updates to chapter 1

chapter-01.tex

@@ -2,7 +2,27 @@
 \section{Allele and genotype frequencies}
 
 \subsection{Allele frequencies}
-Consider a diploid autosomal locus segregating at two alleles ($A_1$ and $A_2$). Let $N_{11}$ and $N_{12}$ be the number of $A_1A_1$ homozygotes and $A_1A_2$ heterozygotes, respectively. Moreover, let $N$ be the total number of diploid individuals in the population. We can then define the relative frequencies of $A_1A_1$ and $A_1A_2$ genotypes as $f_{11} = N_{11}/N$ and $f_{12} = N_{12}/N$, respectively. The frequency of allele $A_1$ in the population is then given by
+Loci and alleles are the basic currency of population genetics--and
+indeed of genetics. A locus (the singular of loci) is a specific location on the genome,
+e.g. a particular DNA pair position in a gene. An allele is the genetic
+information (variant) contained at that position, for example an A-T
+base-pair. As DNA base pairs are complementary, it will suffice to say
+that there is an A allele at this locus. All of the individuals in a
+population (or a sample) may carry the same
+genetic information at this locus, in which case we will say that the
+locus is monomorphic. Or individuals may differ in the genetic
+information they carry at a locus, for example there may be an A
+allele and a T allele at our locus. When multiple alleles are present at a locus
+the locus is said to be polymorphic.  In our example some individuals
+will be be
+homozygote for an A
+allele and some homozygote for a T allele, and some heterozygotes
+(A/T). \\
+
+
+Consider a diploid autosomal locus segregating at two alleles ($A_1$
+and $A_2$). We'll use these arbitrary labels for our alleles, merely
+to keep this general.   Let $N_{11}$ and $N_{12}$ be the number of $A_1A_1$ homozygotes and $A_1A_2$ heterozygotes, respectively. Moreover, let $N$ be the total number of diploid individuals in the population. We can then define the relative frequencies of $A_1A_1$ and $A_1A_2$ genotypes as $f_{11} = N_{11}/N$ and $f_{12} = N_{12}/N$, respectively. The frequency of allele $A_1$ in the population is then given by
 \begin{equation}
 p = \frac{2 N_{11} + N_{12}}{2N} = f_{11} + \frac{1}{2} f_{12}. % Modified by Simon
 \end{equation}
@@ -80,7 +100,30 @@ \subsection{Hardy--Weinberg proportions}
 %figure/QT1.eps
 
 
-\subsection{Coefficient of kinship}
+\subsection{Identity by Descent \& The Coefficient of Kinship}
+All of the individuals in a population are related to each other by a giant pedigree (family
+tree). For most pairs of indivdiduals in a population these relationships are very
+distant (i.e. distant cousins). However, some individuals will be 
+more closely related, e.g. sibling/first cousins. 
+Individuals of different levels of relatedness (kinship). Related individuals
+will share alleles.  With closer relatives sharing more alleles. In
+Figure \ref{fig:IBD_cousins_chr_cartoon} we show the sharing of
+chromosomal regions between two cousins.  As we
+are interested in the genetics of populations we are interested in
+kinship, and we need some way to quantify the degree of kinship among individuals.\\ 
+
+\begin{figure}
+\begin{center}
+\includegraphics[width= 0.5 \textwidth]{figures/Cousins_IBD_chromo_cartoon.png}
+\end{center}
+\caption{First cousins sharing a stretch of chromosome identical by
+  descent. The different grandparental diploid chromosomes are coloured so we
+  can track them and recombinations between them across the
+  generations. Notice that the identity by descent between the cousins persists for a long
+stretch of chromosome due to the limited number of generations for
+recombination.} \label{fig:IBD_cousins_chr_cartoon}  
+\end{figure}
+
 We will define two alleles to be identical by descent (IBD) if they are
 identical due to a common ancestor in the past few generations. For
 the moment, we ignore mutation, 
@@ -160,18 +203,6 @@ \subsection{Coefficient of kinship}
 \end{question}
 
 
-\begin{figure}
-\begin{center}
-\includegraphics[width= 0.5 \textwidth]{figures/Cousins_IBD_chromo_cartoon.png}
-\end{center}
-\caption{First cousins sharing a stretch of chromosome identical by
-  descent. The different grandparental diploid chromosomes are coloured so we
-  can track them and recombinations between them across the
-  generations. Notice that the identity by descent between the cousins persists for a long
-stretch of chromosome due to the limited number of generations for
-recombination.} \label{fig:IBD_cousins_chr_cartoon}  
-\end{figure}
-
 
 \subsection{Inbreeding}
 We can define an inbred individual as an individual whose parents are

chapter-02.tex

@@ -674,6 +674,23 @@ \subsection{The fixation of neutral alleles}
 transmissions. Thus the average number of neutral mutational
 differences separating our pair of species is simply $2\mu (1-C) T$.\\
 
