diff --git a/Chapters/Genetic_drift_selection.tex b/Chapters/Genetic_drift_selection.tex index d5c69da..a56b2d7 100644 --- a/Chapters/Genetic_drift_selection.tex +++ b/Chapters/Genetic_drift_selection.tex @@ -364,7 +364,8 @@ \section{The interaction between genetic drift and weak selection.} \begin{equation} p_F(p) = \frac{1-e^{-2Ns p }}{1-e^{-2Ns}} \label{eqn:prob_fixed} \end{equation} -The proof of this result is sketched out below (see Section \ref{Section:fixation_weakly_sel}). A new allele that arrives in the population at frequency $p=1/(2N)$ has a probability of reaching fixation of +The proof of this result is sketched out below (see Section \ref{Section:fixation_weakly_sel}). %%I think a new paragraph needed here, I got confused and thought the next equation related to the proof -- EBJ +A new allele that arrives in the population at frequency $p=1/(2N)$ has a probability of reaching fixation of \begin{equation} p_F \left(\frac{1}{2N} \right) = \frac{1-e^{-s }}{1-e^{-2Ns}} \label{eqn:new_mut_prob_fixed} \end{equation} @@ -383,7 +384,7 @@ \section{The interaction between genetic drift and weak selection.} p_F \left( \frac{1}{2N} \right) \approx \frac{s}{1-e^{-2Ns}} \label{eqn:escape_from_intro} \end{equation} This is greater than our earlier result $p_F=s$ from the branching process -argument (using our additive model of $h=1/2$), increasingly so for smaller $N$. +argument (using our additive model of $h=1/2$), increasingly so for smaller $N$. %Can you link to the section that does this to remind us? -- EBJ Why is this? The reason why is that $p_F$ is really the probability of "never being lost" in an infinitely large population. So to persist indefinitely, the allele has to escape loss permanently, by never being @@ -486,6 +487,7 @@ \section{The interaction between genetic drift and weak selection.} \begin{question} An additive mutation arises that lowers the relative fitness of heterozygotes by $10^{-5}$. What is the probability that this mutation fixes in a diploid population with effective size of $10^4$? What is the probability it fixes in a population of effective size $10^6$? By comparing both to their neutral probability describe the intuition behind this result. \end{question} +%I got turned around by whether s should be a positive or negative number in these examples. You change the equation shown above to take s as a positive number, but in figure 12.7 it's a negative number. A statement clarifying would be helpful -- EBJ \citeauthor{ohta1973slightly} proposed the `nearly-neutral' theory of diff --git a/Chapters/Interaction_selection_mut_mig.tex b/Chapters/Interaction_selection_mut_mig.tex index 165dc62..0ff0025 100644 --- a/Chapters/Interaction_selection_mut_mig.tex +++ b/Chapters/Interaction_selection_mut_mig.tex @@ -215,7 +215,7 @@ \subsection{Inbreeding depression} genotype frequencies follow from HWE. Only considering the fitness effects of this locus, and measuring fitness relative to the most fit genotype, answer the following questions: \\ {\bf A)} What is the average fitness of an individual in the population? \\ {\bf B)} What is the average fitness of the child of a full-sib - mating? \\ + mating? \\ %% I needed a hint to go find the generalized HWE eq for this one!! -- Em \end{question} \begin{figure} \begin{center} @@ -443,7 +443,7 @@ \subsection{Migration--selection balance} allele $2$ has a relative fitness of $1+s$ and $1-s$ on either side of the environmental change at $x=0$. \gitcode{https://github.com/cooplab/popgen-notes/blob/master/Rcode/cline.R}} \label{fig:cline_main} \end{figure} - +%Maya noticed that the colors in this figure are switched -- EBJ With this setup, we get an equilibrium distribution of our two alleles, where to the left of zero our allele $2$ is at higher frequency, while to the right of zero allele $1$ predominates. As we diff --git a/Chapters/Linked_selection.tex b/Chapters/Linked_selection.tex index 0186b38..a31e308 100644 --- a/Chapters/Linked_selection.tex +++ b/Chapters/Linked_selection.tex @@ -52,7 +52,7 @@ \chapter{The Effects of Linked Selection.} \begin{center} \includegraphics[width= 0.75 \textwidth]{figures/Hitchhiking/No_recom_coal.pdf} \end{center} -\caption{The coalescent of 4 lineages, marked in blue, at a locus completed linked to our selected allele. The frequency trajectory of the selected allele $X(t)$ is shown in red.} \label{fig:no_recom_coal} +\caption{The coalescent of 4 lineages, marked in blue, at a locus completly linked to our selected allele. The frequency trajectory of the selected allele $X(t)$ is shown in red.} \label{fig:no_recom_coal} \end{marginfigure} To better understand hitchhiking, first let's imagine examining variation at a locus fully linked to our selected locus, just after our sweep reached fixation. Neutral alleles sampled at this locus @@ -142,7 +142,7 @@ \chapter{The Effects of Linked Selection.} the right coalesce much deeper back in time.} \label{fig:recom_coal} \end{marginfigure} We know that in the present day our neutral lineage is linked to -the selected allele. The probability that our lineage, in some +the selected allele. If $X(t)$ is the allele frequency of the selected allele, the probability that our lineage, in some generation $t$ back in time, is in a heterozygote is $1-X(t)$, and the probability that a recombination occurs in that individual is $r$. So the probability that our neutral lineage is descended from a @@ -156,7 +156,7 @@ \chapter{The Effects of Linked Selection.} $\tau$ generations it takes our selected allele to move through the population is \begin{equation} -p_{NR}=\prod_{t=1}^{\tau} \big(1- r(1-X(j))\big) +p_{NR}=\prod_{t=1}^{\tau} \big(1- r(1-X(t))\big) \end{equation} Assuming that $r$ is small, then $ \left(1- r(1-X(t))\right) \approx e^{-r(1-X(t))}$, such that @@ -201,7 +201,7 @@ \chapter{The Effects of Linked Selection.} \begin{center} \includegraphics[width=\textwidth]{illustration_images/hitchhiking/malaria/Laveran_Malaria_drawings.jpg} \end{center} -\caption[][-0.5cm]{Laveran's 1880 drawing of various stages of {\it Plasmodium +\caption[-0.5cm]{Laveran's 1880 drawing of various stages of {\it Plasmodium falciparum} as seen in fresh blood. The bottom row shows an exflagellating male gametocyte. Laveran identified {\it P. falciparum} as the protozoan pathogen that caused malaria. \wikimedia{\href{Centers for @@ -784,4 +784,4 @@ \subsection{Background selection} %For strongly deleterious alleles, this continuous loss acts primarily -%to increase the variance of at markers closely linked to loci with high deleterious mutation rates \citep{Hudson:95b,Nordborg:96}. Therefore, this background selection model leads to a reduction in genetic diversity but no skew in the frequency spectrum. However, a skew towards rare neutral alleles can result if weakly deleterious mutations are incorporated into the model \citep{Nordborg:96, Gordo:02}. \ No newline at end of file +%to increase the variance of at markers closely linked to loci with high deleterious mutation rates \citep{Hudson:95b,Nordborg:96}. Therefore, this background selection model leads to a reduction in genetic diversity but no skew in the frequency spectrum. However, a skew towards rare neutral alleles can result if weakly deleterious mutations are incorporated into the model \citep{Nordborg:96, Gordo:02}. diff --git a/popgen_notes.pdf b/popgen_notes.pdf index 1abc6c8..745ae38 100644 Binary files a/popgen_notes.pdf and b/popgen_notes.pdf differ