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substitutionmodels.aux
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\relax
\providecommand\hyper@newdestlabel[2]{}
\providecommand\HyperFirstAtBeginDocument{\AtBeginDocument}
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\global\let\hyper@last\relax
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\@writefile{toc}{\contentsline {subsection}{Probabilistic modeling applied to phylogeny}{1}{section*.1}\protected@file@percent }
\newlabel{probabilistic-modeling-applied-to-phylogeny}{{}{1}{Probabilistic modeling applied to phylogeny}{section*.1}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {1}{\ignorespaces Observed data are sequences in alignment, which are assumed to have evolved from an ancestral sequence along the branches of a bifurcating tree}}{1}{figure.1}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{Substitution as a Markov process}{1}{section*.2}\protected@file@percent }
\newlabel{substitution-as-a-markov-process}{{}{1}{Substitution as a Markov process}{section*.2}{}}
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\@writefile{toc}{\contentsline {subsection}{One-step transition probability matrix}{2}{section*.3}\protected@file@percent }
\newlabel{one-step-transition-probability-matrix}{{}{2}{One-step transition probability matrix}{section*.3}{}}
\@writefile{toc}{\contentsline {subsection}{Nucleotide distribution and how substitution affects it}{2}{section*.4}\protected@file@percent }
\newlabel{nucleotide-distribution-and-how-substitution-affects-it}{{}{2}{Nucleotide distribution and how substitution affects it}{section*.4}{}}
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\@writefile{toc}{\contentsline {subsection}{Multi-step transition probabilities}{3}{section*.5}\protected@file@percent }
\newlabel{multi-step-transition-probabilities}{{}{3}{Multi-step transition probabilities}{section*.5}{}}
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\@writefile{toc}{\contentsline {subsection}{Steady state distribution / equilibrium nucleotide frequencies}{5}{section*.6}\protected@file@percent }
\newlabel{steady-state-distribution-equilibrium-nucleotide-frequencies}{{}{5}{Steady state distribution / equilibrium nucleotide frequencies}{section*.6}{}}
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\@writefile{toc}{\contentsline {subsection}{Time reversibility}{7}{section*.7}\protected@file@percent }
\newlabel{time-reversibility}{{}{7}{Time reversibility}{section*.7}{}}
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\@writefile{lof}{\contentsline {figure}{\numberline {2}{\ignorespaces A genomic site changing along a single branch from a phylogeny}}{8}{figure.2}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{Nucleotide substitution as a continuous-time Markov process}{9}{section*.8}\protected@file@percent }
\newlabel{nucleotide-substitution-as-a-continuous-time-markov-process}{{}{9}{Nucleotide substitution as a continuous-time Markov process}{section*.8}{}}
\@writefile{lof}{\contentsline {figure}{\numberline {3}{\ignorespaces A nucleotide site changing according to a continuous-time Markov process}}{9}{figure.3}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {4}{\ignorespaces Continuous-time transition probabilities \(p_{AA}(t)\) and \(p_{AG}(t)\) as a function of time. Note that the instantaneous rates, \(q_{AA}\) and \(q_{AG}\) are the slopes of the curves at t=0.}}{10}{figure.4}\protected@file@percent }
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\@writefile{lof}{\contentsline {figure}{\numberline {5}{\ignorespaces Exponential sojourn time distribution, with rate parameter \(\lambda = -q_{AA}=2\)}}{11}{figure.5}\protected@file@percent }
\@writefile{lof}{\contentsline {figure}{\numberline {6}{\ignorespaces Continuous-time transition probabilities \(p_{AA}(t)\) and \(p_{AG}(t)\) as a function of time. Note how the transition probabilities converge to the equilibrium frequencies \(\pi _A\) and \(\pi _G\)}}{11}{figure.6}\protected@file@percent }
\@writefile{toc}{\contentsline {subsection}{Relationship between \(\boldsymbol {Q}\) and \(\boldsymbol {P}(t)\)}{11}{section*.9}\protected@file@percent }
\newlabel{relationship-between-boldsymbolq-and-boldsymbolpt}{{}{11}{\texorpdfstring {Relationship between \(\boldsymbol {Q}\) and \(\boldsymbol {P}(t)\)}{Relationship between \textbackslash boldsymbol\{Q\} and \textbackslash boldsymbol\{P\}(t)}}{section*.9}{}}
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\@writefile{toc}{\contentsline {subsection}{Steady-state distribution for continuous-time Markov chains}{12}{section*.10}\protected@file@percent }
\newlabel{steady-state-distribution-for-continuous-time-markov-chains}{{}{12}{Steady-state distribution for continuous-time Markov chains}{section*.10}{}}
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\@writefile{toc}{\contentsline {subsection}{Time-reversibility in continuous-time Markov chains}{13}{section*.11}\protected@file@percent }
\newlabel{time-reversibility-in-continuous-time-markov-chains}{{}{13}{Time-reversibility in continuous-time Markov chains}{section*.11}{}}
\@writefile{toc}{\contentsline {subsection}{Construction of a rate matrix for a continuous-time Markov chain with pre-specified steady-state distribution}{13}{section*.12}\protected@file@percent }
\newlabel{construction-of-a-rate-matrix-for-a-continuous-time-markov-chain-with-pre-specified-steady-state-distribution}{{}{13}{Construction of a rate matrix for a continuous-time Markov chain with pre-specified steady-state distribution}{section*.12}{}}
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\@writefile{toc}{\contentsline {subsection}{Estimation of instantaneous rate matrices in molecular phylogeny}{16}{section*.13}\protected@file@percent }
\newlabel{estimation-of-instantaneous-rate-matrices-in-molecular-phylogeny}{{}{16}{Estimation of instantaneous rate matrices in molecular phylogeny}{section*.13}{}}
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\@writefile{toc}{\contentsline {subsection}{Codon substitution models}{17}{section*.14}\protected@file@percent }
\newlabel{codon-substitution-models}{{}{17}{Codon substitution models}{section*.14}{}}
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