diff --git a/.gitignore b/.gitignore
index c8fa7e1..2d3080a 100644
--- a/.gitignore
+++ b/.gitignore
@@ -7,5 +7,8 @@
 *.aux
 *.toc
 *.state
+*.nav
+main.out
+*.snm
 legotut.out
 msptut.out
diff --git a/legofit/slides/figEarlyND.tex b/legofit/slides/figEarlyND.tex
new file mode 100644
index 0000000..a44a6a3
--- /dev/null
+++ b/legofit/slides/figEarlyND.tex
@@ -0,0 +1,39 @@
+%auto-ignore
+%-*-latex-*-
+\mbox{\beginpicture
+\headingtoplotskip=\baselineskip
+\setcoordinatesystem units <4mm, 3mm> point at 13 0
+\setplotarea x from 0 to 13, y from 0 to 16
+\axis bottom invisible ticks length <0pt>
+  withvalues {$X$} {$Y$} {$N$} {$D$} /  at 1 5 8 12 / /
+%\axis left ticks andacross numbered from 0 to 16 by 1 /
+%\axis top ticks andacross numbered from 0 to 13 by 1 /
+\plotheading{Early $N$-$D$ split} 
+\setplotsymbol ({\normalsize .})
+\plot 0 0 2 6 / %Xl
+\plot 2 6 5.5 13 / % XYl
+\plot 2 0 3 3 / %Xr
+\plot 4 0 3 3 / %Yl
+\plot 6 0 4 5 / %Yr
+\plot 4 5 6.5 10.5 / %XYr
+\plot 7 0 8 6 9 8 / %Nl
+\plot 9 0 10 6 / %Nr
+\plot 11 0 10 6 / %Dl
+\plot 13 0 12 6 10.5 10 / %Dr
+\plot 9 8 6.5 10.5 / %NDl
+\plot 10.5 10 7.5 13 / %NDr
+\plot 5.5 13 5.5 16 / %XYNDl
+\plot 7.5 13 7.5 16 / %XYNDr
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 1 0 2.5 5 3.33 6 / %x
+\plot 5 0 3.5 4 3.33 6 / %y
+\setplotsymbol ({\textcolor{blue}{\scriptsize .}})
+\plot 3.33 6 6 12 6.5 15 / %xy
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 8 0 9 6 9.4 8.4 9 9.75 / %n
+\plot 12 0 11 6 10 9.3 9 9.75 / %d
+\setplotsymbol ({\textcolor{red}{\scriptsize .}})
+\plot 9 9.75 7 11.75 6.5 15 / %nd
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 6.5 15 6.5 16 / %xynd
+\endpicture}
diff --git a/legofit/slides/figLargeND.tex b/legofit/slides/figLargeND.tex
new file mode 100644
index 0000000..4467ec3
--- /dev/null
+++ b/legofit/slides/figLargeND.tex
@@ -0,0 +1,39 @@
+%auto-ignore
+%-*-latex-*-
+\mbox{\beginpicture
+\headingtoplotskip=\baselineskip
+\setcoordinatesystem units <4mm, 3mm> point at -1 0
+\setplotarea x from 0 to 13, y from 0 to 16
+\axis bottom invisible ticks length <0pt>
+  withvalues {$X$} {$Y$} {$N$} {$D$} /  at 1 5 8 12 / /
+%\axis left ticks andacross numbered from 0 to 16 by 1 /
+%\axis top ticks andacross numbered from 0 to 13 by 1 /
+\plotheading{Large \textit{ND}} 
+\setplotsymbol ({\normalsize .})
+\plot 0 0 2 6 / %Xl
+\plot 2 6 5.5 13 / % XYl
+\plot 2 0 3 3 / %Xr
+\plot 4 0 3 3 / %Yl
+\plot 6 0 4 5 / %Yr
+\plot 4 5 6 9 / %XYr
+\plot 7 0 8.5 4 / %Nl
+\plot 9 0 10 3 / %Nr
+\plot 11 0 10 3 / %Dl
+\plot 13 0 11 6 / %Dr
+\plot 8.5 4 6 9 / %NDl
+\plot 11 6 7.5 13 / %NDr
+\plot 5.5 13 5.5 16 / %XYNDl
+\plot 7.5 13 7.5 16 / %XYNDr
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 1 0 2.5 5 3.33 6 / %x
+\plot 5 0 3.5 4 3.33 6 / %y
+\setplotsymbol ({\textcolor{blue}{\scriptsize .}})
+\plot 3.33 6 6 12 6.5 15 / %xy
