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<!DOCTYPE html>
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<meta charset="utf-8">
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<h1 id="estipop">ESTIpop</h1>
<p>ESTIpop is an R-wrapped C++ package to simulate and estimate the parameters of continuous-time Markov branching processes with time-dependent rates.</p>
<h2 id="installation-notes">Installation Notes</h2>
<h3 id="dependencies">Dependencies</h3>
<ul>
<li><a href="https://www.gnu.org/software/gsl/">GNU Scientific Library</a>
<ul>
<li>(OSX) brew install gsl with Homebrew or from <a href="http://ftpmirror.gnu.org/gsl/">(http://ftpmirror.gnu.org/gsl/)</a>.</li>
<li>(Windows) download and extract the file <a href="http://www.stats.ox.ac.uk/pub/Rtools/goodies/multilib/">local###.zip</a> and create an environmental variable LIB_GSL to add the directory (see notes about Windows installation below for more details).</li>
<li>(Linux) install libgsl0-dev and gsl-bin.</li>
</ul></li>
<li><a href="https://cran.r-project.org/bin/windows/Rtools/">Rtools</a> (Windows only)</li>
<li><a href="https://github.com/hadley/devtools">devtools</a></li>
</ul>
<h3 id="important-notes-about-windows-installation">Important notes about Windows installation</h3>
<p>Rtools contains the necessary resources to compile C++ files when installing packages in R. GSL is also required which can be downloaded from <a href="http://www.stats.ox.ac.uk/pub/Rtools/goodies/multilib/local323.zip">(http://www.stats.ox.ac.uk/pub/Rtools/goodies/multilib/local323.zip)</a>. After downloading, unzip to your R directory. Depending on if your computer is 32 or 64-bit, move the library files from local###/lib/i386 (32-bit) or local###/lib/x64 (64-bit) to local###/lib.</p>
<p>To set the environmental variable LIB_GSL on a Windows 7/10 computer, go to “Advanced system settings” in Control Panel > System and Security > System and click Environmental Variables. Create a new system variable with</p>
<ul>
<li>Variable Name: LIB_GSL</li>
<li>Variable Value: “C:/path/to/local323” (include quotes)</li>
</ul>
<h3 id="recommended-r-packages">Recommended R packages</h3>
<ul>
<li>ggplot2</li>
<li>R.utils</li>
</ul>
<h3 id="installation">Installation</h3>
<p>To install in R, type:</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb1-1" data-line-number="1"><span class="kw">install.packages</span>(<span class="st">"devtools"</span>)</a>
<a class="sourceLine" id="cb1-2" data-line-number="2">devtools<span class="op">::</span><span class="kw">install_git</span>(<span class="st">"https://github.com/Michorlab/estipop.git"</span>)</a></code></pre></div>
<h2 id="uses">Uses</h2>
<h3 id="estimation">Estimation</h3>
<p>ESTIpop is an R package that estimates the parameters of continuous-time Markov branching processes (CTMBPs) with constant or time-dependent rates. A CTMBP is a stochastic process in which individuals live for a random amount of time before generating some number of offspring, each of which continues the process. Individuals can belong to one of a finite number of types. Each type has its own continuous lifetime distribution, as well a distirbution that governs the number and types of offspring it produces. The process is Markov because an individual’s remaining lifetime is independent of the individual’s age. However, the rates at which individuals die and reproduce can still vary with time, analogous to the nature of arrivals in a time-inhomogenous Poisson process.</p>
<h3 id="simulation">Simulation</h3>
<p>ESTIpop also provides methods to simulate continuous-time Markov branching processes. Simulated processes can have arbitrary numbers of types and transitions, and may have rates which are constant or time-dependent.</p>
<h2 id="objects-in-estipop">Objects in ESTIPop</h2>
<p>ESTIpop uses a common representation of branching process models for simluation and estimation. A branching process model is represented by a <code>process_model</code> object containing one or more <code>transition</code> objects, and each <code>transition</code> object is associated with a <code>rate</code> object.</p>
<h3 id="rate-objects">rate Objects</h3>
<p>A <code>rate</code> object represents the rate at which some event occurs, and may be a function of time and multiple other parameters. The constructor <code>rate(exp)</code> takes an R expression which describes how the rate depends on time and other parameters. For example:</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" data-line-number="1">r1 =<span class="st"> </span><span class="kw">rate</span>(<span class="fl">3.5</span>) <span class="co"># a constant, known rate</span></a>
<a class="sourceLine" id="cb2-2" data-line-number="2">r2 =<span class="st"> </span><span class="kw">rate</span>(<span class="dv">2</span><span class="op">*</span>t) <span class="co"># a rate which increases linearly with time</span></a>
<a class="sourceLine" id="cb2-3" data-line-number="3">r3 =<span class="st"> </span><span class="kw">rate</span>(<span class="fl">1.5</span><span class="op">*</span>params[<span class="dv">1</span>]) <span class="co">#a rate which depends on one unknown parameter</span></a>
