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mmosmond · Oct 21, 2015 · 86d56aa · 86d56aa
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diff --git a/Makefile b/Makefile
@@ -18,4 +18,4 @@ popgen_notes.pdf: popgen_notes.tex
 	latexmk $<
 
 html/%.html: %.tex
-	(cat template.tex; cat $<; echo "\\\\end{document}") | pandoc -s --mathjax --smart --to html5 --from latex > $@
+	(cat template.tex; cat $<; echo "\\\\end{document}") | pandoc -s --mathjax --toc --css css/style.css --smart --to html5 --from latex > $@
diff --git a/html/chapter-01.html b/html/chapter-01.html
@@ -9,9 +9,22 @@
   <!--[if lt IE 9]>
     <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script>
   <![endif]-->
+  <link rel="stylesheet" href="css/style.css">
   <script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>
 </head>
 <body>
+<nav id="TOC">
+<ul>
+<li><a href="#allele-and-genotype-frequencies">Allele and genotype frequencies</a><ul>
+<li><a href="#allele-frequencies">Allele frequencies</a></li>
+<li><a href="#hardyweinberg-proportions">Hardy–Weinberg proportions</a></li>
+<li><a href="#coefficient-of-kinship">Coefficient of kinship</a></li>
+<li><a href="#inbreeding">Inbreeding</a></li>
+<li><a href="#calculating-inbreeding-coefficients-from-data">Calculating inbreeding coefficients from data</a></li>
+<li><a href="#summarizing-population-structure">Summarizing population structure</a></li>
+</ul></li>
+</ul>
+</nav>
 <h1 id="allele-and-genotype-frequencies">Allele and genotype frequencies</h1>
 <h2 id="allele-frequencies">Allele frequencies</h2>
 <p>Consider a diploid autosomal locus segregating at two alleles (<span class="math inline">\(A_1\)</span> and <span class="math inline">\(A_2\)</span>). Let <span class="math inline">\(N_{11}\)</span> and <span class="math inline">\(N_{12}\)</span> be the number of <span class="math inline">\(A_1A_1\)</span> homozygotes and <span class="math inline">\(A_1A_2\)</span> heterozygotes, respectively. Moreover, let <span class="math inline">\(N\)</span> be the total number of diploid individuals in the population. We can then define the relative frequencies of <span class="math inline">\(A_1A_1\)</span> and <span class="math inline">\(A_1A_2\)</span> genotypes as <span class="math inline">\(f_{11} = N_{11}/N\)</span> and <span class="math inline">\(f_{12} = N_{12}/N\)</span>, respectively. The frequency of allele <span class="math inline">\(A_1\)</span> in the population is then given by <span class="math display">\[p = \frac{2 N_{11} + N_{12}}{2N} = f_{11} + \frac{1}{2} f_{12}. \]</span> Note that this holds independently of Hardy–Weinberg proportions and equilibrium [see below]. The frequency of the alternate allele (<span class="math inline">\(A_2\)</span>) is then just <span class="math inline">\(q=1-p\)</span>.</p>

diff --git a/html/chapter-02.html b/html/chapter-02.html
@@ -9,9 +9,24 @@
   <!--[if lt IE 9]>
     <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script>
   <![endif]-->
+  <link rel="stylesheet" href="css/style.css">
   <script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>
 </head>
 <body>
+<nav id="TOC">
+<ul>
+<li><a href="#genetic-drift-and-neutral-diversity">Genetic Drift and Neutral Diversity</a><ul>
+<li><a href="#LossofHet">Loss of heterozygosity due to drift.</a></li>
+<li><a href="#DriftMutationBalance">Levels of diversity maintained by a balance between mutation and drift</a></li>
+<li><a href="#the-effective-population-size.">The effective population size.</a></li>
+<li><a href="#neutral-diversity-and-population-structure">Neutral diversity and population structure</a></li>
+<li><a href="#other-approaches-to-population-structure">Other approaches to population structure</a><ul>
+<li><a href="#assignment-methods">Assignment Methods</a></li>
+<li><a href="#principal-components-analysis">Principal components analysis</a></li>
+</ul></li>
+</ul></li>
+</ul>
+</nav>
 <h1 id="genetic-drift-and-neutral-diversity">Genetic Drift and Neutral Diversity</h1>
 <p>Various sources of randomness are inherent in evolution. One major source of stochasticity in population genetics is genetic drift. Genetic drift occurs because more or less copies of an allele by chance can be transmitted to the next generation. This can occur because by chance the individuals carrying a particular allele can leave more or less offspring in the next generation. In a sexual population genetic drift also occurs because mendelian transmission means that only one of the two alleles in an individual, chosen at random at a locus, is transmitted to the offspring.</p>
 <p>Genetic drift can play a role in the dynamics of all alleles and populations, but it will play the biggest role for neutral alleles. A neutral polymorphism occurs when the segregating alleles at a polymorphic site have no discernable effect on the fitness (we’ll make clear what we mean by discernable later, for the moment think of this as “no effect” on fitness).</p>

