/
magic.tex
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magic.tex
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\documentclass[12pt]{article}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage[dvips]{graphicx}
\usepackage{eepic}
\usepackage{xcolor}
\usepackage{wasysym} % \female \male
\usepackage[landscape,pdftex]{geometry}
\usepackage{fancyhdr}
\usepackage{wasysym} % for check symbol
\usepackage[hidelinks]{hyperref}
\DeclareOption{bigsym}{\DeclareSymbolFont{largesymbols}{OMX}{psycm}{m}{n}}
\ProcessOptions
\setlength{\oddsidemargin}{-0.75in}
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\setlength{\topmargin}{-1in}
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\setlength{\rightskip}{0pt plus 1fil} % makes ragged right
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% following: color
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\definecolor{citecolor}{rgb}{0.44,0.44,0.44}
\newcommand{\citesize}{\fontsize{14}{18} \selectfont}
% header/footer layout
\pagestyle{fancy}
\lhead{} \chead{} \rhead{}
\lfoot{} \cfoot{} \rfoot{\color{myyellow} \thepage}
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\renewcommand{\footrulewidth}{0pt}
% font sizes
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\newcommand{\evensmaller}{\fontsize{14}{18} \selectfont}
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\newcommand{\lod}{\text{LOD}}
\newcommand{\bic}{\text{BIC}}
\newcommand{\rss}{\text{RSS}}
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%\renewcommand{\log}{\text{log}}
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\pagecolor{mybgcolor}
\color{mywhite}
\begin{document}
\thispagestyle{empty}
\begin{center}
\titlesize \color{myyellow}
\vspace*{15mm}
{\headsize MAGIC design} \\
{\smallsize \color{myblue} and other topics}
\vspace*{5mm}
\color{mypink}
\rule{10in}{1mm}
\vspace*{20mm}
\smallsize
\color{white}
Karl Broman
\vspace{5mm}
\color{deptcolor}
{\smallersize Biostatistics \& Medical Informatics
University of Wisconsin -- Madison
\vspace{10mm}
\color{myblue}
\tt
\href{http://biostat.wisc.edu/~kbroman}{biostat.wisc.edu/~kbroman} \\
{\color{myblue} \href{http://github.com/kbroman}{github.com/kbroman} \\
\href{http://kbroman.wordpress.com}{kbroman.wordpress.com} \\
\href{http://twitter.com/kwbroman}{@kwbroman} }
}
\end{center}
\newpage
\currentpdfbookmark{CC founders}{CC founders}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
CC founders
\end{minipage}
\vfill
\centerline{\includegraphics[height=5.5in]{Figs/ccmice.png}}
\vfill
\hfill {\citesize \color{citecolor} \href{http://compgen.unc.edu/wp/?page_id=99}{compgen.unc.edu}
\vspace*{5mm}
\newpage
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
MAGIC lines
\end{minipage}
\vspace{20mm}
\centerline{\includegraphics[width=10in]{Figs/valdar_genet2006.png}}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/172/3/1783.full}{Valdar et al., Genetics 172:1783, 2006}}
\vspace*{5mm}
\newpage
\addtocounter{page}{-1}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
MAGIC lines
\end{minipage}
\vspace{20mm}
\centerline{\includegraphics[width=10in]{Figs/valdar_genet2006.png}}
\smallsize \color{myyellow}
\hspace*{52mm} combine \hspace*{35mm} mix \hspace*{52mm} fix
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/172/3/1783.full}{Valdar et al., Genetics 172:1783, 2006}}
\vspace*{5mm}
\newpage
\addtocounter{page}{-1}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
MAGIC lines
\end{minipage}
\vspace{20mm}
\centerline{\includegraphics[width=10in]{Figs/valdar_genet2006.png}}
\smallsize \color{myyellow}
\hspace*{52mm} combine \hspace*{35mm} mix \hspace*{52mm} fix
\smallersize
\color{mywhite}
\vspace{20pt}
\hspace*{6mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
How many? \\[20pt]
\end{minipage}
\hspace{57mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
\end{minipage}
\hspace{18mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
\end{minipage}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/172/3/1783.full}{Valdar et al., Genetics 172:1783, 2006}}
\vspace*{5mm}
\newpage
\addtocounter{page}{-1}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
MAGIC lines
\end{minipage}
\vspace{20mm}
\centerline{\includegraphics[width=10in]{Figs/valdar_genet2006.png}}
\smallsize \color{myyellow}
\hspace*{52mm} combine \hspace*{35mm} mix \hspace*{52mm} fix
\smallersize
\color{mywhite}
\vspace{20pt}
\hspace*{6mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
How many? \\[20pt]
Which?