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 8 0 9.5 4 7 10.5 / %n
+\plot 12 0 10.5 5 7 10.5 / %d
+\setplotsymbol ({\textcolor{red}{\scriptsize .}})
+\plot 7 10.5 6.5 15 / %nd
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 6.5 15 6.5 16 / %xynd
+\endpicture}
diff --git a/legofit/slides/figancder.tex b/legofit/slides/figancder.tex
new file mode 100644
index 0000000..6a58958
--- /dev/null
+++ b/legofit/slides/figancder.tex
@@ -0,0 +1,34 @@
+%auto-ignore
+%-*-latex-*-
+\let\put\pictexput
+\mbox{\beginpicture
+\headingtoplotskip=\baselineskip
+\setcoordinatesystem units <0.5cm, 0.5cm> point at 7 0
+\setplotarea x from 0 to 6, y from 0 to 7
+\axis bottom invisible ticks length <0pt>
+  withvalues {\llap{Allelic state:}} {C} {C} {T} {T} /  at -1 0 2 4 6 / /
+%\axis left ticks andacross numbered from 1 to 7 by 1 /
+%\axis top ticks andacross numbered from 1 to 6 by 1 /
+\put {T} [b] <0pt,2pt> at 3 6
+\put {$\bullet$} at 1.5 3
+\plot 0 0 3 6 /
+\plot 2 0 1 2 /
+\plot 4 0 2 4 /
+\plot 6 0 3 6 /
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\setcoordinatesystem units <0.5cm, 0.5cm> point at -1 0
+\setplotarea x from 0 to 6, y from 0 to 7
+\axis bottom invisible ticks length <0pt>
+  withvalues {C} {C} {T} {T} /  at 0 2 4 6 / /
+%\axis left ticks andacross numbered from 1 to 7 by 1 /
+%\axis top ticks andacross numbered from 1 to 6 by 1 /
+\put {C} [b] <0pt,2pt> at 3 6
+\put {$\bullet$} at 3 2
+\put {$\bullet$} at 5 2
+\plot 0 0 3 6 /
+\plot 2 0 1 2 /
+\plot 4 0 2 4 /
+\plot 6 0 3 6 /
+
+\endpicture}
+\let\put\latexput
diff --git a/legofit/slides/figcongruent.tex b/legofit/slides/figcongruent.tex
new file mode 100644
index 0000000..44869cd
--- /dev/null
+++ b/legofit/slides/figcongruent.tex
@@ -0,0 +1,28 @@
+%-*-latex-*-
+\let\put\pictexput
+\mbox{\beginpicture
+\headingtoplotskip=\baselineskip
+\setcoordinatesystem units <0.35cm, 0.35cm>
+\setplotarea x from 1 to 11, y from 1 to 13
+\axis bottom invisible ticks length <0pt>
+  withvalues {$X$} {$Y$} {$N$} /  at 2 6 10 / /
+\axis bottom invisible shiftedto y=-0.3 ticks length <0pt>
+withvalues {1} {1} {0} /  at 2 6 10 / /
+%\axis left ticks andacross numbered from 1 to 13 by 1 /
+%\axis top ticks andacross numbered from 1 to 11 by 1 /
+\plotheading{Pattern \textit{xy}}
+\setplotsymbol ({\normalsize .})
+\plot 1 1 5 9 5 13 /
+\plot 3 1 4 3 5 1 / 
+\plot 7 1 5 5 6 7 8.75 1.5 /
+\plot 10.75 1.5 7 9 7 13 /
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 2 1 4 5 4.5 6 /
+\plot 6 1 4.5 3.5 4.5 5 4.5 6 /
+\setplotsymbol ({\textcolor{red}{\scriptsize .}})
+\plot 4.5 6 5 7 5.75 10 6 11 /
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 9.75 1.5 6.5 8 6 11 6 13 /
+%\arrow <10pt> [.2,.67] from 8.5 2 to 6.5 2
+\endpicture}
+\let\put\latexput
diff --git a/legofit/slides/figgptree.tex b/legofit/slides/figgptree.tex
new file mode 100644
index 0000000..aedf503
