<>>= -->
<!-- %% genotypes <- samplePop(m1) -->
<!-- %% @  -->
<!-- %% What can you do with it? That is up to you. As an example, let us try to -->
<!-- %% infer an oncogenetic tree (and plot it) using the `r CRANpkg("Oncotree")` -->
<!-- %% package \cite{Oncotree} after getting a quick look at the marginal -->
<!-- %% frequencies of events: -->

<!-- %% <<fig.width=4, fig.height=4>>= -->
<!-- %% colSums(genotypes)/nrow(genotypes) -->

<!-- %% require(Oncotree) -->
<!-- %% ot1 <- oncotree.fit(genotypes) -->
<!-- %% plot(ot1) -->
<!-- %% @  -->

<!-- %% Your run will likely differ from mine, but with the defaults (detection -->
<!-- %% size of $10^8$) it is likely that events down the tree will never -->
<!-- %% appear. You can set `detectionSize = 1e9` and you will see that -->
<!-- %% events down the tree are now found in the cross-sectional sample. -->


<!-- %% Alternatively, you can use single cell sampling and that, sometimes, -->
<!-- %% recovers one or a couple more events. -->

<!-- %% <<fig.width=4, fig.height=4>>= -->
<!-- %% genotypesSC <- samplePop(m1, typeSample = "single") -->
<!-- %% colSums(genotypesSC)/nrow(genotypesSC) -->

<!-- %% ot2 <- oncotree.fit(genotypesSC) -->
<!-- %% plot(ot2) -->
<!-- %% @  -->

<!-- %% You can of course rename the columns of the output matrix to something -->
<!-- %% else if you want so the names of the nodes will reflect those potentially -->
<!-- %% more meaningful names. -->



# Showing the relationships of clones {#phylog}

If you run simulations with the `keepPhylog = TRUE` argument, the
simulations keep track of when every clone is generated, and that will
allow us to see the parent-child relationships between clones. (This is
disabled by default: the code runs a little bit slower and the result is
larger.)

In an abuse of terminology, we will use functions with the "phylog"
term, but note these are not proper phylogenies. (Though you could
construct proper phylogenies from the information kept).


Let us re-run a previous example:

```{r}

set.seed(15)
tmp <-  oncoSimulIndiv(examplesFitnessEffects[["o3"]],
                       model = "McFL", 
                       mu = 5e-5,
                       detectionSize = 1e8, 
                       detectionDrivers = 3,
                       sampleEvery = 0.015,
                       max.num.tries = 10,
                       keepEvery = 5,
                       initSize = 2000,
                       finalTime = 20000,
                       onlyCancer = FALSE,
                       extraTime = 1500,
                       keepPhylog = TRUE)
tmp
``` 

We can plot the parent-child relationships^[There are several
  packages in R devoted to phylogenetic inference and related issues. For
  instance, `r CRANpkg("ape")`. I have not used that infrastructure because of
  our very specific needs and circumstances; for instance, internal nodes
  are observed, we can have networks instead of trees, and we have no
  uncertainty about when events occurred.] of every clone ever created
(with fitness larger than 0 ---clones without viability are never shown):

```{r}
plotClonePhylog(tmp, N = 0)
``` 

However, we often only want to show clones that exist (have number of
cells $>0$) at a certain time (while of course showing all of their
ancestors, even if those are now extinct ---i.e., regardless of their
current numbers).

```{r}
plotClonePhylog(tmp, N = 1)
``` 

If we set `keepEvents = TRUE` the arrows show how many times each
clone appeared:

(The next can take a while)
```{r pcpkeepx1}
plotClonePhylog(tmp, N = 1, keepEvents = TRUE)
``` 

And we can show the plot so that the vertical axis is proportional to time
(though you might see overlap of nodes if a child node appeared shortly
after the parent):

```{r}
plotClonePhylog(tmp, N = 1, timeEvents = TRUE)
``` 

We can obtain the adjacency matrix doing

```{r, fig.keep="none"}
get.adjacency(plotClonePhylog(tmp, N = 1, returnGraph = TRUE))