diff --git a/html/chapter-03.html b/html/chapter-03.html
@@ -9,9 +9,15 @@
   <!--[if lt IE 9]>
     <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script>
   <![endif]-->
+  <link rel="stylesheet" href="css/style.css">
   <script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>
 </head>
 <body>
+<nav id="TOC">
+<ul>
+<li><a href="#correlations-between-loci-linkage-disequilibrium-and-recombination">Correlations between loci, linkage disequilibrium, and recombination</a></li>
+</ul>
+</nav>
 <h1 id="correlations-between-loci-linkage-disequilibrium-and-recombination">Correlations between loci, linkage disequilibrium, and recombination</h1>
 <p>Up to now we have been interested in correlations between alleles at the same locus, e.g. correlations within individuals (inbreeding) or between individuals (relatedness). We have seen how relatedness between parents affects the extent to which their offspring is inbred. We now turn to correlations between alleles at different loci. To understand correlations between loci we need to understand recombination.<br />
 </p>

diff --git a/html/chapter-04.html b/html/chapter-04.html
@@ -9,9 +9,19 @@
   <!--[if lt IE 9]>
     <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script>
   <![endif]-->
+  <link rel="stylesheet" href="css/style.css">
   <script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>
 </head>
 <body>
+<nav id="TOC">
+<ul>
+<li><a href="#the-phenotypic-resemblance-between-relatives">The phenotypic resemblance between relatives</a><ul>
+<li><a href="#additive-genetic-variance-and-heritability">Additive genetic variance and heritability</a></li>
+<li><a href="#the-covariance-between-relatives">The covariance between relatives</a></li>
+<li><a href="#the-response-to-selection">The response to selection</a></li>
+</ul></li>
+</ul>
+</nav>
 <h1 id="the-phenotypic-resemblance-between-relatives">The phenotypic resemblance between relatives</h1>
 <p>We can use our understanding of the sharing of alleles between relatives to understand the phenotypic resemblance between relatives in quantitative phenotypes. We can then use this to understand the evolutionary change in quantitative phenotypes in response to selection.<br />
 Let’s imagine that the genetic component of the variation in our trait is controlled by <span class="math inline">\(L\)</span> autosomal loci that act in an additive manner. The frequency of allele <span class="math inline">\(1\)</span> at locus <span class="math inline">\(l\)</span> is <span class="math inline">\(p_l\)</span>, with each copy of allele <span class="math inline">\(1\)</span> at this locus increasing your trait value by <span class="math inline">\(a_l\)</span> above the population mean. The phenotype of an individual, let’s call her <span class="math inline">\(i\)</span>, is <span class="math inline">\(X_i\)</span>. Her genotype at SNP <span class="math inline">\(l\)</span>, is <span class="math inline">\(G_{i,l}\)</span>. Here <span class="math inline">\(G_{i,l}=0,~1,\)</span> or <span class="math inline">\(2\)</span> represents the number of copies of allele <span class="math inline">\(1\)</span> she has at this SNP. Her expected phenotype, given her genotype, is then <span class="math display">\[X_{A,i} = \mu + {\mathbb{E}}(X_i | G_{i,1},\cdots,G_{i,L}) = \mu+ \sum_{l=1}^L G_{i,l} a_{l}\]</span> where <span class="math inline">\(\mu\)</span> is the mean phenotype in our population. Now in reality the genetic phenotype is a function of the expression of those alleles in a particular environment. Therefore, we can think of this expected phenotype as being an average across a set of environments that occur in the population.<br />

