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2 changes: 1 addition & 1 deletion chapter3_bmintro.html
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Expand Up @@ -83,7 +83,7 @@ <h3 id="section-3.3a-brownian-motion-under-genetic-drift">Section 3.3a: Brownian
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<p>Note that this equation already matches the first property of Brownian motion.</p>
<p>Next, we need to also consider the variance of these mean phenotypes, which we will call the between-population phenotypic variance (<span class="math inline"><em>σ</em><sub><em>B</em></sub><sup>2</sup></span>). Importantly, <span class="math inline"><em>σ</em><sub><em>B</em></sub><sup>2</sup></span> is the same quantity we earlier described as the “variance” of traits over time – that is, the variance of mean trait values across many independent “runs” of evolutionary change over a certain time period.</p>
<p>To calculate <span class="math inline"><em>σ</em><sub><em>B</em></sub><sup>2</sup></span>, we need to consider variation within our model populations. Because of our simplifying assumptions, we can focus solely on additive genetic variance within each population at some time <span class="math inline"><em>t</em></span>, which we can denote as <span class="math inline"><em>σ</em><sub><em>a</em></sub><sup>2</sup></span>. Additive genetic variance measures the total amount of genetic variation that acts additively (i.e. the contributions of each allele add together to predict the final phenotype). This excludes genetic variation involving interacions between alleles, such as dominance and epistasis <span class="citation">(see Lynch and Walsh <a href="#ref-Lynch1998-em">1998</a> for a more detailed discussion)</span>. Additive genetic variance in a population will change over time due to genetic drift (which tends to decrease <span class="math inline"><em>σ</em><sub><em>a</em></sub><sup>2</sup></span>) and mutational input (which tends to increase <span class="math inline"><em>σ</em><sub><em>a</em></sub><sup>2</sup></span>). We can model the expected value of <span class="math inline"><em>σ</em><sub><em>a</em></sub><sup>2</sup></span> from one generation to the next as <span class="citation">(Clayton and Robertson <a href="#ref-Clayton1955-vd">1955</a>; Lande <a href="#ref-Lande1979-em">1979</a>, <a href="#ref-Lande1980-yn">1980</a>)</span>:</p>
<p>To calculate <span class="math inline"><em>σ</em><sub><em>B</em></sub><sup>2</sup></span>, we need to consider variation within our model populations. Because of our simplifying assumptions, we can focus solely on additive genetic variance within each population at some time <span class="math inline"><em>t</em></span>, which we can denote as <span class="math inline"><em>σ</em><sub><em>a</em></sub><sup>2</sup></span>. Additive genetic variance measures the total amount of genetic variation that acts additively (i.e. the contributions of each allele add together to predict the final phenotype). This excludes genetic variation involving interactions between alleles, such as dominance and epistasis <span class="citation">(see Lynch and Walsh <a href="#ref-Lynch1998-em">1998</a> for a more detailed discussion)</span>. Additive genetic variance in a population will change over time due to genetic drift (which tends to decrease <span class="math inline"><em>σ</em><sub><em>a</em></sub><sup>2</sup></span>) and mutational input (which tends to increase <span class="math inline"><em>σ</em><sub><em>a</em></sub><sup>2</sup></span>). We can model the expected value of <span class="math inline"><em>σ</em><sub><em>a</em></sub><sup>2</sup></span> from one generation to the next as <span class="citation">(Clayton and Robertson <a href="#ref-Clayton1955-vd">1955</a>; Lande <a href="#ref-Lande1979-em">1979</a>, <a href="#ref-Lande1980-yn">1980</a>)</span>:</p>
(eq. 3.2)
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<p><br /><span class="math display">$$
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