--- /dev/null
+++ b/legofit/slides/figgptree.tex
@@ -0,0 +1,58 @@
+%auto-ignore
+%-*-latex-*-
+\mbox{\beginpicture
+\headingtoplotskip=\baselineskip
+\setcoordinatesystem units <4mm, 3mm> point at 16 1
+%\setcoordinatesystem units <10mm, 10mm> point at 16 1
+\setplotarea x from 1 to 15, y from 1 to 15
+\axis bottom invisible ticks length <0pt>
+  withvalues {$X$} {$Y$} {$N$} {$D$} /  at 2 7 10 14 / /
+\axis bottom invisible shiftedto y=-0.3 ticks length <0pt>
+  withvalues {\llap{$yn$:}} {0} {1} {1} {0} /
+  at 1 2 7 10 14 / /
+\axis bottom invisible shiftedto y=-1.6 ticks length <0pt>
+  withvalues {\llap{$ynd$:}} {0} {1} {1} {1} /
+  at 1 2 7 10 14 / /
+%\axis left ticks andacross numbered from 1 to 15 by 1 /
+%\axis top ticks andacross numbered from 1 to 15 by 1 /
+\setplotsymbol ({\normalsize .})
+\plot 1 1 7 13 7 15 /   %X
+\plot 3 1 4.5 4 6 1 /   %XY
+\plot 8 1 5.5 6 8.12486206354179 11.249724127083585 /    %Y
+\plot 9.17572 1 10.1757 6 11.036 7.7206 / %N
+\plot 11 1 12 6 /       %N
+\plot 13 1 12 6 /            %D
+\plot 14.684 1 13.8151 6 12.3389 8.9523 9 13 9 15 / %Dr
+\plot 8.12486206354179 11.249724127083585 11.036 7.7206 / % ND l
+\arrow <10pt> [.2,.67] from 9.57571931984138 3 to 7 3
+\put {\small $m_N$} [b]  <0pt,5pt> at 8.5 3
+\put {\small $m_D$} [t]  <0pt,-5pt> at 12 2
+\setplotsymbol ({\footnotesize .})
+\setdashes
+\plot 2 1 8 13 8 15 /                      %x
+\plot 7 1 6 3 10 3 10.8879 5 /      %y
+\plot
+   10.187899999999999 1.5
+   10.8879 5 / % n tip
+\setsolid
+\setplotsymbol ({\textcolor{red}{\footnotesize .}})
+\plot
+   10.8879 5
+   11.43202 7.7206
+   10.704493062018068 9.0
+   9.737793206953752 10.7 / % n red
+\setdashes
+\setplotsymbol ({\textcolor{black}{\footnotesize .}})
+\plot
+   13.649562539059012 1.5
+   12.4 7.7206
+   9.737793206953752 10.7
+/ % d
+\setsolid
+\setplotsymbol ({\textcolor{blue}{\footnotesize .}})
+\plot
+   9.737793206953752 10.7
+   8.31003 12.4308
+   8 13 / % nd
+\setsolid
+\endpicture}
diff --git a/legofit/slides/fighyparch.tex b/legofit/slides/fighyparch.tex
new file mode 100644
index 0000000..fc6a498
--- /dev/null
+++ b/legofit/slides/fighyparch.tex
@@ -0,0 +1,71 @@
+%auto-ignore
+%-*-latex-*-
+\let\put\pictexput
+\mbox{\beginpicture
+\headingtoplotskip=\baselineskip
+\setcoordinatesystem units <3.4mm, 3mm>
+\setplotarea x from -2 to 17.5, y from 0 to 20
+\axis bottom invisible ticks length <0pt>
+  withvalues {$X$} {$Y$} {$N$} {$D$} {$S$} /  at 1 6 9 13 17 / /
+\color{red}
+\axis bottom invisible shiftedto y=-1.3 ticks length <0pt>
+  withvalues {\llap{$d$:}} {0} {0} {0} {1} /
+  at 0 1 6 9 13 / /
+\color{blue}
+\axis bottom invisible shiftedto y=-2.6 ticks length <0pt>
+  withvalues {\llap{$xyn$:}} {1} {1} {1} {0} /
+  at 0 1 6 9 13 / /
+\color{black} % I issue this command twice, because otherwise,
+\color{black} % the rest of the document is blue.