``` 


We can see another example here:

```{r}

set.seed(456)
mcf1s <-  oncoSimulIndiv(mcf1,
                         model = "McFL", 
                         mu = 1e-7,
                         detectionSize = 1e8, 
                         detectionDrivers = 100,
                         sampleEvery = 0.02,
                         keepEvery = 2,
                         initSize = 2000,
                         finalTime = 1000,
                         onlyCancer = FALSE,
                         keepPhylog = TRUE)

``` 

Showing only clones that exist at the end of the simulation (and all their
parents):

```{r}
plotClonePhylog(mcf1s, N = 1)
``` 

Notice that the labels here do not have a "_", since there were no order
effects in fitness. However, the labels show the genes that are
mutated, just as before.

Similar, but with vertical axis proportional to time:


```{r}
par(cex = 0.7)
plotClonePhylog(mcf1s, N = 1, timeEvents = TRUE)
``` 

What about those that existed in the last 200 time units?
```{r}
par(cex = 0.7)
plotClonePhylog(mcf1s, N = 1, t = c(800, 1000))
``` 

And try now to show also when the clones appeared (we restrict the time
to between 900 and 1000, to avoid too much clutter):
```{r}
par(cex = 0.7)
plotClonePhylog(mcf1s, N = 1, t = c(900, 1000), timeEvents = TRUE)
``` 

<!-- % % %% For poster -->

<!-- % <<>>= -->

<!-- % pdf("phylog-clone1.pdf", width = 4, height = 3.4) -->
<!-- % par(cex = 0.4); plotClonePhylog(mcf1s, N = 1, t = c(900, 1000), timeEvents = TRUE) -->
<!-- % dev.off() -->

<!-- % @  -->


(By playing with `t`, it should be possible to obtain animations of
the phylogeny. We will not pursue it here.)


If the previous graph seems cluttered, we can represent it in a different
way by calling `r CRANpkg("igraph")` directly after storing the graph and using
the default layout:

```{r fig.keep="none"}
g1 <- plotClonePhylog(mcf1s, N = 1, t = c(900, 1000),
                      returnGraph = TRUE)
``` 

```{r}
plot(g1)
``` 

which might be easier to show complex relationships or identify central or
key clones.


<!-- %% There is support in R for phylog, blablabal. But does not work for our -->
<!-- %% specific problem. So use igraph blablabla -->


<!-- %% <<>>= -->
<!-- %% plotClonePhylog(mcf1s, TRUE, FALSE, FALSE) -->
<!-- %% plotClonePhylog(tmp, FALSE, FALSE, FALSE) -->
<!-- %% @  -->


It is of course quite possible that, especially if we consider few genes,
the parent-child relationships will form a network, not a tree, as the
same child node can have multiple parents. You can play with this example,
modified from one we saw before (section \@ref(mn1)):

```{r, eval=FALSE}
op <- par(ask = TRUE)
while(TRUE) {
    tmp <- oncoSimulIndiv(smn1, model = "McFL",
                          mu = 5e-5, finalTime = 500,
                          detectionDrivers = 3,
                          onlyCancer = FALSE,
                          initSize = 1000, keepPhylog = TRUE)
    plotClonePhylog(tmp, N = 0)
}
par(op)
``` 


## Parent-child relationships from multiple runs {#phylogmult}

If you use *`oncoSimulPop`* you can store and plot the
``phylogenies" of the different runs:

```{r}

oi <- allFitnessEffects(orderEffects =
               c("F > D" = -0.3, "D > F" = 0.4),
               noIntGenes = rexp(5, 10),
                          geneToModule =
                              c("F" = "f1, f2, f3",
                                "D" = "d1, d2") )
oiI1 <- oncoSimulIndiv(oi, model = "Exp")
oiP1 <- oncoSimulPop(4, oi,
                     keepEvery = 10,
                     mc.cores = 2,
                     keepPhylog = TRUE)

``` 

We will plot the first two:
```{r, fig.height=9}

op <- par(mar = rep(0, 4), mfrow = c(2, 1))
plotClonePhylog(oiP1[[1]])
plotClonePhylog(oiP1[[2]])
par(op)

``` 


This is so far disabled in function *`oncoSimulSample`*, since
that function is optimized for other uses. This might change in the future.