<a class="sourceLine" id="cb2-4" data-line-number="4">r4 =<span class="st"> </span><span class="kw">rate</span>(params[<span class="dv">1</span>] <span class="op">+</span><span class="st"> </span>params[<span class="dv">2</span>]<span class="op">*</span><span class="kw">exp</span>(<span class="op">-</span>.<span class="dv">5</span><span class="op">*</span>t)) <span class="co"># a rate which depends on 2 unknown </span></a>
<a class="sourceLine" id="cb2-5" data-line-number="5"> <span class="co"># parameters and time</span></a></code></pre></div>
<p>It is important to note that the variable <code>t</code> and the <code>params</code> vector are not variables which we have defined previously in the program. The <code>rate</code> constructor acts on an <em>expression</em> which encodes how the rate evolves with time and various other parameters. We will be able to evaluate this expression later when we plug in parameter values at a specific time.</p>
<p>The <code>rate</code> constructor expects expressions which conform to the following subset of the R grammar, and will throw an error at other inputs.</p>
<table>
<thead>
<tr class="header">
<th>Type</th>
<th>Allowed Symbols</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td>Unary Operators</td>
<td>+ - ()</td>
</tr>
<tr class="even">
<td>Binary Operators</td>
<td>+ - / * > >= < <=</td>
</tr>
<tr class="odd">
<td>Functions</td>
<td>sin(), cos(), log(), exp()</td>
</tr>
<tr class="even">
<td>names</td>
<td>params[i], t</td>
</tr>
<tr class="odd">
<td>numerics</td>
<td>any scalar numeric value</td>
</tr>
</tbody>
</table>
<h3 id="transition-objects">transition Objects</h3>
<p>A <code>transition</code> object represents a type of birth or death event which can occur in the branching process model. A <code>transition</code> object has 3 attibutes:</p>
<ol>
<li><code>parent</code>: The type of the parent which dies and is removed from the population when the transition occurs</li>
<li><code>offspring</code>: The number of each type of offspring which are produced in the transition. This should be an <code>d</code>-length vector where <code>d</code> is the number of types in the population.</li>
<li><code>rate</code>: A <code>rate</code> object (described above) governing how quickly this transition occurs</li>
</ol>
<p>A <code>transition</code> object can be constructed as follows:</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb3-1" data-line-number="1">r =<span class="st"> </span><span class="kw">rate</span>(.<span class="dv">5</span><span class="op">*</span>params[<span class="dv">1</span>] <span class="op">+</span><span class="st"> </span>params[<span class="dv">2</span>]<span class="op">*</span><span class="kw">exp</span>(<span class="op">-</span>t))</a>
<a class="sourceLine" id="cb3-2" data-line-number="2"><span class="co">#a type 2 parent dies and produces 2 offspring of different types</span></a>
<a class="sourceLine" id="cb3-3" data-line-number="3">trans =<span class="st"> </span><span class="kw">transition</span>(<span class="dt">rate =</span> r, <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> (<span class="dv">2</span>,<span class="dv">0</span>)) </a></code></pre></div>
<p>This transition is illustrated in the following figure:</p>
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" alt="transition" /></p>
<h2 id="process_model-objects">process_model Objects</h2>
<p>A <code>process_model</code> object is a collection of <code>transition</code> objects which together make up a branching process system. A <code>process_model</code> object is constructed from a sequence of <code>transition</code> objects which can occur in the system. All of the <code>transition</code> objects must assume the same number of types, and the <code>process_model</code> constructor will throw an error if this is not the case.</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb4-1" data-line-number="1"><span class="co">#simple one-type birth death model with rates that decay exponentially over time</span></a>
<a class="sourceLine" id="cb4-2" data-line-number="2">birth =<span class="st"> </span><span class="kw">rate</span>(params[<span class="dv">1</span>]<span class="op">*</span><span class="kw">exp</span>(<span class="op">-</span>params[<span class="dv">3</span>]<span class="op">*</span>t))</a>
<a class="sourceLine" id="cb4-3" data-line-number="3">death =<span class="st"> </span><span class="kw">rate</span>(params[<span class="dv">2</span>]<span class="op">*</span><span class="kw">exp</span>(<span class="op">-</span>params[<span class="dv">3</span>]<span class="op">*</span>t))</a>
<a class="sourceLine" id="cb4-4" data-line-number="4">model =<span class="st"> </span><span class="kw">process_model</span>(<span class="kw">transition</span>(<span class="dt">rate =</span> birth, <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="dv">2</span>),</a>
<a class="sourceLine" id="cb4-5" data-line-number="5"> <span class="kw">transition</span>(<span class="dt">rate =</span> death, <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="dv">0</span>))</a></code></pre></div>
<p>Note that <code>model</code> still retains all of the time- and parameter-dependence of its constituent transitions. Also notice that, since <code>params[3]</code> was used in both the birth and death rate, this model has the constraint that birth and death rates decay at equal speed.</p>
<h2 id="simulation-1">Simulation</h2>
