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14 changes: 4 additions & 10 deletions dispersal.Rmd
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Expand Up @@ -4,13 +4,11 @@ WORK IN PROGRESS. **I'm missing a section on gof w/ R2ucare and posterior predic

## Introduction

Blabla.
In this fifth chapter, you will learn about the Arnason-Schwarz model that allows estimating transitions between sites and states based on capture-recapture data. You will also see how to deal with uncertainty in the assignment of states to individuals.

## The Arnason-Schwarz (AS) model

+ Arnason 1972, 1973. Schwarz 1993.

+ Nichols et al. 1992 (microtus and mass as state). Nichols et al. 1994 (microtus and reproductive costs).
In Chapter \@ref(survival), we got acquainted with Cormack-Jolly-Seber (CJS) model which accommodates transitions between the states alive and dead while accounting for imperfect detection. It is often the case that besides being alive, more detailed information is collected on the state of animals when they are detected. For example, if the study area is split into several discrete sites, you may record where an animal is detected, the state being now alive in this particular site. The Arnason-Schwarz (AS) model can be viewed as an extension to the CJS model in which we estimate movements between sites on top of survival. The AS model is named after the two statisticians -- Neil Arnason and Carl Schwarz.

## Multisite capture-recapture data

Expand Down Expand Up @@ -1155,11 +1153,7 @@ Breeders are difficult to assigned to the correct state. Non-breeders are relati

## Suggested reading

+ Lebreton, J.-D., J. D. Nichols, R. J. Barker, R. Pradel and J. A. Spendelow (2009). [Modeling Individual Animal Histories with Multistate Capture–Recapture Models](https://multievent.sciencesconf.org/conference/multievent/pages/Lebretonetal2009AER.pdf). Advances in Ecological Research, 41:87-173.

+ Seminal paper by Pradel (2005) [Multievent: An Extension of Multistate Capture–Recapture Models to Uncertain States](https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1541-0420.2005.00318.x). Biometrics, 61: 442-447.

+ Dupuis (1995) had a similar idea for the Arnason-Schwarz model: Dupuis, J. (1995) [Bayesian estimation of movement and survival probabilities from capture-recapture data](https://academic.oup.com/biomet/article-abstract/82/4/761/252161). Biometrika. Vol. 82, pp 761-772.
+ Sites: Arnason 1972, 1973. Schwarz 1993. States: Nichols et al. 1992 (microtus and mass as state). Nichols et al. 1994 (microtus and reproductive costs). Lebreton, J.-D., J. D. Nichols, R. J. Barker, R. Pradel and J. A. Spendelow (2009). [Modeling Individual Animal Histories with Multistate Capture–Recapture Models](https://multievent.sciencesconf.org/conference/multievent/pages/Lebretonetal2009AER.pdf). Advances in Ecological Research, 41:87-173.

+ See also for a review Gimenez et al. (2012) [Estimating demographic parameters using hidden process dynamic models](https://oliviergimenez.github.io/pubs/Gimenezetal2012TPB.pdf). Theoretical Population Biology 82: 307-316.
+ Uncertainty: Seminal paper by Pradel (2005) [Multievent: An Extension of Multistate Capture–Recapture Models to Uncertain States](https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1541-0420.2005.00318.x). Biometrics, 61: 442-447. Dupuis (1995) had a similar idea for the Arnason-Schwarz model: Dupuis, J. (1995) [Bayesian estimation of movement and survival probabilities from capture-recapture data](https://academic.oup.com/biomet/article-abstract/82/4/761/252161). Biometrika. Vol. 82, pp 761-772. See also for a review Gimenez et al. (2012) [Estimating demographic parameters using hidden process dynamic models](https://oliviergimenez.github.io/pubs/Gimenezetal2012TPB.pdf). Theoretical Population Biology 82: 307-316.