+%\axis left ticks andacross numbered from 0 to 20 by 2 /
+%\axis top ticks andacross numbered from 0 to 20 by 2 /
+\setplotsymbol ({\normalsize .})
+\plot 0 0 6 12 6 20 /   %X
+\plot 2 0 3.5 3 5 0 /   %XY
+\plot 7 0 4.5 5 7.12486206354179 10.249724127083585 /    %Y
+%\arrow <10pt> [.2, .67] from 13.7 9 to 10.6 9
+%\put {\small $\delta$} [t]  <0pt,-5pt> at 12.9 9
+%\put {\small $\gamma$} [b]  <0pt,5pt> at 7.3 6
+%\arrow <10pt> [.2,.67] from 5 6 to 9.6 6
+\plot 8.17572 0 9.1757 5 10.036 6.7206 / %N
+\plot 10 0 11 5 /       %N
+\plot 12 0 11 5 /            %D
+\plot 8 16 14.21226360816738 8.468963009740001 15.684 0 / %Sl
+\plot 8 20 8 18.8112 15.8936 9.24189 17.4997 0 / %Sr
+\plot 13.684 0 12.8151 5 11.3389 7.9523 8 12 8 16 / %Dr
+\plot 7.12486206354179 10.249724127083585 10.036 6.7206 / % ND l
+\arrow <10pt> [.2,.67] from 8.57571931984138 2 to 6 2
+%\arrow <0pt> [.2,.67] from 11.75 1 to 10.25 1
+%\arrow <10pt> [.2,.67] from 8.32572 1 to 6.5 1
+\put {\small $\alpha$} [b]  <0pt,5pt> at 7.5 2
+%\put {\small $\epsilon$} [t]  <0pt,-5pt> at 11 1
+\put {\small $\beta$} [b]  <0pt,5pt> at 13.9889 4
+\arrow <10pt> [.2,.67] from 14.9889 4 to 12.9889 4
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 1 0 7 12 7 13 /         % x, xy, bottom of xynd
+\setplotsymbol ({\textcolor{blue}{\scriptsize .}})
+\plot 7 13 7 20 /             % top of xynd
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+%\plot 6 0 5 2 9 2 9.8879 4 /  %y
+\plot 6 0 4 4 4 6 / %y
+\plot
+   12.649562539059012 0.5
+   11.946500312472102 4
+   12.9889 4
+/ % d
+\plot
+   9.187899999999999 0.5
+   9.8879 4
+   10.581012916966557 7.465564584832791
+   7.31003 11.4308
+   7 13 / % n and nd
+\setplotsymbol ({\textcolor{red}{\scriptsize .}})
+\plot
+  7 20
+  8 17.4055991158
+  15.052936280502118 8.855426848697988
+  15.896712358268855 4
+  14.9889 4
+/ % h
+\endpicture}
+\let\put\latexput
diff --git a/legofit/slides/figlinsort.tex b/legofit/slides/figlinsort.tex
new file mode 100644
index 0000000..b69f982
--- /dev/null
+++ b/legofit/slides/figlinsort.tex
@@ -0,0 +1,52 @@
+%-*-latex-*-
+\let\put\pictexput
+\mbox{\beginpicture
+\headingtoplotskip=\baselineskip
+\setcoordinatesystem units <0.4cm, 0.4cm> point at 12 1
+\setplotarea x from 1 to 11, y from 1 to 13
+\axis bottom invisible ticks length <0pt>
+  withvalues {$X$} {$Y$} {$N$} /  at 2 6 10 / /
+\axis bottom invisible shiftedto y=-0.3 ticks length <0pt>
+  withvalues {1} {0} {1} / at 2 6 10 / /
+%\axis left ticks andacross numbered from 1 to 13 by 1 /
+%\axis top ticks andacross numbered from 1 to 11 by 1 /
+\plotheading{Pattern \textit{xn}}
+\setplotsymbol ({\normalsize .})
+\plot 1 1 5 9 5 13 /
+\plot 3 1 4 3 5 1 / 
+\plot 7 1 5 5 6 7 9 1 /
+\plot 11 1 7 9 7 13 /
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 2 1  6 9 /
+\plot 6 12 6 13 / % xyn
+\plot 6 1 4.5 3.5 4.5 5 6.5 9 6 12 / %y
+\setplotsymbol ({\textcolor{red}{\scriptsize .}})
+\plot 6 9  6 12 / % x
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 10 1 6 9 / %n
+%\arrow <10pt> [.2,.67] from 8.5 2 to 6.5 2
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\setcoordinatesystem units <0.4cm, 0.4cm> point at 0 1
+\setplotarea x from 1 to 11, y from 1 to 13
+\axis bottom invisible ticks length <0pt>