<p>Armed with a <code>process_model</code> object, ESTIpop allows for the simulation of this system under various parameters values. ESTIpop uses C++ for high-performance simulation. In the case of time-dependent rates, ESTIpop parses the expressions and translates them into dynamically loaded C++ code.</p>
<p>The <code>branch</code> function is used to simulate the system specified by a <code>process_model</code> object. It’s parameters are as follows:</p>
<table>
<thead>
<tr class="header">
<th>Argument</th>
<th>Type</th>
<th>Description</th>
<th>Optional?</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><code>model</code></td>
<td><code>process_model</code> object</td>
<td>The system to simulate</td>
<td>No</td>
</tr>
<tr class="even">
<td><code>params</code></td>
<td>numeric vector</td>
<td>The parameters to plug into the system during simulation</td>
<td>No</td>
</tr>
<tr class="odd">
<td><code>init_pop</code></td>
<td>numeric vector</td>
<td>The population at the start of the simulation (time 0)</td>
<td>No</td>
</tr>
<tr class="even">
<td><code>time_obs</code></td>
<td>numeric vector</td>
<td>The timepoints at which to record the state of the population</td>
<td>No</td>
</tr>
<tr class="odd">
<td><code>reps</code></td>
<td>numeric scalar</td>
<td>The number of times to run the simulation</td>
<td>No</td>
</tr>
<tr class="even">
<td><code>silent</code></td>
<td>logical</td>
<td>Whether to silence intermediate printouts form the C++ simulator</td>
<td>Yes</td>
</tr>
<tr class="odd">
<td><code>keep</code></td>
<td>logical</td>
<td>Whether to keep logs files from the C++ simulation</td>
<td>Yes</td>
</tr>
<tr class="even">
<td><code>seed</code></td>
<td>logical</td>
<td>A seed for the random number generator</td>
<td>Yes</td>
</tr>
</tbody>
</table>
<p>The following examples demonstrate ESTIPop’s simulation features:</p>
<h3 id="one-type-birth-death-process">One-Type Birth-Death Process</h3>
<p>We’ll start by simulation the one-type birth-death model shown in the following figure. In this model, a population of a single type experiences birth events, in which an individual from the population is chosen to replicate, and death events, in which an individual from the population is chosen for removal. To test our estimation procedure, we begin by simulating data using functions available in ESTIpop. We initiate the population with size 100 and allow it expand for 5 units of time with birth parameter 1 and death parameter 0.7. Using the following code, we generate 1,000 samples from this process.</p>
<p><img 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" alt="birthdeath" /></p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb5-1" data-line-number="1"><span class="kw">library</span>(estipop)</a>
<a class="sourceLine" id="cb5-2" data-line-number="2"></a>
<a class="sourceLine" id="cb5-3" data-line-number="3"><span class="co">#Create a one-type birth-death model where the birth rate increases over time</span></a>
<a class="sourceLine" id="cb5-4" data-line-number="4">model =<span class="st"> </span><span class="kw">process_model</span>(<span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">1</span>] <span class="op">-</span><span class="st"> </span>params[<span class="dv">2</span>]<span class="op">*</span><span class="kw">exp</span>(<span class="op">-</span>params[<span class="dv">3</span>]<span class="op">*</span>t)), </a>
<a class="sourceLine" id="cb5-5" data-line-number="5"> <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="dv">2</span>),</a>
<a class="sourceLine" id="cb5-6" data-line-number="6"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">4</span>]), <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="dv">0</span>))</a>
<a class="sourceLine" id="cb5-7" data-line-number="7"></a>
<a class="sourceLine" id="cb5-8" data-line-number="8"><span class="co">#Specify the time points at which we will record the state of the simulation</span></a>
<a class="sourceLine" id="cb5-9" data-line-number="9">time =<span class="st"> </span><span class="kw">seq</span>(<span class="dv">0</span>,<span class="dv">20</span>,.<span class="dv">5</span>)</a>
<a class="sourceLine" id="cb5-10" data-line-number="10"></a>
<a class="sourceLine" id="cb5-11" data-line-number="11"><span class="co">#The initial size of the simulated population</span></a>
<a class="sourceLine" id="cb5-12" data-line-number="12">init_pop =<span class="st"> </span><span class="kw">c</span>(<span class="dv">500</span>)</a>
<a class="sourceLine" id="cb5-13" data-line-number="13"></a>
<a class="sourceLine" id="cb5-14" data-line-number="14"><span class="co">#Parameters to plug into the model for this simulation run</span></a>
<a class="sourceLine" id="cb5-15" data-line-number="15">params =<span class="st"> </span><span class="kw">c</span>(.<span class="dv">3</span>,.<span class="dv">25</span>,.<span class="dv">1</span>, <span class="fl">.2</span>) </a>
<a class="sourceLine" id="cb5-16" data-line-number="16"></a>
<a class="sourceLine" id="cb5-17" data-line-number="17"><span class="co">#Numer of times to run the simulation</span></a>
<a class="sourceLine" id="cb5-18" data-line-number="18">reps <-<span class="st"> </span><span class="dv">1000</span></a>
<a class="sourceLine" id="cb5-19" data-line-number="19"></a>