2 changes: 1 addition & 1 deletion docs/404.html
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<li><a class="" href="hmmcapturerecapture.html"><span class="header-section-number">3</span> Hidden Markov models</a></li>
<li class="book-part">II. Transitions</li>
<li><a class="" href="introduction-4.html">Introduction</a></li>
<li><a class="" href="survival.html"><span class="header-section-number">4</span> Live and dead</a></li>
<li><a class="" href="survival.html"><span class="header-section-number">4</span> Alive and dead</a></li>
<li><a class="" href="dispersal.html"><span class="header-section-number">5</span> Sites and states</a></li>
<li class="book-part">III. Case studies</li>
<li><a class="" href="introduction-7.html">Introduction</a></li>
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2 changes: 1 addition & 1 deletion docs/about-the-author.html
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Expand Up @@ -78,7 +78,7 @@ <h1>
<li><a class="" href="hmmcapturerecapture.html"><span class="header-section-number">3</span> Hidden Markov models</a></li>
<li class="book-part">II. Transitions</li>
<li><a class="" href="introduction-4.html">Introduction</a></li>
<li><a class="" href="survival.html"><span class="header-section-number">4</span> Live and dead</a></li>
<li><a class="" href="survival.html"><span class="header-section-number">4</span> Alive and dead</a></li>
<li><a class="" href="dispersal.html"><span class="header-section-number">5</span> Sites and states</a></li>
<li class="book-part">III. Case studies</li>
<li><a class="" href="introduction-7.html">Introduction</a></li>
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2 changes: 1 addition & 1 deletion docs/covariateschapter.html
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Expand Up @@ -78,7 +78,7 @@ <h1>
<li><a class="" href="hmmcapturerecapture.html"><span class="header-section-number">3</span> Hidden Markov models</a></li>
<li class="book-part">II. Transitions</li>
<li><a class="" href="introduction-4.html">Introduction</a></li>
<li><a class="" href="survival.html"><span class="header-section-number">4</span> Live and dead</a></li>
<li><a class="" href="survival.html"><span class="header-section-number">4</span> Alive and dead</a></li>
<li><a class="" href="dispersal.html"><span class="header-section-number">5</span> Sites and states</a></li>
<li class="book-part">III. Case studies</li>
<li><a class="" href="introduction-7.html">Introduction</a></li>
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6 changes: 3 additions & 3 deletions docs/crashcourse.html
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Expand Up @@ -78,7 +78,7 @@ <h1>
<li><a class="" href="hmmcapturerecapture.html"><span class="header-section-number">3</span> Hidden Markov models</a></li>
<li class="book-part">II. Transitions</li>
<li><a class="" href="introduction-4.html">Introduction</a></li>
<li><a class="" href="survival.html"><span class="header-section-number">4</span> Live and dead</a></li>
<li><a class="" href="survival.html"><span class="header-section-number">4</span> Alive and dead</a></li>
<li><a class="" href="dispersal.html"><span class="header-section-number">5</span> Sites and states</a></li>
<li class="book-part">III. Case studies</li>
<li><a class="" href="introduction-7.html">Introduction</a></li>
Expand Down Expand Up @@ -260,7 +260,7 @@ <h3>
<div class="sourceCode" id="cb7"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="va">sample_from_posterior</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/stats/Beta.html">rbeta</a></span><span class="op">(</span><span class="fl">1000</span>, <span class="fl">20</span>, <span class="fl">39</span><span class="op">)</span> <span class="co"># draw 1000 values from posterior survival beta(20,39)</span></span>
<span><span class="fu"><a href="https://rdrr.io/r/base/mean.html">mean</a></span><span class="op">(</span><span class="va">sample_from_posterior</span><span class="op">)</span> <span class="co"># compute mean with Monte Carlo integration</span></span>
<span><span class="co">## [1] 0.3365</span></span></code></pre></div>
<span><span class="co">## [1] 0.3381</span></span></code></pre></div>
<p>You may check that the mean we have just calculated matches closely the expectation of a beta distribution<a class="footnote-ref" tabindex="0" data-toggle="popover" data-content='&lt;p&gt;If &lt;span class="math inline"&gt;\(X\)&lt;/span&gt; is a random variable with distribution &lt;span class="math inline"&gt;\(\text{beta}(a, b)\)&lt;/span&gt;, then &lt;span class="math inline"&gt;\(E(X) = \displaystyle{\frac{a}{a + b}}\)&lt;/span&gt;&lt;/p&gt;'><sup>10</sup></a>:</p>
<div class="sourceCode" id="cb8"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fl">20</span><span class="op">/</span><span class="op">(</span><span class="fl">20</span><span class="op">+</span><span class="fl">39</span><span class="op">)</span> <span class="co"># expectation of beta(20,39)</span></span>
Expand All @@ -269,7 +269,7 @@ <h3>
<div class="sourceCode" id="cb9"><pre class="downlit sourceCode r">
<code class="sourceCode R"><span><span class="fu"><a href="https://rdrr.io/r/stats/quantile.html">quantile</a></span><span class="op">(</span><span class="va">sample_from_posterior</span>, probs <span class="op">=</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html">c</a></span><span class="op">(</span><span class="fl">2.5</span><span class="op">/</span><span class="fl">100</span>, <span class="fl">97.5</span><span class="op">/</span><span class="fl">100</span><span class="op">)</span><span class="op">)</span></span>
