User:Carl Boettiger/Notebook/Comparative Phylogenetics/2010/06/27

Comparative Phylogenetics

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Evolution 2010 Day 2 Clay Cressler : Can you trust evolutionary parameters estimated by complex phylogenetic comparative methods? A simulation study with OUCH Jeet Sukumaran (Mark Holder lab) Performance and robustness of phylogeographic analytical studies Tests common macroscopic models of inferring population structure (i.e. via coalescent) an individual based simulation model. Graham Slater, Luke Harmon, Liam Revell, Marc Suchard, Mike Alfaro. Estimating rates of phenotypic evolution and speciation from incomplete trees. Fascinating talk on estimating rates when the tree is not resolved to the species level. Approximate Bayesian Computing based approach which simulates the tree to the species level as a pure birth process with trait evolution by Brownian motion, estimating parameter posteriors by ABC. Seemed to me this calculation could be done analytically, since the Brownian rate inference depends only on the distribution of branch lengths, which is simply exponential under the pure-birth (or constant birth-death) model. For instance: [math]\displaystyle{ \begin{align} L(\beta | u ) &= \frac{1}{\beta^N} \exp \left( \frac{- Q(\vec u)}{2 \beta} \right)\\ Q(\vec u) &= \sum_i \frac{(u_i - u_{i'})^2 }{v_{ii'} } \end{align} }[/math] Well, if the branch length [math]\displaystyle{ v_{ii'} }[/math] is exponentially distributed with parameter [math]\displaystyle{ \lambda }[/math] [math]\displaystyle{ \begin{align} L(\beta | u) &= \int \exp\left(- \sum_i \frac{(u_i - u_{i'})^2 }{v }/2\beta \right) \lambda e^{-\lambda v} / \beta^N dv \\ L(\beta | u) &= \int \exp\left(- \frac{\sum_i (u_i - u_{i'})^2 }{2\beta v} - \lambda v \right) \lambda / \beta^N dv \\\end{align} }[/math] If we simply estimated the branch length as the mean always, we'd have [math]\displaystyle{ \beta = \sum_i \frac{(u_i - u_{i'})^2 }{2 N \lambda T } }[/math] Andrew Hipp Chromosome and genome size evolution in sedges John Huelsenbeck The growth of Bayesian phylogenetics