Updated pdf

Chapters/One_locus_selection.tex

@@ -545,7 +545,7 @@ \subsection{Diploid model}
 \marginnote{To see this is take
 \begin{align*}
   \frac{d\bar{w}}{dp} &= \frac{d}{dp} \left( W_{11} p^2 + 2 W_{12} p \right. \nonumber\\
-   & \left. - 2 W_{12} p^2 + W_{22} -  2 W_{22} p +  W_{22} p^2\right) \nonumber\\
+   & ~~ \left. - 2 W_{12} p^2 + W_{22} -  2 W_{22} p +  W_{22} p^2\right) \nonumber\\
   &= 2\left(w_{11} p + w_{12} - 2pw_{12} - w_{22} - w_{22} + w_{22} p\right)
 \end{align*}
 On expansion of $\bar{w}_1 - \bar{w}_2$, we see that it matched the terms in
@@ -836,7 +836,9 @@ \subsection{Heterozygote advantage}
 
 
 We can solve for this equilibrium frequency by setting $\Delta p_t = 0$ in  eqn.\ \eqref{deltap_dip2}, 
-i.e.\ $p_tq_t (\wbar_1-\wbar_2)=0$. Doing so, we find that there are three equilibria, all of which are stable. Two of them are not very interesting ($p=0$ or $q=0$), but the third one is the polymorphic equilibrium,  where
+i.e.\ $p_tq_t (\wbar_1-\wbar_2)=0$. Doing so, we find that there are
+three equilibria. Two of them are not very interesting ($p=0$ or
+$q=0$), but the third one is a stable polymorphic equilibrium,  where
 $\wbar_1-\wbar_2=0$ holds.
 Using our $s_1$ and $s_2$ parametrization above, we see that the marginal fitnesses of
 the two alleles are equal when
@@ -1729,8 +1731,8 @@ \subsection{Selfish genetic elements and selection below the level of
 \caption{
 The fate of an unfit transmission distorter allele. If transmission is
 fair ($\alpha =\nicefrac
-{1}{2}$) the allele is lost, but the stronger its drive in
-heterozygotes the fast its spread and the higher its final frequency
+{1}{2}$, blue curve) the allele is lost, but the stronger its drive in
+heterozygotes the faster its spread and the higher its final frequency
 in the population (black and red curves, $\alpha =0.7$ \& $0.9$
 respectively).  With fitnesses $w_{dd}=1$,
 $w_{Dd}=0.95$, and $ w_{DD}=0.1$. The dotted lines show the predicted

Chapters/Pheno_var.tex

@@ -602,7 +602,7 @@ \subsection{Non-additive variation.}
 
 Now consider an autosomal biallelic locus $\ell$, with frequency $p$ for allele 1, and
 genotypes $0$, $1$, and $2$ corresponding to how many copies of allele
-1 individuals carry. We'll denote the mean phenotype of an individual
+$1$ individuals carry. We'll denote the mean phenotype of an individual
 with genotype $0$, $1$, and $2$ as $\overline{X}_{\ell,0}$,
 $\overline{X}_{\ell,1}$, $\overline{X}_{\ell,2}$ respectively. This mean is
 taking an average phenotype over all the environments and genetic backgrounds the alleles
@@ -633,8 +633,8 @@ \subsection{Non-additive variation.}
 %The additive MC genetic values (breeding values) of genotype 0, 1, and
 %2 are then
 
-Let's now consider the average phenotype of an offspring of each of our
-three genotypes
+Let's now consider the average phenotype of an offspring by how many
+copies of the allele $1$ they carry
 \begin{center}
 \begin{tabular}{cccc}
 genotype: & 0, & 1, & 2.\\
@@ -653,10 +653,11 @@ \subsection{Non-additive variation.}
 \begin{center}
 \includegraphics[width=\textwidth]{figures/additive_effect.pdf}
 \end{center}
-\caption{The average mean-centered (MC) phenotypes of each genotype. 
+\caption{The average mean-centered (MC) phenotypes plotted against the
+  number of allele $1$ carried (from $0$ for $22$ to $2$ for $11$). 
 {\bf Top Row:} Additive relationship between genotype and phenotype. 
 {\bf Bottom Row:} Allele 1 is dominant over allele 2, such that the
-heterozygote has the same phenotype as the $22$ genotype ($2$). 
+heterozygote has the same phenotype as the $11$ genotype. 
 The area of each circle is proportion to the fraction of
 the population in each genotypic class ($p^2$, $2pq$, and $q^2$). 
 One the left column $p=0.1$ and the right column is $p=0.9$.
@@ -711,7 +712,17 @@ \subsection{Non-additive variation.}
 \end{marginfigure}
 
 
-As as an example of how dominance and population allele frequencies can change the additive effect of an allele, let's consider the genetics of the age of sexual maturity in Atlantic Salmon. A single allele of large effect segregates in Atlantic Salmon that influences the sexual maturation rate in salmon \citep{ayllon2015vgll3,barson2015sex}, and hence the timing of their return from the sea to spawn (sea age). The allele falls close to the autosomal gene VGLL3 \citep[variation at this gene in humans also influences the timing of puberty]{cousminer2013genome}. The left side of Figure \ref{fig:salmon_add_dom} shows the age at  sexual maturity in males. The allele (E) associated with slower sexual maturity is recessive in males. While the LL homozygotes mature on average a whole year later, the additive effect of the allele is weak while the L allele is rare in the population. The right panel shows the effect of the L allele in females. Note how the allele is much more dominant in females, and has a much more pronounced additive effect. The dominance of an allele is not a fixed property of the allele but rather a statement of the relationship of genotype to phenotype, such that the dominance relationship between alleles may vary across phenotypes and contexts (e.g. sexes). %\erin{there are no black vertical arrows as referred to in the caption for the salmon dominance figure} 
+As as an example of how dominance and population allele frequencies
+can change the additive effect of an allele, let's consider the
+genetics of the age of sexual maturity in Atlantic Salmon. A single
+allele of large effect segregates in Atlantic Salmon that influences
+the sexual maturation rate in salmon
+\citep{ayllon2015vgll3,barson2015sex}, and hence the timing of their
+return from the sea to spawn (sea age). The allele falls close to the
+autosomal gene VGLL3 \citep[variation at this gene in humans also
+influences the timing of puberty]{cousminer2013genome}. The left side
+of Figure \ref{fig:salmon_add_dom} shows the age at  sexual maturity
+in males. The L allele associated with slower sexual maturity is recessive in males. While the LL homozygotes mature on average a whole year later, the additive effect of the allele is weak while the L allele is rare in the population. The right panel shows the effect of the L allele in females. Note how the allele is much more dominant in females, and has a much more pronounced additive effect. The dominance of an allele is not a fixed property of the allele but rather a statement of the relationship of genotype to phenotype, such that the dominance relationship between alleles may vary across phenotypes and contexts (e.g. sexes). %\erin{there are no black vertical arrows as referred to in the caption for the salmon dominance figure}