<span><span class="co">## 2.5% 97.5% </span></span>
<span><span class="co">## 0.2266 0.4695</span></span></code></pre></div>
<span><span class="co">## 0.2231 0.4687</span></span></code></pre></div>
</div>
<div id="markovmodelmcmc" class="section level3" number="1.5.2">
<h3>
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23 changes: 9 additions & 14 deletions docs/dispersal.html
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Expand Down Expand Up @@ -78,7 +78,7 @@ <h1>
<li><a class="" href="hmmcapturerecapture.html"><span class="header-section-number">3</span> Hidden Markov models</a></li>
<li class="book-part">II. Transitions</li>
<li><a class="" href="introduction-4.html">Introduction</a></li>
<li><a class="" href="survival.html"><span class="header-section-number">4</span> Live and dead</a></li>
<li><a class="" href="survival.html"><span class="header-section-number">4</span> Alive and dead</a></li>
<li><a class="active" href="dispersal.html"><span class="header-section-number">5</span> Sites and states</a></li>
<li class="book-part">III. Case studies</li>
<li><a class="" href="introduction-7.html">Introduction</a></li>
Expand Down Expand Up @@ -106,16 +106,13 @@ <h1>
<h2>
<span class="header-section-number">5.1</span> Introduction<a class="anchor" aria-label="anchor" href="#introduction-6"><i class="fas fa-link"></i></a>
</h2>
<p>Blabla.</p>
<p>In this fifth chapter, you will learn about the Arnason-Schwarz model that allows estimating transitions between sites and states based on capture-recapture data. You will also see how to deal with uncertainty in the assignment of states to individuals.</p>
</div>
<div id="the-arnason-schwarz-as-model" class="section level2" number="5.2">
<h2>
<span class="header-section-number">5.2</span> The Arnason-Schwarz (AS) model<a class="anchor" aria-label="anchor" href="#the-arnason-schwarz-as-model"><i class="fas fa-link"></i></a>
</h2>
<ul>
<li><p>Arnason 1972, 1973. Schwarz 1993.</p></li>
<li><p>Nichols et al. 1992 (microtus and mass as state). Nichols et al. 1994 (microtus and reproductive costs).</p></li>
</ul>
<p>In Chapter <a href="survival.html#survival">4</a>, we got acquainted with Cormack-Jolly-Seber (CJS) model which accommodates transitions between the states alive and dead while accounting for imperfect detection. It is often the case that besides being alive, more detailed information is collected on the state of animals when they are detected. For example, if the study area is split into several discrete sites, you may record where an animal is detected, the state being now alive in this particular site. The Arnason-Schwarz (AS) model can be viewed as an extension to the CJS model in which we estimate movements between sites on top of survival. The AS model is named after the two statisticians – Neil Arnason and Carl Schwarz.</p>
</div>
<div id="multisite-capture-recapture-data" class="section level2" number="5.3">
<h2>
Expand Down Expand Up @@ -35055,18 +35052,16 @@ <h2>
<span class="header-section-number">5.11</span> Suggested reading<a class="anchor" aria-label="anchor" href="#suggested-reading-4"><i class="fas fa-link"></i></a>
</h2>
<ul>
<li><p>Lebreton, J.-D., J. D. Nichols, R. J. Barker, R. Pradel and J. A. Spendelow (2009). <a href="https://multievent.sciencesconf.org/conference/multievent/pages/Lebretonetal2009AER.pdf">Modeling Individual Animal Histories with Multistate Capture–Recapture Models</a>. Advances in Ecological Research, 41:87-173.</p></li>
<li><p>Seminal paper by Pradel (2005) <a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1541-0420.2005.00318.x">Multievent: An Extension of Multistate Capture–Recapture Models to Uncertain States</a>. Biometrics, 61: 442-447.</p></li>
<li><p>Dupuis (1995) had a similar idea for the Arnason-Schwarz model: Dupuis, J. (1995) <a href="https://academic.oup.com/biomet/article-abstract/82/4/761/252161">Bayesian estimation of movement and survival probabilities from capture-recapture data</a>. Biometrika. Vol. 82, pp 761-772.</p></li>
<li><p>See also for a review Gimenez et al. (2012) <a href="https://oliviergimenez.github.io/pubs/Gimenezetal2012TPB.pdf">Estimating demographic parameters using hidden process dynamic models</a>. Theoretical Population Biology 82: 307-316.</p></li>
<li><p>Sites: Arnason 1972, 1973. Schwarz 1993. States: Nichols et al. 1992 (microtus and mass as state). Nichols et al. 1994 (microtus and reproductive costs). Lebreton, J.-D., J. D. Nichols, R. J. Barker, R. Pradel and J. A. Spendelow (2009). <a href="https://multievent.sciencesconf.org/conference/multievent/pages/Lebretonetal2009AER.pdf">Modeling Individual Animal Histories with Multistate Capture–Recapture Models</a>. Advances in Ecological Research, 41:87-173.</p></li>
<li><p>Uncertainty: Seminal paper by Pradel (2005) <a href="https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1541-0420.2005.00318.x">Multievent: An Extension of Multistate Capture–Recapture Models to Uncertain States</a>. Biometrics, 61: 442-447. Dupuis (1995) had a similar idea for the Arnason-Schwarz model: Dupuis, J. (1995) <a href="https://academic.oup.com/biomet/article-abstract/82/4/761/252161">Bayesian estimation of movement and survival probabilities from capture-recapture data</a>. Biometrika. Vol. 82, pp 761-772. See also for a review Gimenez et al. (2012) <a href="https://oliviergimenez.github.io/pubs/Gimenezetal2012TPB.pdf">Estimating demographic parameters using hidden process dynamic models</a>. Theoretical Population Biology 82: 307-316.</p></li>
</ul>
</div>
</div>



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