# Generating random fitness landscapes {#gener-fit-land}

It is possible to generate mappings of genotype to fitness using the
function *`rfitness`* that allows you to use from a pure House of
Cards model to a purely additive model. I have followed
@szendro_quantitative_2013, @franke_evolutionary_2011 and model
fitness as

<!-- $$ -->
<!--   f_i = -c d(i, reference) + x_i -->
<!-- $$ {#eq:1} -->


\begin{equation}
  f_i = -c\ d(i, reference) + x_i
  \label{eq:1}
\end{equation} 


where $d(i, j)$ is the Hamming distance between genotypes $i$ and $j$ (the
number of positions that differ), $c$ is the decrease in fitness of a
genotype per each unit increase in Hamming distance from the reference
genotype, and $x_i$ is a random variable (in this
case, a normal deviate of mean 0 and standard deviation $sd$).  You can
change the reference genotype to any of the genotypes: for the
deterministic part, you make the fittest genotype be the one with all
positions mutated by setting `reference = "max"`, or use the
wildtype by using a string of 0s, or randomly select a genotype as a
reference by using `reference = "random"`.  And by playing with $c$
and $sd$ you can flexibly modify the relative weight of the purely House
of Cards vs. additive component. The expression used above is also very
similar to the one on @greene_changing_2014 if you use
*`rfitness`* with the argument `reference = "max"`.


What can you do with these genotype to fitness mappings? You could plot
them, you could use them as input for *`oncoSimulIndiv`* and
related functions, or you could export them and plot them externally
(e.g., in MAGELLAN: <http://wwwabi.snv.jussieu.fr/public/Magellan/>,
@brouillet_magellan:_2015).


```{r}
## A small example
rfitness(3)

## A 5-gene example, where the reference genotype is the one the one with
## all positions mutated, similar to Greene and Crona, 2014.  We will plot
## the landscape and use it for simulations We downplay the random
## component with a sd = 0.5

r1 <- rfitness(5, reference = rep(1, 5), sd = 0.6)
plot(r1)
oncoSimulIndiv(allFitnessEffects(genotFitness = r1))
``` 

<!-- % % % % %% For poster -->

<!-- % <<>>= -->

<!-- % pdf(file = "fl1.pdf", height = 5.8, width = 5) -->
<!-- % plot(r1, use_ggrepel = TRUE) -->
<!-- % dev.off() -->

<!-- % @  -->

# Using v.1 posets and simulations {#v1}

It is strongly recommended that you use the new (v.2) procedures for
specifying fitness effects. However, the former v.1 procedures are still
available, with only very minor changes to function calls. What follows
below is the former vignette. You might want to use v.1 because for
certain models (e.g., small number of genes, with restrictions as
specified by a simple poset) simulations might be faster with v.1 (fitness
evaluation is much simpler ---we are working on further improving speed).

## Specifying restrictions: posets {#poset}

How to specify the restrictions is shown in the help for
*`poset`*. It is often useful, to make sure you did not make any
mistakes, to plot the poset. This is from the examples (we use an "L"
after a number so that the numbers are integers, not doubles; we could
alternatively have modified `storage.mode`).

```{r, fig.height=3}
## Node 2 and 3 depend on 1, and 4 depends on no one
p1 <- cbind(c(1L, 1L, 0L), c(2L, 3L, 4L))
plotPoset(p1, addroot = TRUE)
``` 

```{r, fig.height=3}
## A simple way to create a poset where no gene (in a set of 15) depends
## on any other.
p4 <- cbind(0L, 15L)
plotPoset(p4, addroot = TRUE)
``` 



Specifying posets is actually straightforward. For instance, we can
specify the pancreatic cancer poset in 
@Gerstung2011 (their figure 2B, left). We specify the poset using
numbers, but for nicer plotting we will use names (KRAS is 1, SMAD4 is 2,
etc). This example is also in the help for *`poset`*:

```{r, fig.height=3}
pancreaticCancerPoset <- cbind(c(1, 1, 1, 1, 2, 3, 4, 4, 5),
                               c(2, 3, 4, 5, 6, 6, 6, 7, 7))
storage.mode(pancreaticCancerPoset) <- "integer"
plotPoset(pancreaticCancerPoset,
          names = c("KRAS", "SMAD4", "CDNK2A", "TP53",
                    "MLL3","PXDN", "TGFBR2"))