+  withvalues {$X$} {$Y$} {$N$} /  at 2 6 10 / /
+\axis bottom invisible shiftedto y=-0.3 ticks length <0pt>
+  withvalues {0} {1} {1} / at 2 6 10 / /
+%\axis left ticks andacross numbered from 1 to 13 by 1 /
+%\axis top ticks andacross numbered from 1 to 11 by 1 /
+\plotheading{Pattern \textit{yn}}
+\setplotsymbol ({\normalsize .})
+\plot 1 1 5 9 5 13 /
+\plot 3 1 4 3 5 1 / 
+\plot 7 1 5 5 6 7 9 1 /
+\plot 11 1 7 9 7 13 /
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 2 1  6 9 6 13 /
+\plot 6 1 4.5 3.5 4.5 5 6.5 9 / %y
+\setplotsymbol ({\textcolor{red}{\scriptsize .}})
+\plot 6.5 9  6 12 / % x
+\setplotsymbol ({\scriptsize .})
+\plot 10 1 6.5 8 6.5 9 / %n
+%\arrow <10pt> [.2,.67] from 8.5 2 to 6.5 2
+\endpicture}
+\let\put\latexput
diff --git a/legofit/slides/figmix.tex b/legofit/slides/figmix.tex
new file mode 100644
index 0000000..f90f0ef
--- /dev/null
+++ b/legofit/slides/figmix.tex
@@ -0,0 +1,59 @@
+%-*-latex-*-
+\let\put\pictexput
+\mbox{\beginpicture
+\headingtoplotskip=\baselineskip
+\setcoordinatesystem units <0.35cm, 0.35cm> point at 12 1
+\setplotarea x from 1 to 11, y from 1 to 13
+\axis bottom invisible ticks length <0pt>
+  withvalues {$X$} {$Y$} {$N$} /  at 2 6 10 / /
+\axis bottom invisible shiftedto y=-0.3 ticks length <0pt>
+withvalues  {1} {0} {0} /  at 2 6 10 / /
+%\axis left ticks andacross numbered from 1 to 13 by 1 /
+%\axis top ticks andacross numbered from 1 to 11 by 1 /
+\plotheading{Without admixture}
+\setplotsymbol ({\normalsize .})
+\plot 1 1 5 9 5 13 /
+\plot 3 1 4 3 5 1 / 
+\plot 7 1 5 5 6 7 9 1 /
+\plot 11 1 7 9 7 13 /
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 4 5 5 7 5.75 10 6 11 6 13 / %x
+\plot 6 1 4 5 / %y
+\setplotsymbol ({\textcolor{blue}{\scriptsize .}})
+\plot 2 1 4 5  / %x
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 8.5 4 6.5 8 6 11 / %n
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 10 1 8.5 4 / %n
+\setplotsymbol ({\normalsize .})
+%\arrow <10pt> [.2,.67] from 8.5 2 to 6.5 2
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\setcoordinatesystem units <0.35cm, 0.35cm> point at -1 1
+\setplotarea x from 1 to 11, y from 1 to 13
+\axis bottom invisible ticks length <0pt>
+  withvalues {$X$} {$Y$} {$N$} /  at 2 6 10 / /
+\axis bottom invisible shiftedto y=-0.3 ticks length <0pt>
+withvalues {1} {0} {0} /  at 2 6 10 / /
+\axis bottom invisible shiftedto y=-1.3 ticks length <0pt>
+withvalues  {0} {1} {1} /  at 2 6 10 / /
+%\axis left ticks andacross numbered from 1 to 13 by 1 /
+%\axis top ticks andacross numbered from 1 to 11 by 1 /
+\plotheading{With admixture}
+\setplotsymbol ({\normalsize .})
+\plot 1 1 5 9 5 13 /
+\plot 3 1 4 3 5 1 / 
+\plot 7 1 5 5 6 7 9 1 /
+\plot 11 1 7 9 7 13 /
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 2 1 5 7 5.75 10 6 11 6 13 / %x
+\plot 6 1 5.5 2 9 2  8.5 4 / %y
+\setplotsymbol ({\textcolor{blue}{\scriptsize .}})
+\plot 2 1 5 7 5.75 10 6 11 / %x
+\setplotsymbol ({\textcolor{red}{\scriptsize .}})
+\plot 8.5 4 6.5 8 6 11 /
+\setplotsymbol ({\textcolor{gray}{\scriptsize .}})
+\plot 10.5 1 8.5 4 / %n
+\setplotsymbol ({\normalsize .})
+\arrow <10pt> [.2,.67] from 8.5 2 to 6.5 2
+\endpicture}
+\let\put\latexput
diff --git a/legofit/slides/fignotation.tex b/legofit/slides/fignotation.tex
