Merge branch 'master' of https://github.com/cooplab/popgen-notes

Chapters/Pheno_var.tex

@@ -352,13 +352,13 @@ \subsection{The covariance between relatives}
    should be $1$, $0.5$, $0.25$, and $0.125$ respectively in good agreement with
    the empirical covariances reported in the title of each graph. The
    data were simulated as described in
- the caption of Figure \ref{fig:QT1}. The blue line shows $x=y$ and the red
+ the caption of Figure \ref{fig:QT1}. The dashed red line shows $x=y$ and the solid blue
 line shows the best fitting linear regression line. \gitcode{https://github.com/cooplab/popgen-notes/blob/master/Rcode/Quant_gen/QT4.R}}\label{fig:Varying_rellys_phenos}
  \end{figure*}
 
 \paragraph{The covariance between identical twins}
 Let's first consider the case of a pair of identical twins, monzygotic
-twins, from two
+(MZ) twins, from two
 unrelated parents. Our pair of twins share their maternal and paternal
 allele identical by descent ($X_{1M}=X_{2M}$ and $X_{1P}=X_{2P}$). As their maternal and
 paternal alleles are not correlated draws from the population,
@@ -474,7 +474,7 @@ \subsection{The covariance between relatives}
  In these figures, we simulate $100$ loci, as described in
  the caption of Figure \ref{fig:QT1}.We simulate the genotypes and
  phenotypes of the two parents, and then simulate the child's genotype
-following mendelian transmission. The blue line shows $x=y$ and the red
+following mendelian transmission. The red line shows $x=y$ and the blue
 line shows the best fitting linear regression
 line. \gitcode{https://github.com/cooplab/popgen-notes/blob/master/Rcode/Quant_gen/QT2.R}
 } \label{fig:midpar}
@@ -588,7 +588,8 @@ \subsection{The covariance between relatives}
 \begin{equation}
 Cov(X_1,X_2) = r_0 \times 0 + r_1 \frac{1}{2}V_A + r_2  V_A =
 2 F_{1,2} V_A  \label{additive_covar_general_rellys}
-\end{equation}\\
+\end{equation}\\ 
+%% Need to define F 1,2 -- EBJ
 So under a simple additive model of the genetic basis of a phenotype,
 to measure the narrow sense heritability we need to measure the
 covariance between pairs of relatives (assuming that we can remove the effect of

Chapters/genetic_drift_pop_structure.tex

@@ -209,8 +209,8 @@ \section{A simple model of migration between an island and the mainland.}
 \end{question}
 
 \section{Incomplete Lineage Sorting}
-Finally we turn to the interaction of 
-Because it can take a long time for an polymorphism to drift up or down in frequency, multiple population splits may occur during the time an allele is still segregating. This can lead to incongruence between the overall population tree and the information about relationships present at
+Finally we turn to the interaction of the coalescent and speciation. %%this is a guess
+Because it can take a long time for a polymorphism to drift up or down in frequency, multiple population splits may occur during the time an allele is still segregating. This can lead to incongruence between the overall population tree and the information about relationships present at
 individual loci. In Figure \ref{fig:NoILS_poly} and \ref{fig:ILS_poly}
 we show a simulation of three populations where the bottom population splits off from the other two first, followed by the subsequent splitting of the the top and the middle populations. We start both simulations with a newly
 introduced red allele being polymorphic in the combined ancestral population. The most likely fate of this allele is that it is
@@ -351,18 +351,18 @@ \section{Incomplete Lineage Sorting}
 \begin{center}
 \includegraphics[width=\textwidth]{figures/Genetic_drift/ILS/ABBA_BABA_coal.pdf}
 \end{center}
-\caption{ In both the left and and right trees ILS has occurred between our single lineages sampled from populations A, B, and C. Imagine that population D is a somewhat distant outgroup
-such that the lineages from A through C (nearly) always coalesce with each other before any coalesce with D. The small dash on the branch indicates the mutation A$\rightarrow$B occurring, giving rise to the
+\caption{ In both the left and and right trees ILS has occurred between our single lineages sampled from populations 1, 2, and 3. Imagine that population 4 is a somewhat distant outgroup
+such that the lineages from 1 through 3 (nearly) always coalesce with each other before any coalesce with 4. The small dash on the branch indicates the mutation A$\rightarrow$B occurring, giving rise to the
 ABBA or BABA mutational pattern shown at the bottom. } \label{fig:ABBA_BABA}
 \end{figure}
 %JRI: here and in text you refer to populations ABCD but figure is labelled ``species'' and 1234. I think ABCD for populations and AB for alleles is confusing. I don't know if you need A/B for alleles. Why not use A1A2 or just 1/2 as you have previously? sure you miss the fun mnemonic, but it's clearer for a novice reader
 
-Take a look at Figure \ref{fig:ABBA_BABA}. In both cases the lineages from A and B fail to coalesce in
+Take a look at Figure \ref{fig:ABBA_BABA}. In both cases the lineages from 1 and 2 fail to coalesce in
 their initial shared ancestral population, and one or the other of them
-coalesces with the lineage from C before they coalesce with each other. Each option is equally
+coalesces with the lineage from 3 before they coalesce with each other. Each option is equally
 likely; therefore the mutational patterns ABBA and BABA are equally likely to occur under ILS.  \sidenote{Here we have to assume no structure in the ancestral population.}
 
-However, if gene flow occurs from population C into population B, in addition to ILS the lineage from B can more recently coalesce with the lineage from C, and so we should see more ABBAs than BABAs. To test for this effect of gene flow, we can sample a sequence from each of our 4 populations and count up the number of sites that show the two mutational patterns consistent with the gene-tree discordance $n_{ABBA}$ and
+However, if gene flow occurs from population 3 into population 2, in addition to ILS the lineage from 2 can more recently coalesce with the lineage from 3, and so we should see more ABBAs than BABAs. To test for this effect of gene flow, we can sample a sequence from each of our 4 populations and count up the number of sites that show the two mutational patterns consistent with the gene-tree discordance $n_{ABBA}$ and
 $n_{BABA}$ and calculate
 \begin{equation}
 \frac{n_{ABBA}-n_{BABA}}{n_{ABBA}+n_{BABA}}
@@ -374,4 +374,4 @@ \section{Incomplete Lineage Sorting}
 
 %% Isolation by distance
 % https://en.wikipedia.org/wiki/Tobler%27s_first_law_of_geography
-%  Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things."
+%  Waldo Tobler, is "everything is related to everything else, but near things are more related than distant things."