```
## Simulating cancer progression {#simul1}


We can simulate the progression in a single subject. Using an example
very similar to the one in the help:


```{r, echo=FALSE,results='hide',error=FALSE}
options(width=60)
``` 

```{r}
## use poset p1101
data(examplePosets)
p1101 <- examplePosets[["p1101"]]

## Bozic Model
b1 <- oncoSimulIndiv(p1101, keepEvery = 15)
summary(b1)
``` 


The first thing we do is make it simpler (for future examples) to use a
set of restrictions. In this case, those encoded in poset p1101. Then, we
run the simulations and look at a simple summary and a plot. 

<!-- %% We explicitly -->
<!-- %% set `silent = TRUE` to prevent the vignette from filling up with -->
<!-- %% intermediate output. -->

If you want to plot the trajectories, it is better to keep more frequent
samples,  so you can see when clones appear:

```{r pb2bothx1,fig.height=5.5, fig.width=5.5}
b2 <- oncoSimulIndiv(p1101, keepEvery = 1)
summary(b2)
plot(b2)
``` 

As we have seen before, the stacked plot here is less useful and that is
why I do not evaluate that code for this vignette.

```{r pbssttx1,eval=FALSE}
plot(b2, type = "stacked")
``` 




The following is an example where we do not care about passengers, but we
want to use a different graph, and we want a few more drivers before
considering cancer has been reached. And we allow it to run for longer.
Note that in the McF model `detectionSize` really plays no
role. Note also how we pass the poset: it is the same as before, but now
we directly access the poset in the list of posets.

```{r, echo=FALSE,eval=TRUE}
set.seed(1) ## for repeatability. Once I saw it not reach cancer.
``` 
```{r}

m2 <- oncoSimulIndiv(examplePosets[["p1101"]], model = "McFL", 
                     numPassengers = 0, detectionDrivers = 8, 
                     mu = 5e-7, initSize = 4000, 
                     sampleEvery = 0.025,
                     finalTime = 25000, keepEvery = 5, 
                     detectionSize = 1e6) 
``` 

(Very rarely the above run will fail to reach cancer. If that
happens, execute it again.)


As usual, we will plot using both a line and a stacked plot:

```{r m2x1,fig.width=6.5, fig.height=10}
par(mfrow = c(2, 1))
plot(m2, addtot = TRUE, log = "",
     thinData = TRUE, thinData.keep = 0.5)
plot(m2, type = "stacked",
     thinData = TRUE, thinData.keep = 0.5)
``` 

The default is to simulate progression until a simulation reaches cancer
(i.e., only simulations that satisfy the detectionDrivers or the
detectionSize will be returned). If you use the McF model with large
enough `initSize` this will often be the case but not if you use
very small `initSize`. Likewise, most of the Bozic runs do not
reach cancer. Lets try a few:

```{r}
b3 <- oncoSimulIndiv(p1101, onlyCancer = FALSE)
summary(b3)

b4 <- oncoSimulIndiv(p1101, onlyCancer = FALSE)
summary(b4)
``` 

Plot those runs:

```{r b3b4x1ch1, fig.width=8, fig.height=4}
par(mfrow = c(1, 2))
par(cex = 0.8) ## smaller font
plot(b3)
plot(b4)
``` 


### Simulating progression in several subjects

To simulate the progression in a bunch of subjects (we will use only
four, so as not to fill the vignette with plots) we can do, with the same
settings as above:

```{r ch2}
p1 <- oncoSimulPop(4, p1101, mc.cores = 2)
par(mfrow = c(2, 2))
plot(p1, ask = FALSE)
``` 