new file mode 100644
index 0000000..ceb2c89
--- /dev/null
+++ b/legofit/slides/fignotation.tex
@@ -0,0 +1,19 @@
+%-*-latex-*-
+\let\put\pictexput
+\mbox{\beginpicture
+\headingtoplotskip=\baselineskip
+\setcoordinatesystem units <0.35cm, 0.35cm>
+\setplotarea x from 1 to 11, y from 1 to 13
+\axis bottom invisible ticks length <0pt>
+  withvalues {$X$} {$Y$} {$N$} /  at 2 6 10 / /
+%\axis left ticks andacross numbered from 1 to 13 by 1 /
+%\axis top ticks andacross numbered from 1 to 11 by 1 /
+\setplotsymbol ({\normalsize .})
+\plot 1 1 5 9 5 13 /
+\plot 3 1 4 3 5 1 / 
+\plot 7 1 5 5 6 7 8.75 1.5 /
+\plot 10.75 1.5 7 9 7 13 /
+\put {\textit{XY}} at 4 4
+\put {\textit{XYN}} at 6 8
+\endpicture}
+\let\put\latexput
diff --git a/legofit/slides/main.pdf b/legofit/slides/main.pdf
new file mode 100644
index 0000000..b1b1c60
Binary files /dev/null and b/legofit/slides/main.pdf differ
diff --git a/legofit/slides/main.tex b/legofit/slides/main.tex
new file mode 100644
index 0000000..fdb0a45
--- /dev/null
+++ b/legofit/slides/main.tex
@@ -0,0 +1,431 @@
+% -*-latex-*-
+%\documentclass[pdftex,handout]{beamer}
+\documentclass[pdftex,12pt]{beamer}
+\usepackage{etex}
+\let\latexput\put
+\usepackage{pictex}
+\let\pictexput\put
+\let\put\latexput
+\newcommand{\mutation}{$\cdot$}
+\usepackage{ifthen}
+\newcounter{showthis}
+\setcounter{showthis}{1}
+\newdimen\thusfar
+\newdimen\plotht
+\newdimen\plotwd
+\newdimen\plotsp
+\newdimen\xunit
+\newdimen\yunit
+\newdimen\offsety
+\setbeamercovered{transparent}
+\setbeamertemplate{footline}[frame number]
+\author{Alan R. Rogers}
+\date{\today}
+\begin{document}
+
+\title{Site Patterns and Population History: the Intuition that
+  Underlies Legofit}
+\frame{\titlepage}
+
+\begin{frame}
+  \frametitle{Notation for populations}
+  \begin{columns}
+    \column{0.3\textwidth}
+    \input{fignotation}
+    \column{0.7\textwidth}
+    \raggedleft
+    $X$, $Y$, and $N$ are populations: African, European, and Neanderthal.
+
+    \bigskip
+    
+    \textit{XY}: population ancestral to $X$ and $Y$.
+
+    \bigskip
+    
+    \textit{XYN}: ancestral to $X$, $Y$, and $N$.
+    \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Nucleotide site patterns}
+  \begin{columns}
+    \column{0.3\textwidth}
+    \input{figcongruent}
+    \column{0.7\textwidth}
+    \raggedleft
+    Haploid sample: 1 nucleotide from each population.
+
+    \bigskip
+    
+    Mutation on red segment would appear in samples from $X$, $Y$, not
+    that from $N$.
+
+    \bigskip
+    Call this the \textit{xy} site pattern.
+  \end{columns}
+  \bigskip\raggedleft I will write $xy\succ yn$ to mean that $xy$ is more
+  common than $yn$.
+\end{frame}
+
+\begin{frame}
+  \frametitle{Why haploid samples?}
+  No variation within populations $\Rightarrow$ results not affected
+  by recent history of population size.
+
+  \bigskip
+
+  The haploid samples are hypothetical; our real samples are
+  larger. We use all the genomes in the real data to calculate the
+  probability of observing site pattern \emph{xy} in a hypothetical
+  haploid sample:
+  \[
+  \Pr[xy] = p_X p_Y (1-p_N)
+  \]
+  where $p_i$ is the frequency of the derived allele in the sample
+  from population $i$. These site pattern frequencies are our data.
