# Joshua Plotkin : Generalized Markov models in population genetics

Population geneticists study the dynamics of alternative genetic types in a replicating population. Most theoretical work rests on a simple Markov chain, called the Wright-Fisher model, to describe how an allele's frequency changes from one generation to the next. We have introduced a broad class of Markov models that share the same mean and variance as the Wright-Fisher model, but may otherwise differ. Even though these models all have the same variance effective population size, they encode a rich diversity of alternative forms of genetic drift, with significant consequences for allele dynamics. We have characterized the behavior of standard population-genetic quantities across this family of generalized models. The generalized population models can produce startling phenomena that differ qualitatively from classical behavior -- such as assured fixation of a new mutant despite the presence of genetic drift. We have derived the forward-time continuum limits of the generalized processes, analogous to Kimura's diffusion limit of the Wright-Fisher process. Finally, we have shown that some of these exotic models are more likely than the Wright-Fisher model itself, given empirical data on genetic variation in Drosophila populations. Joint work with Ricky Der and Charlie Epstein.

**Category**: Mathematical Biology**Duration**: 01:14:56**Date**: April 20, 2012 at 11:55 AM**Views**: 123-
**Tags:**seminar, Mathematical Biology Seminar

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