From 741b05c06d3ee9fc34dfe62b58caaf3c8f894b11 Mon Sep 17 00:00:00 2001 From: "Alan R. Rogers" Date: Tue, 26 Jul 2022 13:33:04 -0600 Subject: [PATCH] Add slides to legofit/slides. --- .gitignore | 3 + legofit/slides/figEarlyND.tex | 39 +++ legofit/slides/figLargeND.tex | 39 +++ legofit/slides/figancder.tex | 34 +++ legofit/slides/figcongruent.tex | 28 +++ legofit/slides/figgptree.tex | 58 +++++ legofit/slides/fighyparch.tex | 71 ++++++ legofit/slides/figlinsort.tex | 52 ++++ legofit/slides/figmix.tex | 59 +++++ legofit/slides/fignotation.tex | 19 ++ legofit/slides/main.pdf | Bin 0 -> 144318 bytes legofit/slides/main.tex | 431 ++++++++++++++++++++++++++++++++ legofit/slides/xynd-frq.pdf | Bin 0 -> 6441 bytes 13 files changed, 833 insertions(+) create mode 100644 legofit/slides/figEarlyND.tex create mode 100644 legofit/slides/figLargeND.tex create mode 100644 legofit/slides/figancder.tex create mode 100644 legofit/slides/figcongruent.tex create mode 100644 legofit/slides/figgptree.tex create mode 100644 legofit/slides/fighyparch.tex create mode 100644 legofit/slides/figlinsort.tex create mode 100644 legofit/slides/figmix.tex create mode 100644 legofit/slides/fignotation.tex create mode 100644 legofit/slides/main.pdf create mode 100644 legofit/slides/main.tex create mode 100644 legofit/slides/xynd-frq.pdf 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 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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} diff --git a/legofit/slides/xynd-frq.pdf b/legofit/slides/xynd-frq.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9ea364908441ad177cd9ab6dd0afb1d29f118562 GIT binary patch literal 6441 zcmai32{=@3`J4K(ok5`^JMzDyz=fZ=@cOrjx?K=mLB9ylP#VA6?rvS7d~ zwQ-~koWlUi<3iwZ(O`s+JFBz0oUuG9L3i}jIUI9%0YM_ggkh-^CXvEq0PLKs1YuT02Gx&FATj{tFToL_2MKRL4FH_rpa6x@1~jzbE`p#r z9kc^9e`hG#~Vxg701Ec{REM~6ogs(xif!8#!