+\end{frame}  
+
+\begin{frame}
+  \frametitle{Calling ancestral and derived alleles}
+{\centering\input{figancder}\\}
+    \bigskip
+    
+    2 mutations needed if $C$ is ancestral.
+
+    \bigskip
+
+    Only 1 needed if $T$ is ancestral.
+
+    \bigskip
+
+    Prefer hypothesis requiring fewer mutations, because mutations
+    are rare.
+\end{frame}
+
+\begin{frame}
+  \frametitle{Observed site pattern frequencies}
+  \begin{columns}
+    \column{0.7\textwidth}
+    \includegraphics[width=\linewidth]{xynd-frq.pdf}
+    \column{0.3\textwidth}
+    \raggedleft
+
+    $X$, Africa; $Y$, Europe; $N$, Neanderthal; $D$, Denisovan.
+
+    \bigskip
+
+    Horizontal axis: rel.\ freq.\ of each site pattern
+
+    \bigskip
+
+    ``Dots'' w/i circles are 95\% confidence intervals.
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{The pattern in the data}
+  \begin{columns}
+    \column{0.7\textwidth}
+    \includegraphics[width=\linewidth]{xynd-frq.pdf}
+    \column{0.3\textwidth}
+    \raggedleft
+
+    Lots of singletons ($x$, $y$, $n$, and $d$)
+
+    \bigskip
+
+    Two doubletons (\textit{xy} and \textit{nd}) especially common
+
+    \bigskip
+
+    \textit{yn} more common than other rare doubletons.
+
+    \bigskip
+
+    \textit{xyn} more common than other tripletons.
+  \end{columns}
+  \bigskip\raggedleft
+How can we understand this pattern?
+\end{frame}
+
+\begin{frame}
+  \frametitle{1st pass: no frills}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \input{figEarlyND}
+    \column{0.5\textwidth}
+    \raggedleft
+    No gene flow; gene genealogy matches population tree.
+
+    \bigskip
+
+    Many other genealogies are possible, but this one will be common.
+
+    \bigskip
+
+    Captures large-scale pattern; misses subtleties.
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Why are \textit{xy} and \textit{nd} so common?}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \input{figEarlyND}
+    \column{0.5\textwidth}
+    \raggedleft
+    Mutation on blue $\rightarrow$ \textit{xy};
+    mutation on red $\rightarrow$ \textit{nd}.
+
+    \bigskip
+
+    \textit{xy} and \textit{nd} are common because $X$ and $Y$ are
+    closely related, as are $N$ and $D$.
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Why is $xy \succ nd$?}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \input{figEarlyND}
+    \column{0.5\textwidth}
+    \raggedleft
+    Blue branch is longer than red, because $X$ and $Y$ separated more
+    recently than $N$ and $D$.
+
+    \bigskip
+
+    Explains why $xy \succ nd$.
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Data again: \textit{xy} and \textit{nd} common, but
+  $xy \succ nd$}
+    {\centering\includegraphics[width=0.9\linewidth]{xynd-frq.pdf}\\}
+\end{frame}
+
+\begin{frame}
+  \frametitle{An alternate hypothesis}
+  \begin{columns}
+    \column{0.5\textwidth}
+    \input{figLargeND}
+    \column{0.5\textwidth}
+    \raggedleft
+    Separation times are equal.
+
+    \bigskip
+    
+    But $ND$ is large, so coalescence is slow, and red branch is short.
+
+    \bigskip
+
+    $xy \succ nd$ because $ND$ is larger than $XY$.
+
+    \bigskip
+
+    The two hypotheses are hard to tell apart.
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Counterintuitive site patterns}
+  {\centering\input{figlinsort}\\}  
+\end{frame}
+
+\begin{frame}
+  \frametitle{Incomplete lineage sorting}
+  Suppose that, as we trace the ancestry of our sample backwards in
+  time, the lineages from $X$ and $Y$ don't
+  coalesce until we reach \textit{XYN}.
+
+  \bigskip
+
+  Then there are three lineages, $X$, $Y$, and $N$, in the same
+  population.
+
+  \bigskip
+
+  They can coalesce in any order.
+
+  \bigskip
+
+  Site patterns \textit{xy}, \textit{xn}, and \textit{yn} are equally
+  likely.
+
+  \bigskip
+
+  This process is called ``incomplete lineage sorting.''
+\end{frame}  
+
+\begin{frame}
+  \frametitle{Pattern \textit{xy} can also arise another way}
+  \begin{columns}
+    \column{0.3\textwidth}
+    \input{figcongruent}
+    \column{0.7\textwidth}
+    \raggedleft
+    The lineages from $X$ and $Y$ may also coalesce w/i \textit{XY},
+    generating site pattern \textit{xy}.