\end{minipage}
\hspace{57mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
\end{minipage}
\hspace{18mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
\end{minipage}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/172/3/1783.full}{Valdar et al., Genetics 172:1783, 2006}}
\vspace*{5mm}
\newpage
\addtocounter{page}{-1}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
MAGIC lines
\end{minipage}
\vspace{20mm}
\centerline{\includegraphics[width=10in]{Figs/valdar_genet2006.png}}
\smallsize \color{myyellow}
\hspace*{52mm} combine \hspace*{35mm} mix \hspace*{52mm} fix
\smallersize
\color{mywhite}
\vspace{20pt}
\hspace*{6mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
How many? \\[20pt]
Which?
\end{minipage}
\hspace{57mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
How long?
\end{minipage}
\hspace{18mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
\end{minipage}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/172/3/1783.full}{Valdar et al., Genetics 172:1783, 2006}}
\vspace*{5mm}
\newpage
\currentpdfbookmark{MAGIC lines}{MAGIC lines}
\addtocounter{page}{-1}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
MAGIC lines
\end{minipage}
\vspace{20mm}
\centerline{\includegraphics[width=10in]{Figs/valdar_genet2006.png}}
\smallsize \color{myyellow}
\hspace*{52mm} combine \hspace*{35mm} mix \hspace*{52mm} fix
\smallersize
\color{mywhite}
\vspace{20pt}
\hspace*{6mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
How many? \\[20pt]
Which?
\end{minipage}
\hspace{57mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
How long?
\end{minipage}
\hspace{18mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
How?
\end{minipage}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/172/3/1783.full}{Valdar et al., Genetics 172:1783, 2006}}
\vspace*{5mm}
\newpage
\currentpdfbookmark{Collaborative Cross design}{CC}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
But first \dots
\end{minipage}
\vfill
\centerline{\includegraphics{Figs/ri8.pdf}}
\newpage
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
Simulation results
\end{minipage}
\vfill
\centerline{\includegraphics{Figs/rf_by_sim.pdf}}
\vspace{15mm}
\newpage
\currentpdfbookmark{H\&W 1931}{HW1931}
\headsize \color{myyellow}
\hfill
\begin{minipage}{6.55in}
\centering
Haldane \& Waddington 1931
\end{minipage}
\vspace{25mm}
\centerline{\includegraphics[width=8.5in]{Figs/haldane_title.pdf}}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/16/4/357.full}{Haldane \& Waddington, Genetics
16:357, 1931}}
\vspace*{5mm}
\newpage
\headsize \color{myyellow}
\hfill
\begin{minipage}{5.75in}
\centering
Result for selfing
\end{minipage}
\vspace{35mm}
\centerline{\includegraphics[width=8.5in]{Figs/haldane_selfing.png}}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/16/4/357.full}{Haldane \& Waddington, Genetics
16:357, 1931}}
\vspace*{5mm}
\newpage
\headsize \color{myyellow}
\hfill
\begin{minipage}{5.75in}
\centering
Result for sib-mating
\end{minipage}
\vspace{35mm}
\centerline{\includegraphics[width=8.5in]{Figs/haldane_sibmating3.png}}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/16/4/357.full}{Haldane \& Waddington, Genetics
16:357, 1931}}
\vspace*{5mm}
\newpage
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
Simulation results
\end{minipage}
\vfill
\centerline{\includegraphics{Figs/rf_by_sim.pdf}}
\vspace{15mm}
\newpage
\addtocounter{page}{-1}
\currentpdfbookmark{Simulation results}{Simulation results}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
Simulation results
\end{minipage}
\vfill
\centerline{\includegraphics{Figs/rf_by_sim_genformula.pdf}}
\vspace{15mm}
\newpage
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
Non-linear regression
\end{minipage}
\vspace{30mm}
\textsize
{\color{myblue}
\verb| out <- nls(| {\tt \color{mypink} R \verb|~| a*r/(1 + b*r)}\verb|,| \\