<a class="sourceLine" id="cb5-20" data-line-number="20">res =<span class="st"> </span><span class="kw">branch</span>(<span class="dt">model =</span> model, <span class="dt">params =</span> params, <span class="dt">init_pop =</span> init_pop, </a>
<a class="sourceLine" id="cb5-21" data-line-number="21"> <span class="dt">time_obs =</span> time, <span class="dt">reps =</span> reps)</a>
<a class="sourceLine" id="cb5-22" data-line-number="22"></a>
<a class="sourceLine" id="cb5-23" data-line-number="23"><span class="co">#Plot a single replication of the simulation</span></a>
<a class="sourceLine" id="cb5-24" data-line-number="24">single <-<span class="st"> </span>dplyr<span class="op">::</span><span class="kw">filter</span>(res, rep <span class="op">==</span><span class="st"> </span><span class="dv">1</span>)</a>
<a class="sourceLine" id="cb5-25" data-line-number="25"><span class="kw">plot</span>(single<span class="op">$</span>time, single<span class="op">$</span>type1, <span class="dt">xlab =</span> <span class="st">"time"</span>, <span class="dt">ylab =</span> <span class="st">"population size"</span>)</a></code></pre></div>
<p><img 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" /><!-- --></p>
<p><code>res</code> now contains a dataframe with the result of the simulation. We can now analyze the results of the simulation.</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb6-1" data-line-number="1">res <-<span class="st"> </span>dplyr<span class="op">::</span><span class="kw">filter</span>(res, time <span class="op">==</span><span class="st"> </span><span class="dv">20</span>) <span class="co">#just take the last timepoint</span></a>
<a class="sourceLine" id="cb6-2" data-line-number="2"><span class="co">#compute the theoretical moments of the population distribution</span></a>
<a class="sourceLine" id="cb6-3" data-line-number="3">mom <-<span class="st"> </span><span class="kw">compute_mu_sigma</span>(model, params, <span class="dv">0</span>, <span class="dv">20</span>, init_pop)</a>
<a class="sourceLine" id="cb6-4" data-line-number="4"></a>
<a class="sourceLine" id="cb6-5" data-line-number="5"><span class="kw">print</span>(<span class="kw">paste</span>(<span class="st">"Sample Mean: "</span>, <span class="kw">mean</span>(res<span class="op">$</span>type1)))</a></code></pre></div>
<pre><code>## [1] "Sample Mean: 426.535"
</code></pre>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb8-1" data-line-number="1"><span class="kw">print</span>(<span class="kw">paste</span>(<span class="st">"True Mean: "</span>, mom<span class="op">$</span>mu))</a></code></pre></div>
<pre><code>## [1] "True Mean: 425.364259883693"
</code></pre>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb10-1" data-line-number="1"><span class="kw">print</span>(<span class="kw">paste</span>(<span class="st">"Sample Variance: "</span>, <span class="kw">var</span>(res<span class="op">$</span>type1)))</a></code></pre></div>
<pre><code>## [1] "Sample Variance: 4502.39116616617"
</code></pre>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb12-1" data-line-number="1"><span class="kw">print</span>(<span class="kw">paste</span>(<span class="st">"True Variance: "</span>, mom<span class="op">$</span>Sigma))</a></code></pre></div>
<pre><code>## [1] "True Variance: 4386.38004944714"
</code></pre>
<h3 id="two-type-birth-death-mutation-process">Two-Type Birth-Death-Mutation Process</h3>
<p>We now consider the two-type process shown in the following figure. Here, each of the two population types has separate birth and death rates, as well a mutation rate from the type 1 population to the type 2 population. We’ll again simulate 1000 examples and compare the results with the theoretical moments.</p>
<p><img src="data:image/png;base64,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" alt="bdm" /></p>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb14-1" data-line-number="1"><span class="kw">library</span>(estipop)</a>
<a class="sourceLine" id="cb14-2" data-line-number="2"></a>
<a class="sourceLine" id="cb14-3" data-line-number="3">time =<span class="st"> </span><span class="dv">5</span></a>
<a class="sourceLine" id="cb14-4" data-line-number="4">init_pop=<span class="st"> </span><span class="kw">c</span>(<span class="dv">100</span>, <span class="dv">0</span>)</a>
<a class="sourceLine" id="cb14-5" data-line-number="5"></a>
<a class="sourceLine" id="cb14-6" data-line-number="6">params =<span class="st"> </span><span class="kw">c</span>(.<span class="dv">4</span>,.<span class="dv">1</span>,.<span class="dv">7</span>,.<span class="dv">1</span>, <span class="fl">.3</span>)</a>
<a class="sourceLine" id="cb14-7" data-line-number="7"></a>
<a class="sourceLine" id="cb14-8" data-line-number="8"><span class="co">#time-homogenous two-type model</span></a>
<a class="sourceLine" id="cb14-9" data-line-number="9">model =<span class="st"> </span><span class="kw">process_model</span>(<span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">1</span>]), <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">2</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb14-10" data-line-number="10"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">2</span>]), <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb14-11" data-line-number="11"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">3</span>]), <span class="dt">parent =</span> <span class="dv">2</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">2</span>)),</a>