+
+    \bigskip
+    
+    So $xy \succ xn, yn$.
+
+    \bigskip
+
+    \textit{xn} and \textit{yn} should be equally common.
+  \end{columns}
+
+  \bigskip\raggedleft
+  
+This is the pattern expected in the absence of gene flow.
+\end{frame}
+
+\begin{frame}
+  \frametitle{Does incomplete lineage sorting (ILS) explain the data?}
+  \begin{columns}
+    \column{0.7\textwidth}
+    \includegraphics[width=\linewidth]{xynd-frq.pdf}
+    \column{0.3\textwidth}
+    \raggedleft
+
+    \textit{xd} and \textit{yd} have equal frequencies, as they should
+    under ILS.
+
+    \bigskip
+
+    But $yn \succ xn$, and the difference $>$ the confidence intervals.
+
+    \bigskip
+
+    Why?
+
+  \end{columns}
+  \bigskip\raggedleft
+\end{frame}
+
+\begin{frame}
+  \frametitle{The effect of gene flow}
+  \begin{columns}
+  \column{0.7\textwidth}
+  \input{figmix}
+  \column{0.3\textwidth}
+  \raggedleft
+
+  $N\rightarrow Y$ gene flow inflates the frequency of \textit{yn}.
+
+  \bigskip
+
+  Also inflates frequency of $x$.
+
+  \bigskip
+
+  Effects are small unless the rate of gene flow is high.
+  \end{columns}
+\end{frame}
+
+
+\begin{frame}
+  \frametitle{Data are consistent with $N \rightarrow Y$ gene flow}
+  \begin{columns}
+    \column{0.7\textwidth}
+    \includegraphics[width=\linewidth]{xynd-frq.pdf}
+    \column{0.3\textwidth}
+    \raggedleft
+
+    $yn \succ xn$, and $x \succ y$.
+
+    \bigskip
+
+    Signature of $N \rightarrow Y$ gene flow.
+    
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Puzzling excess of $d$ site pattern}
+  \begin{columns}
+    \column{0.7\textwidth}
+    \includegraphics[width=\linewidth]{xynd-frq.pdf}
+    \column{0.3\textwidth}
+      \raggedleft
+
+      $d$ is most common singleton
+
+      \bigskip
+
+      Suggests Denisovan fossil is young and $N$-$D$ separation old.
+
+      \bigskip
+
+      But our 2017 analysis of this hypothesis led to absurd result:
+      Denisovan fossil only 4000 y old.
+  \end{columns}
+
+  \bigskip\raggedleft
+      
+  Something was missing from our model
+\end{frame}
+
+\begin{frame}
+  \frametitle{Admixture from superarchaics into Denisovans}
+  \begin{columns}
+    \column{0.7\textwidth}
+    \input{fighyparch}
+    \column{0.3\textwidth}
+    \raggedleft
+    $S$ is a ``superarchaic'' hominin, distantly related to all
+    others.
+
+    \bigskip
+
+    $S \rightarrow D$ gene flow inflates frequency of $d$ and
+    \textit{xyn}. 
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{Superarchaic gene flow into $D$}
+  \begin{columns}
+    \column{0.7\textwidth}
+    \includegraphics[width=\linewidth]{xynd-frq.pdf}
+    \column{0.3\textwidth}
+      \raggedleft
+
+      $d$ most common singleton
+
+      \bigskip
+
+      \textit{xyn} most common tripleton
+
+      \bigskip
+
+      Signature of $S \rightarrow D$ gene flow (Pr{\"u}fer et al 2014).
+  \end{columns}
+\end{frame}
+
+\begin{frame}
+  \frametitle{What we learned, just by staring at the data}
+  \begin{enumerate}
+    \item Europeans and Africans are close relatives.
+    \item So were Neanderthals and Denisovans.
+    \item European-African separation more recent than
+      Neanderthal-Denisovan.
+    \item Neanderthals contributed genes to Europeans
+    \item Superarchaics contributed genes to Denisovans.
+  \end{enumerate}
+
+  \bigskip
+  
+This analysis has been exploratory. Legofit extends these ideas to
+estimate parameters and test hypotheses about history.
+\end{frame}  
+
+\end{document}
+
+
+\begin{frame}
+\frametitle{}
+\end{frame}
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