\verb| data = data.frame(r=r, R=R),| \\
\verb| start = list(a=4, b=6))| \\
\verb| summary(out)|
}
\newpage
\addtocounter{page}{-1}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
Non-linear regression
\end{minipage}
\vspace{30mm}
\textsize
{\color{myblue}
\verb| out <- nls(| {\tt \color{mypink} R \verb|~| a*r/(1 + b*r)}\verb|,| \\
\verb| data = data.frame(r=r, R=R),| \\
\verb| start = list(a=4, b=6))| \\
\verb| summary(out)|
}
\vspace{15mm}
\color{mywhite}
\verb| | \\
\verb| Estimate Std. Error| \\
\verb| a 7.016 0.011| \\
\verb| b 6.023 0.016|
\newpage
\currentpdfbookmark{Nonlinear regression}{NLR}
\addtocounter{page}{-1}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
Non-linear regression
\end{minipage}
\vspace{30mm}
\textsize
{\color{myblue}
\verb| out <- nls(| {\tt \color{mypink} R \verb|~| a*r/(1 + b*r)}\verb|,| \\
\verb| data = data.frame(r=r, R=R),| \\
\verb| start = list(a=4, b=6))| \\
\verb| summary(out)|
}
\vspace{15mm}
\color{mypink}
\verb| More data | \\
\color{mywhite}
\verb| Estimate Std. Error Estimate Std. Error| \\
\verb| a 7.016 0.011 a 7.003 0.008| \\
\verb| b 6.023 0.016 b 6.005 0.012|
\newpage
\currentpdfbookmark{Simulation results}{Simulation results with formula}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
Simulation results
\end{minipage}
\vfill
\centerline{\includegraphics{Figs/rf_by_sim_moredata.pdf}}
\vspace{15mm}
\newpage
\currentpdfbookmark{Coincidence definition}{Coincidence definition}
\headsize \color{myyellow}
\hfill
\begin{minipage}{5.75in}
\centering
3-point coincidence
\end{minipage}
\vspace*{1cm}
\hfill \begin{minipage}{9in}
\hspace{-0.5in} \includegraphics[height=0.7in]{Figs/threepoints.pdf}
\vspace{1cm}
\color{mywhite} \smallersize
\begin{itemize}
\itemsep24pt
\setlength{\rightskip}{0pt plus 1fil} % makes ragged right
\item $\mathsf{r_{ij}}$ = recombination fraction for interval (i, j)
{\color{myblue} Assume $\mathsf{r_{12} = r_{23} = r}$.}
\item {\color{mypink} Coincidence} = $\mathsf{c = Pr(\text{double
recombinant}) / r^2}$
\hspace{20mm} {\color{myblue} = $\mathsf{Pr(\text{rec'n in 23} \ |
\ \text{rec'n in 12}) /
Pr(\text{rec'n in 23})}$}
\item
No interference { \color{myblue} = 1 }
Positive interference { \color{myblue} $<$ 1 }
Negative interference { \color{myblue} $>$ 1 }
\item Generally {\color{myblue} $\mathsf{c}$} is a function of
{\color{myblue} $\mathsf{r}$}
\end{itemize}
\end{minipage} \hspace{0.25in}
\newpage
\currentpdfbookmark{Coincidence plot}{Coincidence plot}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
Coincidence function
\end{minipage}
\vspace{15mm}
\centerline{\includegraphics{Figs/coincidence_8way.pdf}}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/169/2/1133.full}{Broman, Genetics
169:1133, 2005}}
\vspace*{5mm}
\newpage
\currentpdfbookmark{non-Markov property}{nonMarkov property}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
{\color{mypink} non-}Markov property
\end{minipage}
\vspace{15mm}
\color{myblue} \smallsize
$$ \mathsf{log_2 \left\{ \frac{
Pr(M_3 = A \ | \ M_2 = {\color{mypink} E}, M_1 = x)}{
Pr(M_3 = A \ | \ M_2 = {\color{mypink} E})}\right\}}$$
\centerline{\includegraphics[scale=0.85]{Figs/3pt_markov4.pdf}}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/169/2/1133.full}{Broman, Genetics
169:1133, 2005}}
\vspace*{5mm}
\newpage
\currentpdfbookmark{Coincidence formula}{Coincidence formula}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
Coincidence formula
\end{minipage}
\vspace{5cm}
\supersmall \color{mywhite}
$$ \mathsf{C = \frac{(1+6r)[280 + 1208r - 848r^2 + 5c(7-28r - 368r^2 + 344r^3)
- 2c^2(49 - 324r + 452r^2)r^2 - 16c^3(1-2r)r^4]}{49 (1+12r-12cr^2)
[5+10r-4(2+c)r^2+8cr^3]} }$$
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/175/3/1267.full}{Teuscher \& Broman, Genetics
175:1267, 2007}}