<a class="sourceLine" id="cb14-12" data-line-number="12"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">4</span>]), <span class="dt">parent =</span> <span class="dv">2</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb14-13" data-line-number="13"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">5</span>]), <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">1</span>)))</a>
<a class="sourceLine" id="cb14-14" data-line-number="14"></a>
<a class="sourceLine" id="cb14-15" data-line-number="15">res =<span class="st"> </span><span class="kw">branch</span>(model, params, init_pop, time, <span class="dv">1000</span>)</a></code></pre></div>
<p>Now we analyze the simulation results and compare them with theory</p>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb15-1" data-line-number="1">mom =<span class="st"> </span><span class="kw">compute_mu_sigma</span>(model, params, <span class="dv">0</span>, <span class="dv">5</span>, init_pop)</a>
<a class="sourceLine" id="cb15-2" data-line-number="2"><span class="kw">print</span>(<span class="kw">paste</span>(<span class="st">"Sample Mean: "</span>, <span class="kw">toString</span>(<span class="kw">c</span>(<span class="kw">mean</span>(res<span class="op">$</span>type1), <span class="kw">mean</span>(res<span class="op">$</span>type2)))))</a></code></pre></div>
<pre><code>## [1] "Sample Mean: 448.151, 1571.425"
</code></pre>
<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb17-1" data-line-number="1"><span class="kw">print</span>(<span class="kw">paste</span>(<span class="st">"True Mean: "</span>, <span class="kw">toString</span>(mom<span class="op">$</span>mu)))</a></code></pre></div>
<pre><code>## [1] "True Mean: 448.168943658686, 1560.38542784701"
</code></pre>
<div class="sourceCode" id="cb19"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb19-1" data-line-number="1"><span class="kw">print</span>(<span class="kw">paste</span>(<span class="st">"Sample Variance: "</span>, <span class="kw">toString</span>(<span class="kw">c</span>(<span class="kw">var</span>(res<span class="op">$</span>type1), <span class="kw">var</span>(res<span class="op">$</span>type2)))))</a></code></pre></div>
<pre><code>## [1] "Sample Variance: 2756.96316216216, 41241.8542292292"
</code></pre>
<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb21-1" data-line-number="1"><span class="kw">print</span>(<span class="kw">paste</span>(<span class="st">"Sample Covariance:"</span>, <span class="kw">cov</span>(res<span class="op">$</span>type1, res<span class="op">$</span>type2)))</a></code></pre></div>
<pre><code>## [1] "Sample Covariance: 4801.0769019019"
</code></pre>
<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb23-1" data-line-number="1"><span class="kw">print</span>(<span class="kw">paste</span>(<span class="st">"True Variance: "</span>, <span class="kw">toString</span>(<span class="kw">diag</span>(mom<span class="op">$</span>Sigma))))</a></code></pre></div>
<pre><code>## [1] "True Variance: 2600.64200784677, 39457.2214316809"
</code></pre>
<div class="sourceCode" id="cb25"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb25-1" data-line-number="1"><span class="kw">print</span>(<span class="kw">paste</span>(<span class="st">"True Covariance: "</span>, <span class="kw">toString</span>(mom<span class="op">$</span>Sigma[<span class="dv">1</span>,<span class="dv">2</span>])))</a></code></pre></div>
<pre><code>## [1] "True Covariance: 4527.31533883025"
</code></pre>
<h2 id="estimation-1">Estimation</h2>
<p>Given <code>process_model</code> object and a set of datapoints generated from that model, ESTIpop can estimate the model’s unknown parameter values.</p>
<p>The <code>estimate</code> and <code>estimate_td</code> functions are used to estimate the parameters of <code>process_model</code> object. The arguments these function as as follows:</p>
<table>
<thead>
<tr class="header">
<th>Argument</th>
<th>Type</th>
<th>Description</th>
</tr>
</thead>
<tbody>
<tr class="odd">
<td><code>model</code></td>
<td><code>process_model</code> object</td>
<td>The system whose parameters are being estimated</td>
</tr>
<tr class="even">
<td><code>init_pop</code></td>
<td><code>N</code> x <code>d</code> matrix</td>
<td>The initial population in each of the observations in the dataset</td>
</tr>
<tr class="odd">
<td><code>final_pop</code></td>
<td><code>N</code> x <code>d</code> matrix</td>
<td>The final observed population in each observation</td>
</tr>
<tr class="even">
<td><code>start_times</code></td>
<td><code>N</code> x 1 vector</td>
<td>The time at which each entry in <code>init_pop</code> was observed</td>
</tr>
<tr class="odd">
<td><code>end_times</code></td>
<td><code>N</code> x 1 vector</td>
<td>The time at which each entry in <code>final_pop</code> was observed</td>
</tr>
<tr class="even">
<td><code>initial_ params</code></td>
<td><code>m</code> x 1 vector</td>
<td>The parameter values at which to initialize the estimation procedure</td>
</tr>
<tr class="odd">
<td><code>lower</code></td>
<td><code>m</code> x 1 vector</td>
<td>Lower bounds on each parameter to be estimated</td>
</tr>
<tr class="even">
<td><code>upper</code></td>
<td><code>m</code> x 1 vector</td>
<td>Uppose bounds on each parameter to be estimated</td>
</tr>
<tr class="odd">