+\begin{question}
+For this, and the next question, assume that humans and chimp diverged
+around 5.5$\times 10^6$ years, a generation time ~20 years, that the speciation occurred instantaneously in allopatry with no subsequent gene flow, and the ancestral effective population size of the human and chimp common ancestor population was 10,000 individuals.\\
+Nachman and Crowell sequenced 12 pseudogenes in human and chimp found substitutions at 1.3\% of sites. \\
+{\bf A) } What can you say about the mutation rate per site per generation at these genes, and how does it compare to other estimates of human mutation rate?\\
+{\bf B)} All of the pseudogenes they sequenced are on the autosomes. What
+would you prediction be for pseudogenes on the X and Y chromosomes,
+given that there are fewer rounds of replication in the female
+germline than in the male germline.
+\end{question}
+
+\begin{question}
+The gorilla lineage split from the human-chimp lineage $\sim$7 million years ago. Let’s assume that this speciation event occurred instantaneously in allopatry with no subsequent gene flow. \\
+{\bf A)}	What is the probability of that Gorilla is not an outgroup to human and chimp at a single locus?\\
+{\bf B)}	It has been estimated that the Gorilla lineage is not an outgroup at around ~30\% of autosomal loci. What effective population size would you need to assume to explain this observation? Is that only plausible explanation?\\
+{\bf C)}	The Gorilla lineage is an outgroup for large portions of the X chromosome, what is a plausible explanation for this finding?
+\end{question}
 
 
 \subsection{Neutral diversity and population structure}
@@ -832,6 +849,14 @@ \subsection{Neutral diversity and population structure}
 island. Therefore, considering our island our sub-population we have
 derived another simple model of $F_{ST}$ .
 
-
+\begin{question}
+You are investigating a small river population of sticklebacks, which receives infrequent migrants from a very large marine population. At a set of (putativelyneutral biallelic markers the freshwater population has frequencies:\\
+0.2, 0.7, 0.8\\
+at the same markers the marine population has frequencies:\\
+0.4, 0.5 and 0.7.\\
+ From studying patterns of heterozygosity at a large collection of markers, you have estimated the long term effective size of your freshwater population is 2000 individuals.\\
+What is your estimate of the migration rate from the marine
+populations into the river?
+\end{question}
 \newpage
 

chapter-04.tex

@@ -5,6 +5,7 @@ \section{The phenotypic resemblance between relatives}
 quantitative phenotypes. We can then use this to understand the
 evolutionary change in quantitative phenotypes in response to selection. \\
 
+\subsection{A simple additive model of a trait}
 Let's imagine that the genetic component of the variation in our trait
 is controlled by $L$ autosomal loci that act in an additive manner. The frequency of allele $1$ at locus $l$ is $p_l$, with each copy of
 allele $1$ at this locus increasing your trait value by $a_l$ above
@@ -84,7 +85,7 @@ \section{The phenotypic resemblance between relatives}
 (i.e. the additive effect of the alleles that their genotype consists of).
 
 
-\subsubsection{Additive genetic variance and heritability}
+\subsection{Additive genetic variance and heritability}
 As we are talking about an additive genetic model we'll talk about the
 additive genetic variance ($V_A$), the variance due to the additive
 effects of segregating genetic variation. This is a subset of the total genetic
@@ -144,7 +145,7 @@ \subsubsection{Additive genetic variance and heritability}
 that relatives also share an environment, so may resemble each other
 due to shared environmental effects. \\
 
-\subsubsection{The covariance between relatives}
+\subsection{The covariance between relatives}
 So we'll go ahead and calculate the covariance in phenotype between two individuals
 ($1$ and $2$) who have a phenotype $X_1$ and $X_2$ respectively.
 \begin{equation}
@@ -313,58 +314,8 @@ \subsubsection{The covariance between relatives}
 This is sometimes called the ``animal model'', and also goes by the
 name of variance components analysis.
 