We can also use stream and stacked plots, though they might not be as
useful in this case. For the sake of keeping the vignette small, these are
commented out.
```{r p1multx1,eval=FALSE}
par(mfrow = c(2, 2))
plot(p1, type = "stream", ask = FALSE)
```

```{r p1multstx1,eval=FALSE}
par(mfrow = c(2, 2))
plot(p1, type = "stacked", ask = FALSE)
```


## Sampling from a set of simulated subjects {#sample-1}


You will often want to do something with the simulated data. For instance,
sample the simulated data. Here we will obtain the trajectories for 100
subjects in a scenario without passengers. Then we will sample with the
default options and store that as a vector of genotypes (or a matrix of
subjects by genes):


```{r}

m1 <- oncoSimulPop(100, examplePosets[["p1101"]], 
                   numPassengers = 0, mc.cores = 2)

``` 

The function *`samplePop`* samples that object, and also gives you
some information about the output:

```{r}
genotypes <- samplePop(m1)
``` 



What can you do with it? That is up to you. As an example, let us try to
infer an oncogenetic tree (and plot it) using the `r CRANpkg("Oncotree")`
package @Oncotree after getting a quick look at the marginal
frequencies of events:

```{r fxot1,fig.width=4, fig.height=4}
colSums(genotypes)/nrow(genotypes)

require(Oncotree)
ot1 <- oncotree.fit(genotypes)
plot(ot1)
``` 

Your run will likely differ from mine, but with the defaults (detection
size of $10^8$) it is likely that events down the tree will never
appear. You can set `detectionSize = 1e9` and you will see that
events down the tree are now found in the cross-sectional sample.


Alternatively, you can use single cell sampling and that, sometimes,
recovers one or a couple more events.

```{r fxot2,fig.width=4, fig.height=4}
genotypesSC <- samplePop(m1, typeSample = "single")
colSums(genotypesSC)/nrow(genotypesSC)

ot2 <- oncotree.fit(genotypesSC)
plot(ot2)
``` 

You can of course rename the columns of the output matrix to something
else if you want so the names of the nodes will reflect those potentially
more meaningful names.




# Generating random DAGs for restrictions {#simo}

You might want to randomly generate DAGs like those often found in the
literature on oncogenetic trees et al. Function *`simOGraph`*
might help here. 

```{r}
## No seed fixed, so reruns will give different DAGs.
(a1 <- simOGraph(10))
library(graph) ## for simple plotting
plot(as(a1, "graphNEL"))
``` 

Once you obtain the adjacency matrices, it is for now up to you to convert
them into appropriate posets or fitnessEffects objects.



Why this function? I searched for, and could not find any that did what I
wanted, in particular bounding the number of parents, being able to
specify the approximate depth^[Where depth is defined in the usual
  way to mean smallest number of nodes ---or edges--- to traverse to get
  from the bottom to the top of the DAG.] of the graph, and optionally
being able to have DAGs where no node is connected to another both
directly (an edge between the two) and indirectly (there is a path between
the two through other nodes). So I wrote my own code. The code is fairly
simple to understand (all in file `generate-random-trees.R`). I
would not be surprised if this way of generating random graphs has been
proposed and named before; please let me know, best if with a reference.


Should we remove direct connections if there are indirect? Or, should we
set `removeDirectIndirect = TRUE`? Except for @Farahani2013,
none of the DAGs I've seen in the context of CBNs, oncogenetic trees, etc,
include both direct and indirect connections between nodes. If these
exist, reasoning about the model can be harder. For example, with CBN (AND
or CMPN or monotone relationships) adding a direct connection makes no
difference iff we assume that the relationships encoded in the DAG are
fully respected (e.g., all $s_h = -\infty$). But it can make a difference
if we allow for deviations from the monotonicity, specially if we only
check for the satisfaction of the presence of the immediate ancestors. And
things get even trickier if we combine XOR with AND. The code for
computing fitness, however, should deal with all of this just fine.





# Session info and packages used

This is the information about the version of R and packages used:
```{r}
sessionInfo()
``` 

# Funding

Supported by BFU2015-67302-R (MINECO/FEDER, EU).

```{r, echo=FALSE, eval=TRUE}
## reinitialize the seed
set.seed(NULL)
``` 

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