<td><code>trace</code></td>
<td>logical</td>
<td>Whether to enable output during optimization</td>
</tr>
</tbody>
</table>
<p>The <code>estimate</code> function is a wrapper for the <code>estimate_td</code> function. <code>estimate</code> only requires the elapsed time between the initial and final obervations of each entry in the dataset, rather then the exact times of each observation. <code>estimate</code> can be used when the rates of a model do not depend on time.</p>
<p>The following examples demonstrate ESTIPop’s estimation features:</p>
<h3 id="time-dependent-one-type-model">Time-dependent one-type model</h3>
<p>We now return to the one-type time-dependent model explored in the simulation section. In this model the birth rate declines as an unknown exponential function while the death rate remains constant. This could represent the dynamics of a population recovering from a drug for which we want to estimate a pharmacokinetic model. First we will simulate the model, this time with far fewer replications:</p>
<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb27-1" data-line-number="1"><span class="kw">library</span>(estipop)</a>
<a class="sourceLine" id="cb27-2" data-line-number="2"></a>
<a class="sourceLine" id="cb27-3" data-line-number="3"><span class="co">#Create a one-type birth-death model where the birth rate increases over time</span></a>
<a class="sourceLine" id="cb27-4" data-line-number="4">model =<span class="st"> </span><span class="kw">process_model</span>(<span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">1</span>] <span class="op">-</span><span class="st"> </span>params[<span class="dv">2</span>]<span class="op">*</span><span class="kw">exp</span>(<span class="op">-</span>params[<span class="dv">3</span>]<span class="op">*</span>t)), </a>
<a class="sourceLine" id="cb27-5" data-line-number="5"> <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="dv">2</span>),</a>
<a class="sourceLine" id="cb27-6" data-line-number="6"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">4</span>]), <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="dv">0</span>))</a>
<a class="sourceLine" id="cb27-7" data-line-number="7"></a>
<a class="sourceLine" id="cb27-8" data-line-number="8"><span class="co">#Specify the time points at which we will record the state of the simulation</span></a>
<a class="sourceLine" id="cb27-9" data-line-number="9">time =<span class="st"> </span><span class="kw">seq</span>(<span class="dv">0</span>,<span class="dv">20</span>,<span class="dv">1</span>)</a>
<a class="sourceLine" id="cb27-10" data-line-number="10"></a>
<a class="sourceLine" id="cb27-11" data-line-number="11"><span class="co">#The initial size of the simulated population</span></a>
<a class="sourceLine" id="cb27-12" data-line-number="12">init_pop =<span class="st"> </span><span class="kw">c</span>(<span class="dv">500</span>)</a>
<a class="sourceLine" id="cb27-13" data-line-number="13"></a>
<a class="sourceLine" id="cb27-14" data-line-number="14"><span class="co">#Parameters to plug into the model for this simulation run</span></a>
<a class="sourceLine" id="cb27-15" data-line-number="15">params =<span class="st"> </span><span class="kw">c</span>(.<span class="dv">3</span>,.<span class="dv">25</span>,.<span class="dv">1</span>, <span class="fl">.2</span>) </a>
<a class="sourceLine" id="cb27-16" data-line-number="16"></a>
<a class="sourceLine" id="cb27-17" data-line-number="17"><span class="co">#Numer of times to run the simulation</span></a>
<a class="sourceLine" id="cb27-18" data-line-number="18">reps <-<span class="st"> </span><span class="dv">20</span></a>
<a class="sourceLine" id="cb27-19" data-line-number="19"></a>
<a class="sourceLine" id="cb27-20" data-line-number="20">res =<span class="st"> </span><span class="kw">branch</span>(<span class="dt">model =</span> model, <span class="dt">params =</span> params, <span class="dt">init_pop =</span> init_pop, </a>
<a class="sourceLine" id="cb27-21" data-line-number="21"> <span class="dt">time_obs =</span> time, <span class="dt">reps =</span> reps)</a>
<a class="sourceLine" id="cb27-22" data-line-number="22">simdat <-<span class="st"> </span><span class="kw">format_sim_data</span>(res, <span class="dt">ntypes =</span> <span class="dv">1</span>)</a></code></pre></div>
<p>The last line converts the dataset into the format expected by our estimation functions. Note that, because the process is Markov, we can compute the likelihood of the entire dataset by computing the likelihood of each observation conditioned on the previous observation. We now estimate the parameters of the model:</p>
<div class="sourceCode" id="cb28"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb28-1" data-line-number="1">est =<span class="st"> </span><span class="kw">estimate_td</span>(model, <span class="dt">init_pop =</span> simdat<span class="op">$</span>type1_prev, </a>
<a class="sourceLine" id="cb28-2" data-line-number="2"> <span class="dt">final_pop =</span>simdat<span class="op">$</span>type1,</a>
<a class="sourceLine" id="cb28-3" data-line-number="3"> <span class="dt">start_times =</span> simdat<span class="op">$</span>prev_time, </a>
<a class="sourceLine" id="cb28-4" data-line-number="4"> <span class="dt">end_times =</span> simdat<span class="op">$</span>time,</a>