=~HaFyWwrv?IaW^>3v9b7i? zD4t9NAnLGy(-aS=C;g;4&BIgm_dGk{qkd#}urwPc#uQJgA&I~Q(7%#3_&ZTexCQ`z z!9@RA5xd+LbSlA`$ON3g0vO@|m<=(234mHSunvH(E?9IVpv86uE(vxhfO*)O32p*7 z1MUD=EMF?!nuaI*6u=l(hYbMj-vwan|K3Z4wg&2d?&7sv2U8yxtu4cEj%N|?7Zk1# z(z+!%p=9!uf`_Fn-*$KG#bor4`sIEZO!H?Yq2s!LQ9Ttq;+V=c_Ubh&^TmC|qCcuf zur%m8#zmMXdMHiwG3)-x2eq|*D;dG-OVzdCnK6J+=l9?myQSFnA7aPrS7oYSe`5rG zYvEb>Ecse(^~~9r@sIg^*!qlOe#WwZFQ+%o-thyb`dS(Fcq{)NRm^%U;(+hSYl07d z{RBaHba=bxBBpT3N#0bQe~nh7oBJ~8ePn1iZgo%=a&IYN6?=^$zRp_kx7k zkQPj=O}cmn6Q68y5&3NZ_cYc0(jTGp_}EgXp|Y)JqroWKrkf77 z4nKHi>aw#ryB#hmob48Eai%+1nF-yJ98e~YN=^y;;e{$BD>@_xJ>Tq^yeH}NcA_H3 zwXJ3t;N$Df(lebJ62yhUunCVLMQz1YsN))CA}(WZi#BXz0mw6f$ybs;75xsNH?;w6X78p5N# zS>HyUD;%@V5f>h}x~@X?x29OWU(CMWQ2 zmpz+R_3bQew{1~ldNeekCkyRT6EzNHD7^FL_99$*ZSDY{(X860tL&9XSLv9;*NFqhBrCcS10neDb z%~frh>MfL$%Z`h}gnFz9u91i}>*m<)zcjY^S~uD4c+!E6D-xsIi*1u)6`F2$$QB3` zP@CN?%``i>_rwyC=ti4|I43mqF6F5n+mkb| z=%h-#S1b;d2)%uw5UyYsF*5e3amy{Uw!BPpPj6J%pnLP8TxziH+RE1_BGUASrHxCb zT!|?q74y?O6+=?YRlehEdJ9YPVry&sy6T7O>S*>0<_DdV=JG?bqzoPdt8W+&g<)5t zs>tq(Ddi0oxvGMz^Y2I6s&<$gZDAdKS(-V+ZJv4HbZaMHQ?t-y*B}eMZC7*R`rWDW z{co*#rqjEoH`AKiMGjkauLjg+h_n>*EIMx==HNfD`$PkJ&kmiN8YQWr>8PXGbqA!K zR?9MZ)a-<)9pfV>fZ3(>PtHr<%|zyd0+eoFu842)9&e=2wGE=4wtad&5P`?tk)A~h z?Hiv#l*Tv4Im?+2DuOf6d&1x#qh?TcHnBM6E1Fk>{>^(J&kc7+&UD3dn1axgOwcbb}DEzOm z6#QsCe_0@|dFjgQMnZs&uDQu~Vb_HhvrQ?J-KdTzXDljPq{_x)zYz}`Eo@}-3-PeA#J}JUTL=P{ zpU?(`7lJSYJcIZXZ@`R*zWzieiGT;O1_i`i|_dH@JE z6ti;K&|q8qX9gS2e#P1t0WfD1G3ft|$F5&K zWn(?CHL|NttIp!WmYC#jA8#v8BjGxuB=tQAfh{Hv6FC&nhBh=q%cMMhBxEEc8=F+B z5EH)1vUG-9#<2e+O>)O&V~--4H}_93bfmqJTM72bsOx&|wZM8_!;$#)JWr#UgFwjU zECyl|ST8reO`8`vxO_QAXyxSwTUT+MshmMC<9t&kR;BA|M1U{rd-@K>HE{gM zNUlDnfZ(vW5;yr_b--Ch`my$Y`)f*7=8vybqK)oNtDGT}VaI6|+5I$kOhbQH}2xiF+Y!Lau5 zg%U16kfG4Gr#VK99v@%qg*iO!l4uug?tJQ~F0Pm#C8O+Y9T9&~B6hT^>&Rqm^HaEp zR{ZWU#LHBfW3r=k4$rQy$0SdaWy%!xz0}5N!^u!`J*5Av%h$9EEB=>V!_Lmj7|N|S zeYOuy73L_(BUTKoMUqKU94<4PENZ_+cDTVfV#@0ML|7+x)daa(JsR8VrFLs*$k}vL zhL0+2YGExyxFmtfaQzY7nlgFs}{vGFwgK&Tjv<<%jSuU$W=MM?