diff --git a/html/chapter-05.html b/html/chapter-05.html
@@ -9,9 +9,28 @@
   <!--[if lt IE 9]>
     <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script>
   <![endif]-->
+  <link rel="stylesheet" href="css/style.css">
   <script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>
 </head>
 <body>
+<nav id="TOC">
+<ul>
+<li><a href="#one-locus-models-of-selection">One-locus models of selection</a><ul>
+<li><a href="#fitness">Fitness</a></li>
+<li><a href="#haploid-selection-model">Haploid selection model</a></li>
+<li><a href="#diploid-model">Diploid model</a><ul>
+<li><a href="#diploid-directional-selection">Diploid directional selection</a></li>
+<li><a href="#heterozygote-advantage">Heterozygote advantage</a></li>
+</ul></li>
+<li><a href="#mutationselection-balance">Mutation–selection balance</a><ul>
+<li><a href="#inbreeding-depression">Inbreeding depression</a></li>
+</ul></li>
+<li><a href="#migrationselection-balance">Migration–selection balance</a><ul>
+<li><a href="#some-theory-of-the-spatial-distribution-of-allele-frequencies-under-deterministic-models-of-selection">Some theory of the spatial distribution of allele frequencies under deterministic models of selection</a></li>
+</ul></li>
+</ul></li>
+</ul>
+</nav>
 <h1 id="one-locus-models-of-selection">One-locus models of selection</h1>
 <h2 id="fitness">Fitness</h2>
 <p>As we have seen, natural selection occurs when there are differences between individuals in fitness. We may define fitness in various ways. Most commonly, it is defined with respect to the contribution of a phenotype or genotype to the next generation. Differences in fitness can arise at any point during the life cycle. For instance, different genotypes or phenotypes may have different survival probabilities from one stage in their life to the stage of reproduction (viability), or they may differ in the number of offspring produced (fertility), or both. Here, we define the absolute fitness of a genotype as the expected number of offspring of an individual of that genotype.<br />

diff --git a/html/chapter-06.html b/html/chapter-06.html
@@ -9,9 +9,21 @@
   <!--[if lt IE 9]>
     <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script>
   <![endif]-->
+  <link rel="stylesheet" href="css/style.css">
   <script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>
 </head>
 <body>
+<nav id="TOC">
+<ul>
+<li><a href="#stochasticity-and-genetic-drift-in-allele-frequencies">Stochasticity and Genetic Drift in allele frequencies</a><ul>
+<li><a href="#stochastic-loss-of-strongly-selected-alleles">Stochastic loss of strongly selected alleles</a></li>
+<li><a href="#the-interaction-between-genetic-drift-and-weak-selection.">The interaction between genetic drift and weak selection.</a><ul>
+<li><a href="#the-fixation-of-slightly-deleterious-alleles.">The fixation of slightly deleterious alleles.</a></li>
+<li><a href="#Section:fixation_weakly_sel">A Sketch Proof of the probability of fixation of weakly selected alleles</a></li>
+</ul></li>
+</ul></li>
+</ul>
+</nav>
 <h1 id="stochasticity-and-genetic-drift-in-allele-frequencies">Stochasticity and Genetic Drift in allele frequencies</h1>
 <h2 id="stochastic-loss-of-strongly-selected-alleles">Stochastic loss of strongly selected alleles</h2>
 <p>Even strongly selected alleles can be lost from the population when they are sufficiently rare. This is because the number of offspring left by individuals to the next generation is fundamentally stochastic. A selection coefficient of s=<span class="math inline">\(1\%\)</span> is a strong selection coefficient, which can drive an allele through the population in a few hundred generations once the allele is established. However, if individuals have on average a small number of offspring per generation the first individual to carry our allele who has on average <span class="math inline">\(1\%\)</span> more children could easily have zero offspring, leading to the loss of our allele before it ever get a chance to spread.<br />