<a class="sourceLine" id="cb28-5" data-line-number="5"> <span class="dt">initial =</span> <span class="kw">runif</span>(<span class="dv">4</span>,<span class="dv">0</span>,.<span class="dv">5</span>), </a>
<a class="sourceLine" id="cb28-6" data-line-number="6"> <span class="dt">lower =</span> <span class="kw">rep</span>(<span class="dv">0</span>,<span class="dv">4</span>),</a>
<a class="sourceLine" id="cb28-7" data-line-number="7"> <span class="dt">upper =</span> <span class="kw">rep</span>(.<span class="dv">5</span>,<span class="dv">4</span>),</a>
<a class="sourceLine" id="cb28-8" data-line-number="8"> <span class="dt">method =</span> <span class="st">"L-BFGS-B"</span>)</a></code></pre></div>
<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb29-1" data-line-number="1"><span class="kw">print</span>(est<span class="op">$</span>par)</a></code></pre></div>
<pre><code>## [1] 0.2632411 0.2414000 0.1098404 0.1774179
</code></pre>
<p>After estimation we recover parameter values very close to ground truth.</p>
<h3 id="time-homogenous-birth-death-mutation-model">Time-homogenous birth-death-mutation model</h3>
<p>We’ll now estimate the parameters of the two-type birth-death-mutation model we simulated earlier.</p>
<div class="sourceCode" id="cb31"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb31-1" data-line-number="1">time =<span class="st"> </span><span class="kw">seq</span>(<span class="dv">0</span>,<span class="dv">10</span>,<span class="dv">1</span>) </a>
<a class="sourceLine" id="cb31-2" data-line-number="2">initial =<span class="st"> </span><span class="kw">c</span>(<span class="dv">100</span>, <span class="dv">0</span>)</a>
<a class="sourceLine" id="cb31-3" data-line-number="3"></a>
<a class="sourceLine" id="cb31-4" data-line-number="4">params =<span class="st"> </span><span class="kw">c</span>(.<span class="dv">4</span>,.<span class="dv">1</span>,.<span class="dv">7</span>,.<span class="dv">1</span>, <span class="fl">.3</span>)</a>
<a class="sourceLine" id="cb31-5" data-line-number="5"></a>
<a class="sourceLine" id="cb31-6" data-line-number="6">model =<span class="st"> </span><span class="kw">process_model</span>(<span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">1</span>]), <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">2</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb31-7" data-line-number="7"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">2</span>]), <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb31-8" data-line-number="8"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">3</span>]), <span class="dt">parent =</span> <span class="dv">2</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">2</span>)),</a>
<a class="sourceLine" id="cb31-9" data-line-number="9"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">4</span>]), <span class="dt">parent =</span> <span class="dv">2</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb31-10" data-line-number="10"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">5</span>]), <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">1</span>)))</a>
<a class="sourceLine" id="cb31-11" data-line-number="11"></a>
<a class="sourceLine" id="cb31-12" data-line-number="12"></a>
<a class="sourceLine" id="cb31-13" data-line-number="13"></a>
<a class="sourceLine" id="cb31-14" data-line-number="14">res =<span class="st"> </span><span class="kw">branch</span>(model, params, initial, time, <span class="dv">30</span>)</a>
<a class="sourceLine" id="cb31-15" data-line-number="15">simdata =<span class="st"> </span><span class="kw">format_sim_data</span>(res, model<span class="op">$</span>ntypes)</a>
<a class="sourceLine" id="cb31-16" data-line-number="16">est =<span class="st"> </span><span class="kw">estimate</span>(model, <span class="dt">init_pop =</span> <span class="kw">cbind</span>(simdata<span class="op">$</span>type1_prev, simdata<span class="op">$</span>type2_prev), </a>
<a class="sourceLine" id="cb31-17" data-line-number="17"> <span class="dt">final_pop =</span> <span class="kw">cbind</span>(simdata<span class="op">$</span>type1, simdata<span class="op">$</span>type2),</a>
<a class="sourceLine" id="cb31-18" data-line-number="18"> <span class="dt">times =</span> simdata<span class="op">$</span>dtime,</a>
<a class="sourceLine" id="cb31-19" data-line-number="19"> <span class="dt">initial =</span> <span class="kw">runif</span>(<span class="dv">5</span>,<span class="dv">0</span>,.<span class="dv">5</span>),</a>
<a class="sourceLine" id="cb31-20" data-line-number="20"> <span class="dt">lower =</span> <span class="kw">rep</span>(<span class="fl">1e-5</span>,<span class="dv">5</span>),</a>
<a class="sourceLine" id="cb31-21" data-line-number="21"> <span class="dt">upper =</span> <span class="kw">rep</span>(<span class="dv">1</span>,<span class="dv">5</span>),</a>
<a class="sourceLine" id="cb31-22" data-line-number="22"> <span class="dt">method =</span> <span class="st">"L-BFGS-B"</span>)</a></code></pre></div>
<div class="sourceCode" id="cb32"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb32-1" data-line-number="1"><span class="kw">print</span>(est<span class="op">$</span>par)</a></code></pre></div>
<pre><code>## [1] 0.4084356 0.1097101 0.6591385 0.0601875 0.3050673
</code></pre>
<p>Once again we estimate values close to ground truth.</p>