|!?s zihWhAkAfv1GHlN?1I#X0IJHSc@uV6==&fd4T@`Kmo-2Lz}GNBIzNji-J$}wuFVZZIQByWCGYW*|Knl#2w>YJXkRc z*<^kttbq}yl-^9HRe@|_#B`SDl+zT1xxI!%7+aNT=`Fq{709<6E|AyYSR&@jQ|@N2 z&7Tk^-SBu3sV%1-TJ`V}jVox&e3*Gt%7~bQ;K6hGVj)|^bZ*4L#kMx$43YvA1;pfU zC5q>8lJs6B?#hv?jxkEgZ*!95J#+|RVU{fPL{2Jv?8fCRyDW5ep(UTi^@0Qaw*8P3 zf}g~W;Cya$^mI;fF!$=nT#r@9*=MG8@0=>168osVCdGR`ix7uM*ml-TR#~c?vs|Wp zM_&RaT&5)spI7Q|Tj#m#OpI_dy~N!YQ7L$4%Ng-AJo^$@=XZ}WX_eZ?opp~!sXekC zaipox>}eABWbTU(Z&`>FZC+k%Um~vJf<%M)4<=;DLnPt^?t~c`?7>5`E_CCxP4Afo z=qrkUiaPp;b|d6ogoClJp{}{CQoWL;k*6YB^_-$SS$VCg| z-1M<&ZDFiN9#6LwDfceb`}|#1shF7SCU;HJP2!)Nlv3T9wWEh?>itLL8h*`hZJ#aF z*4(y!TKO6JnOb4-vx$P!1xwFN`d>Z6^$*|F=x6o!^;g|Ib@NT19_b1x%xC<>Y>)P> zC8h{Dp9d5@>yg8m<=DxbPC|rW)5WCD0*{Y~Jf^1KH$SDCPc`RjGy+=!Ed#>?=K@zg3ast@ zruc2=THTs8uMV#~FAr}KZy+2ttkwv332$rfKEm>?qEzUM%9hWs zoIg0fslGMo-^HSMQCh1838(tfPsq7HXsCbj{rvgt^KDrj_}-p}h@R5tOT4iyf&{YX z^-~7>PGgGvbtXPOA80r>8}#yvv~-^7Rnyq^?9(mFtIOLbCQ7Qxs=UShE;VG zt5Ytg63(1o=MrU!rXRl88kT?4t8h}k%ggn-t3t6z@e5zC&nBN$sgDM`Y9F2HjvSMC zXFbPwW8bAUQ1$H8ldfTE_#4%;ch4sNK>ygW$#K(A$VA9Zz1D}9&aw1!GI{i$>5GPT zgdS?xFHbXaYx|s7yDU5@G^8iF<(8fYAvJD~ zLof3bE7U2pD=ZkM8XDgS%$CZQxRI89yfvUTxz&hJM8q*gg@yM^0@HYEx+E~8y z+TNjRnr_2^EbY-Xg|~-J$Expr?r^Psbyd7s>6+4E@t$ZzG&FhvlXZ=^^J8yFZiQ+7 zJ>Pltd5LsBDj)U2!V}n}xni~QC6)aq{zrz>byLUEt&%?2Jltv{l%Btq|2((;sL+wY zjL)k3mFxC%r6gTBX=5aoC$NsJ&{#%BmOm|zDbH!YmNMszRuUA~Bw`0*%W9iZ16}XunLmTS;$@Wy|AEabx#-bB)gugH%dPR&p5?O#T;tZLf`W( z7>s%ad8vJmG@n;^M9wroN!ql?RL$fKb%IjAda1+y(s9vULe|!wSKPCSK-yGIyxV(GtaH}#)1$NMNHQ=l9^NXqZ%?H(fIIlk) zA2{_O;42a?wNLZA^T)4!#c9V29=!a~J5O9-zWn&jUZ&X7HRZnLS;h!-hWw-U$|(tr z>V?t;wS!lJr@n0axHO+1XPyzvwGy_x{%0q`=14bi=x?6$Cy8iGMgVLk)CyqJg8z?m z{5O(i)2AB_el-tlmXpEeW&J=x5^NhxNgg0HXVbSJ;Qy!VK>SIxV)0D8FVzc-$9C~2 zGyCsk|7mYPg4KrTz$T~R>PU9O^mms7iZ_P;rNKhLp>VVc9IgWD{g*!L-zqj>mqi2H z7Z?uj%K*9OU#zd6udh3vLSeUBHr^x#0DgYuv=^`=(ivcAKtmmYLTF-;XiW_$QXRdK zENDP<0L)1KM1bA)sRBMUJky&&!~_1n4bkcv?9T0Fo;K#sxLSxm^fa~5|B^B3c#w0agYO{#m^CSo$gT^_ib@3!-p|u32xAlM z0D^sTz;^@2hJcf