Typo fixes and final corrections.

introduction/introduction.tex

@@ -329,9 +329,9 @@ \subsection{Linkage disequilibrium approach}
 
 LD is measured in a pairwise fashion, considering allele frequencies at each pair of markers in the genome.
 From measurements of LD within a number of unrelated samples, methods based on coalescent theory have been developed to estimate the recombination rate\cite{Auton2012}.
-In software such as LDhat\cite{Mcvean2004,Auton2007,Auton2014}, the population-scale recombination rate, $\rho$, is estimated from the data, and the per-generation recombination rate can be calculated by the relationship
-$\rho = 4 N_e r$
-where $N_e$ represents the effective population size, and $r$ the per-generation recombination rate.
+In software such as LDhat\cite{Mcvean2004,Auton2007,Auton2014}, the population-scale recombination rate, $\rho$, is estimated from the data, and the per-generation recombination rate, $r$, can be calculated by the relationship
+$\rho = 4 N_e r$,
+where $N_e$ represents the effective population size.
 These methods are quite powerful and have produced high-quality estimates of recombination in humans\cite{hapmap2007}, however, they are subject to limitations.
 First, this method requires the knowledge of the genealogical history of a sample, which is unknown, and thus relies on a simplifying approximation to the true genealogical structure.
 Second, these maps by their nature generate sex-averaged data only, since recombination events that are inferred have occurred over the course of potentially thousands of generations.
@@ -939,7 +939,7 @@ \subsubsection{Crossover interference models}
 
 The gamma model is an extension of the counting model, in which inter-crossover distances are modeled instead of counts, which are not observed in inferential studies of interference.
 The gamma model starts with the assumption that all crossovers are capable of interfering with each other, and chromatid interference is neutral.
-The location of chiasmata on a tetrad bundle are determined by a stationary renewal process(*).
+The location of chiasmata on a tetrad bundle are determined by a stationary renewal process.
 Each chiasmata is considered an ``arrival'' that resets the probability controlling the distance from the previous arrival.
 The inter-chiasmata distances are represented by a gamma distribution with a single parameter, $\nu$, representing the strength of interference.
 In this model, $\nu <$ 0 corresponds to negative interference, $\nu=$ 0 no interference, and $\nu>$0 positive interference.
@@ -1092,14 +1092,14 @@ \section{Recombination in non humans}
 the first sign that dog PRDM9 might be missing came with the publication of the first draft sequence of the domestic dog genome, in a boxer, in 2005\cite{Lindblad-Toh2005}.
 Since then a number of studies have looked at dogs and their close relative within the family Canidae to determine when and how PRDM9 became inactivated.
 PRDM9 was found to be disrupted in the closest relative of dogs, wolves, as well as coyotes\cite{Munoz-Fuentes2011}, revealing that inactivation was not a result of domestication, or a limited event.
-Additional studies found multiple PRDM9 mutations in both the Island Fox and Andean Fox\cite{Auton2013}, but not the cat and panda\cite{Axelsson2012}.
+Additional studies found multiple PRDM9 mutations in both the Island Fox and Andean Fox\cite{Auton2013}, but not the cat or panda\cite{Axelsson2012}.
 This indicates that the mutations must have happened at some point after the divergence of canids from the panda, which occurred approximately 49 Mya\cite{Oliver2009,Axelsson2012}.
 Despite the loss of this gene, canids are able to successfully complete meiosis and recombination and produce fertile offspring, raising questions as to the requirement of PRDM9 in meiosis.
 Evidence for hotspots has been found in dogs and these hotspots are characteristically different from those found in humans.
 Dog hotspots appear to have a lowered intensity and occupy a wider range (4-18 kb)\cite{Axelsson2012,Auton2013} when compared to humans.
 Direct comparisons of these results between the two species must be made with care, however, as the LD approach is sensitive to population genetic parameters.
 In particular, an accurate estimate of the recombination rate depends directly on accurate measurements of the effective population size, which is well characterized in humans, but not dogs.
-Additionally, dog hotspot appear to be localized near gene promoter regions\cite{Auton2013}, a seemingly common feature of PRDM9-absent species.
+Additionally, dog hotspots appear to be localized near gene promoter regions\cite{Auton2013}, a seemingly common feature of PRDM9-absent species.
 
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@@ -1436,7 +1436,7 @@ \subsubsection{The Li and Stephens model}
 The key innovation of this model was to consider gene conversion and crossover chains independently and simultaneously:
 \begin{equation} \Pr(X_{j+1}, G_{j+1} | X_{j},G_{j} ) = \Pr(X_{j+1}|X_{j}) \Pr(G_{j+1}|G_{j}) ~. \end{equation}
 %
-These two model will be revisited in Chapter \ref{ch:geneConv}.
+These two models will be revisited in Chapter \ref{ch:geneConv}.
 
 
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main.tex

@@ -221,11 +221,11 @@
 % Using this data, I characterized sex differences in human recombination in detail.
 % , and created sex-specific maps of recombination in the human genome.
 % These results extend previous work showing that females have a higher recombination rate than males, by a ratio of 1.6 in the autosomes, and that male recombination tends to be focused towards the telomeres.
-I find that males and females have different hotspot usage, with males having a higher hotspot overlap proportion than females, by 4.6\%.
+I find that males and females had different hotspot usage, with males having a higher hotspot overlap proportion than females, by 4.6\%.
 I measure crossover interference, which affects the spatial positioning of crossovers, finding that older mothers had a steep increase in crossovers that escape regulation by interference.
-These crossovers appear closely spaced, pointing to a possible deregulation of recombination that increases with age in females.
+These crossovers appear closely spaced, pointing to a possible deregulation of recombination that increases with maternal age.
 
-In Chapter \ref{ch:cointExtras}, I present an extension to Chapter \ref{ch:cointEsc}, which confirms the age effects using samples from older individuals.
+In Chapter \ref{ch:cointExtras}, I present an extension to Chapter \ref{ch:cointEsc}, which confirms the age effect using samples from older individuals.
 I include a re-analysis of public data from single cell sperm and oocytes, showing that interference varies widely on an individual basis.
 
 In Chapter \ref{ch:dogPed}, I focused on crossover patterns using a complex pedigree of inbred domestic dogs, consisting of 408 meioses.
@@ -333,7 +333,7 @@ \chapter{Crossover interference varies by age and individual} \label{ch:cointExt
 \noindent Christopher L Campbell$^1$, Claude Bh\'{e}rer$^{1*,2}$, Bernice E Morrow$^1$, Adam R Boyko$^3$, and Adam Auton$^{1*}$
 
 \vspace{0.5cm}
-\noindent This manuscript has been submitted to \textit{Genetics}. \\
+\noindent This manuscript is currently under review:
 
 \vspace{0.5cm}
 \noindent $^1$ Department of Genetics, Albert Einstein College of Medicine, 1301 Morris Park Avenue, Bronx, New York 10461, USA. \\
@@ -385,7 +385,7 @@ \chapter{Appendix A} \label{ch:appendixCB}
 Christopher L Campbell
 
 \vspace{0.5cm}
-\noindent Results presented within this appendix were extracted from a manuscript currently under review at \textit{Nature Communications}:
+\noindent Results presented within this appendix were extracted from a manuscript currently under review:
 
 \vspace{0.5cm}
 \noindent Refined genetic maps reveal sexual dimorphism in human meiotic recombination at multiple scales. \\