<h3 id="two-type-drug-resistance-model-(four-types)">Two-Type Drug Resistance Model (Four Types)</h3>
<p>The two-type drug resistance model is a four-type process in which two types of mutation are possible. The type 0 population harbors no mutations, the type 1 population harbors mutation 1, the type 2 population harbors mutation 2, and the type 12 population harbors both mutations 1 and 2. Each type undergoes birth and death events, as well as the possibility for further mutation as illustrated in the following figure.</p>
<p><img 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" alt="twotype" /></p>
<p>We now simulate and estimate this model. To reduce the number of parameters, we assume that all types share the same death rate.</p>
<div class="sourceCode" id="cb34"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb34-1" data-line-number="1">time =<span class="st"> </span><span class="kw">seq</span>(<span class="dv">0</span>,<span class="dv">10</span>,<span class="dv">1</span>) </a>
<a class="sourceLine" id="cb34-2" data-line-number="2">initial =<span class="st"> </span><span class="kw">c</span>(<span class="dv">100</span>, <span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">0</span>)</a>
<a class="sourceLine" id="cb34-3" data-line-number="3"></a>
<a class="sourceLine" id="cb34-4" data-line-number="4">params =<span class="st"> </span><span class="kw">c</span>(.<span class="dv">4</span>,.<span class="dv">7</span>,.<span class="dv">5</span>,.<span class="dv">2</span>,.<span class="dv">3</span>,.<span class="dv">1</span>,.<span class="dv">4</span>,.<span class="dv">3</span>, <span class="fl">.3</span>)</a>
<a class="sourceLine" id="cb34-5" data-line-number="5"></a>
<a class="sourceLine" id="cb34-6" data-line-number="6">model =<span class="st"> </span><span class="kw">process_model</span>(</a>
<a class="sourceLine" id="cb34-7" data-line-number="7"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">1</span>]), <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">2</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb34-8" data-line-number="8"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">2</span>]), <span class="dt">parent =</span> <span class="dv">2</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">2</span>,<span class="dv">0</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb34-9" data-line-number="9"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">3</span>]), <span class="dt">parent =</span> <span class="dv">3</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">2</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb34-10" data-line-number="10"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">4</span>]), <span class="dt">parent =</span> <span class="dv">4</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">2</span>)),</a>
<a class="sourceLine" id="cb34-11" data-line-number="11"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">5</span>]), <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb34-12" data-line-number="12"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">6</span>]), <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb34-13" data-line-number="13"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">7</span>]), <span class="dt">parent =</span> <span class="dv">2</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">0</span>,<span class="dv">1</span>)),</a>
<a class="sourceLine" id="cb34-14" data-line-number="14"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">8</span>]), <span class="dt">parent =</span> <span class="dv">3</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">1</span>)),</a>
<a class="sourceLine" id="cb34-15" data-line-number="15"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">9</span>]), <span class="dt">parent =</span> <span class="dv">1</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb34-16" data-line-number="16"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">9</span>]), <span class="dt">parent =</span> <span class="dv">2</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb34-17" data-line-number="17"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">9</span>]), <span class="dt">parent =</span> <span class="dv">3</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">0</span>)),</a>
<a class="sourceLine" id="cb34-18" data-line-number="18"> <span class="kw">transition</span>(<span class="dt">rate =</span> <span class="kw">rate</span>(params[<span class="dv">9</span>]), <span class="dt">parent =</span> <span class="dv">4</span>, <span class="dt">offspring =</span> <span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">0</span>,<span class="dv">0</span>)))</a>
<a class="sourceLine" id="cb34-19" data-line-number="19"></a>
<a class="sourceLine" id="cb34-20" data-line-number="20"></a>
<a class="sourceLine" id="cb34-21" data-line-number="21">res =<span class="st"> </span><span class="kw">branch</span>(model, params, initial, time, <span class="dv">30</span>)</a>
<a class="sourceLine" id="cb34-22" data-line-number="22">simdata =<span class="st"> </span><span class="kw">format_sim_data</span>(res, model<span class="op">$</span>ntypes)</a>
<a class="sourceLine" id="cb34-23" data-line-number="23">init_pop =<span class="st"> </span><span class="kw">cbind</span>(simdata<span class="op">$</span>type1_prev, simdata<span class="op">$</span>type2_prev,</a>