-\paragraph{Multiple traits.}
 
-Traits often covary with each other, due to both environmentally
-induced effects (e.g. due to the effects of diet on multiple traits)
-and due to the expression of underlying genetic covariance between
-traits. In turn this genetic covariance can reflect pleiotropy, a
-mechanistic effect of an allele on multiple traits (e.g. variants that
-effect skin pigmentation often effect hair color) or the genetic
-linkage of loci independently affecting multiple traits. If we are
-interested in evolution over short time-scales we can (often) ignore
-the genetic basis of this correlation. 
-
-Consider two traits $X_{1,i}$ and $X_{2,i}$ in an indivdual $i$, these could be
-say the individual's leg length and nose length. As before we can write
-these as 
-\begin{eqnarray}
-X_{1,i} &= \mu_1+ X_{1,A,i} + X_{1,E,i}  \nonumber \\
-X_{2,i} &= \mu_2 +X_{2,A,i} + X_{2,E,i} \nonumber \\
-\end{eqnarray}
-As before we can talk about the total phenotypic variance ($V_1,V_2$),
-environmental variance  ($V_{1,E}$ and $V_{2,E}$), and the additive genetic variance in trait one and two
-($V_{1,A}$, $V_{2,A}$). But now we also have to consider the 
-total covariance $V_{1,2}=Cov(X_{1},X_{2})$, the environmentally induced covariance between the traits ($V_{E,1,2}=Cov(X_{1,E}
-,X_{2,E} )$) and the additive genetic covariance ($V_{A,1,2}
-=Cov(X_{1,A} ,X_{2,A} )$) between trait one and two.
-
-We can store these values in a matrices 
-\begin{equation}
-\bf{V}= \left( \begin{array}{cc} 
-V_{1} & V_{1,2} \\
-V_{1,2} & V_{2} \\
-\end{array} \right) \label{P_matrix}
-\end{equation}
-and
-\begin{equation}
-\bf{G}= \left( \begin{array}{cc} 
-V_{1,A} & V_{A,1,2} \\
-V_{A,1,2} & V_{2,A} \\
-\end{array} \right)  \label{G_matrix}
-\end{equation}
-we can generalize this to an abitrary number of traits.
-
-We can estimate these quantities, in a similar way to before, by
-studying the covariance in different traits between relatives: 
-
-\begin{equation}
-Cov(X_{1,i},X_{2,j}) = 2 F_{i,j} V_{A,1,2}
-\end{equation}
-
-
-
-\subsubsection{The response to selection}
+\subsection{The response to selection}
 Evolution by natural selection requires:
 \begin{enumerate}
 \item Variation in a phenotype
@@ -521,6 +472,56 @@ \subsubsection{The response to selection}
 
 {\bf C)}	What do you have to assume to perform the calculations in B. Assuming we only have fossils from the founding population and the population after 6000 years, should we assume that the calculations accurately reflect what actually occurred within our population?
 \end{question}
+
+\subsection{Multiple traits.}
+
+Traits often covary with each other, due to both environmentally
+induced effects (e.g. due to the effects of diet on multiple traits)
+and due to the expression of underlying genetic covariance between
+traits. In turn this genetic covariance can reflect pleiotropy, a
+mechanistic effect of an allele on multiple traits (e.g. variants that
+effect skin pigmentation often effect hair color) or the genetic
+linkage of loci independently affecting multiple traits. If we are
+interested in evolution over short time-scales we can (often) ignore
+the genetic basis of this correlation. 
+
+Consider two traits $X_{1,i}$ and $X_{2,i}$ in an indivdual $i$, these could be
+say the individual's leg length and nose length. As before we can write
+these as 
+\begin{eqnarray}
+X_{1,i} &= \mu_1+ X_{1,A,i} + X_{1,E,i}  \nonumber \\
+X_{2,i} &= \mu_2 +X_{2,A,i} + X_{2,E,i} \nonumber \\
+\end{eqnarray}
+As before we can talk about the total phenotypic variance ($V_1,V_2$),
+environmental variance  ($V_{1,E}$ and $V_{2,E}$), and the additive genetic variance in trait one and two
+($V_{1,A}$, $V_{2,A}$). But now we also have to consider the 
+total covariance $V_{1,2}=Cov(X_{1},X_{2})$, the environmentally induced covariance between the traits ($V_{E,1,2}=Cov(X_{1,E}
+,X_{2,E} )$) and the additive genetic covariance ($V_{A,1,2}
+=Cov(X_{1,A} ,X_{2,A} )$) between trait one and two.
+
+We can store these values in a matrices 
+\begin{equation}
+\bf{V}= \left( \begin{array}{cc} 
+V_{1} & V_{1,2} \\
+V_{1,2} & V_{2} \\
+\end{array} \right) \label{P_matrix}
+\end{equation}
+and
+\begin{equation}
+\bf{G}= \left( \begin{array}{cc} 
+V_{1,A} & V_{A,1,2} \\
+V_{A,1,2} & V_{2,A} \\
+\end{array} \right)  \label{G_matrix}
+\end{equation}
+we can generalize this to an abitrary number of traits.
+
+We can estimate these quantities, in a similar way to before, by
+studying the covariance in different traits between relatives: 
+
+\begin{equation}
+Cov(X_{1,i},X_{2,j}) = 2 F_{i,j} V_{A,1,2}
+\end{equation}
+
 \paragraph{The response of multiple traits to selection, the
   multivariate breeder's equation.}
 We can generalize these results for multiple traits, to ask how selection on