\vspace*{5mm}
\newpage
\currentpdfbookmark{Collaborative Cross design}{CC2}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
The CC again
\end{minipage}
\vfill
\centerline{\includegraphics{Figs/ri8.pdf}}
\newpage
\currentpdfbookmark{Crazy table}{Crazy table}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
Crazy table
\end{minipage}
\vspace{20mm}
\centerline{\colorbox{white}{\includegraphics[width=9in]{Figs/preCC_hap_prob_table.pdf}}}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/190/2/403.full}{Broman, Genetics
190:403, 2012}}
\vspace*{5mm}
\newpage
\currentpdfbookmark{Time to fixation}{Time to fixation}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
Time to fixation
\end{minipage}
\vspace{15mm}
\centerline{\includegraphics{Figs/fixation_time.pdf}}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/190/2/403.full}{Broman, Genetics
190:403, 2012}}
\vspace*{5mm}
\newpage
\currentpdfbookmark{Map expansion}{Map expansion}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
Map expansion
\end{minipage}
\vspace{12mm}
\centerline{\includegraphics{Figs/map_expansion.pdf}}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/190/2/403.full}{Broman, Genetics
190:403, 2012}}
\vspace*{5mm}
\newpage
\currentpdfbookmark{MAGIC lines}{MAGIC lines 2}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
MAGIC lines
\end{minipage}
\vspace{20mm}
\centerline{\includegraphics[width=10in]{Figs/valdar_genet2006.png}}
\smallsize \color{myyellow}
\hspace*{52mm} combine \hspace*{35mm} mix \hspace*{52mm} fix
\smallersize
\color{mywhite}
\vspace{20pt}
\hspace*{6mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
How many? \\[20pt]
Which?
\end{minipage}
\hspace{57mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
How long?
\end{minipage}
\hspace{18mm}
\begin{minipage}[t]{45mm}
\vspace*{0mm}
\centering
How?
\end{minipage}
\vfill
\hfill {\citesize \color{citecolor} \href{http://www.genetics.org/content/172/3/1783.full}{Valdar et al., Genetics 172:1783, 2006}}
\vspace*{5mm}
\newpage
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
MAGIC is magic
\end{minipage}
\vspace{25mm}
\color{mywhite}
\smallsize
\hfill \begin{minipage}{10in}
\begin{itemize}
\itemsep24pt
\item Genetic diversity
\item High-precision mapping
\item Predictable linkage disequilibrium
\item Phenotype replicates to reduce individual variation
\item Pool phenotypes from multiple labs, environments, treatments
\item Genotype once
\color{mybgcolor}
\item Cool name
\end{itemize}
\end{minipage}
\newpage
\addtocounter{page}{-1}
\currentpdfbookmark{MAGIC is magic}{MAGIC is magic}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
MAGIC is magic
\end{minipage}
\vspace{25mm}
\color{mywhite}
\smallsize
\hfill \begin{minipage}{10in}
\begin{itemize}
\itemsep24pt
\item Genetic diversity
\item High-precision mapping
\item Predictable linkage disequilibrium
\item Phenotype replicates to reduce individual variation
\item Pool phenotypes from multiple labs, environments, treatments
\item Genotype once
\color{myblue}
\item Cool name
\end{itemize}
\end{minipage}
\newpage
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
The goal
\end{minipage}
\vspace{25mm}
\color{mywhite}
\smallsize
\hfill \begin{minipage}{9.5in}
Identify QTL
\end{minipage}
\vspace{15mm}
\hfill \begin{minipage}{9in}
\color{myblue}
\begin{itemize}
\itemsep24pt
\item Power
\item Mapping precision
\end{itemize}
\end{minipage}
\newpage
\addtocounter{page}{-1}
\headsize \color{myyellow}
\hfill \begin{minipage}{5.75in}
\centering
The goal
\end{minipage}
\vspace{25mm}
\color{mywhite}
\smallsize
\hfill \begin{minipage}{9.5in}
Identify QT{\color{mypink} G}
\end{minipage}
\vspace{15mm}
\hfill \begin{minipage}{9in}
\color{myblue}
\begin{itemize}
\itemsep24pt
\item Power
\item Mapping precision
\end{itemize}
\end{minipage}