diff --git a/html/chapter-07.html b/html/chapter-07.html
@@ -9,9 +9,21 @@
   <!--[if lt IE 9]>
     <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script>
   <![endif]-->
+  <link rel="stylesheet" href="css/style.css">
   <script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>
 </head>
 <body>
+<nav id="TOC">
+<ul>
+<li><a href="#genetic-drift-and-neutral-alleles">Genetic drift and Neutral alleles</a><ul>
+<li><a href="#the-fixation-of-neutral-alleles">The fixation of neutral alleles</a></li>
+<li><a href="#the-coalescent-and-patterns-of-neutral-diversity">The Coalescent and patterns of neutral diversity</a></li>
+<li><a href="#the-coalescent-process-of-a-sample-of-alleles.">The coalescent process of a sample of alleles.</a></li>
+<li><a href="#comparing-polymorphism-and-divergence">Comparing polymorphism and divergence</a></li>
+<li><a href="#deviations-from-the-constant-population-model.">Deviations from the constant population model.</a></li>
+</ul></li>
+</ul>
+</nav>
 <h1 id="genetic-drift-and-neutral-alleles">Genetic drift and Neutral alleles</h1>
 <h2 id="the-fixation-of-neutral-alleles">The fixation of neutral alleles</h2>
 <p>It is very unlikely that a rare neutral allele accidentally drifts up to fixation, it is much more likely that such an allele is eventually lost from the population. However, there is a large and constant influx of rare alleles into the population due to mutation, so even if it is very unlikely that an individual allele fixes within the population, some neutral alleles will fix.<br />

diff --git a/html/chapter-08.html b/html/chapter-08.html
@@ -9,9 +9,17 @@
   <!--[if lt IE 9]>
     <script src="http://html5shim.googlecode.com/svn/trunk/html5.js"></script>
   <![endif]-->
+  <link rel="stylesheet" href="css/style.css">
   <script src="https://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML" type="text/javascript"></script>
 </head>
 <body>
+<nav id="TOC">
+<ul>
+<li><a href="#the-effect-of-linked-selection-on-patterns-of-neutral-diversity">The effect of linked selection on patterns of neutral diversity</a><ul>
+<li><a href="#a-simple-recurrent-model-of-selective-sweeps">A simple recurrent model of selective sweeps</a></li>
+</ul></li>
+</ul>
+</nav>
 <h1 id="the-effect-of-linked-selection-on-patterns-of-neutral-diversity">The effect of linked selection on patterns of neutral diversity</h1>
 <p>A newly derived allele with an additive selection coefficient <span class="math inline">\(s\)</span> will take a time <span class="math inline">\(\tau \approx 2\log(2N)/s\)</span> generations to reach to fixation within our population. This short time window offers very little time for recombination between the selected site and linked neutral sites.<br />
 First lets imagine examining variation at a locus fully linked to our selected locus, just after our sweep reached fixation. A pair of neutral alleles sampled at this locus must both trace their ancestral lineages back through to the neutral allele on whose background the selected allele initially arose. As that neutral allele, which existed <span class="math inline">\(\tau\)</span> generations ago is the ancestor of the entire population at this locus. Our individuals who carry the beneficial allele are, from the perspective of these two alleles, exactly like a rapidly expanding population. Therefore, our pair of neutral alleles sampled at our locus will be forced to coalesce <span class="math inline">\(\approx \tau\)</span> generations ago. This is a very short-time scale compared to the average neutral coalescent tie of <span class="math inline">\(2N\)</span> generations of a pair of alleles.<br />

diff --git a/html/css/style.css b/html/css/style.css
@@ -0,0 +1,35 @@
+@import url(https://fonts.googleapis.com/css?family=Alegreya+Sans:400,300);
+
+body {
+  font-family: "Alegreya Sans", Helvatica, sans-serif;
+  width: 60%;
+  margin-left: auto;
+  margin-right: auto;
+}
+
+caption {
+  font-size: 0.8em;
+  font-style: italic;
+  padding: 1em;
+}
+
+table {
+  text-align: center;
+  margin-left:auto; 
+  margin-right:auto;
+  padding: 1.2em;
+  border: 1px solid #ccc;
+  border-collapse: collapse;
+}
+
+tr {
+  border: 1px solid #ccc;
+}
+
+td {
+  padding: 0.8em;
+}
+
+th {
+  padding: 0.5em;
+}