User:Carl Boettiger/Notebook/Comparative Phylogenetics/2010/06/27
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Evolution 2010 Day 2
Tests common macroscopic models of inferring population structure (i.e. via coalescent) an individual based simulation model.
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 purebirth (or constant birthdeath) model. For instance:
Well, if the branch length Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle v_{ii'} } is exponentially distributed with parameter Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \lambda }
If we simply estimated the branch length as the mean always, we'd have Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \beta = \sum_i \frac{(u_i  u_{i'})^2 }{2 N \lambda T } }
