Robust Estimates of Divergence Times and Selection with a Poisson Random Field Model: A Case Study of Comparative Phylogeographic Data

Abstract

Mutation frequencies can be modeled as a Poisson random field (PRF) to estimate speciation times and the degree of selection on newly arisen mutations. This approach provides a quantitative theory for comparing intraspecific polymorphism with interspecific divergence in the presence of selection and can be used to estimate population genetic parameters. Although the original PRF model has been extended to more general biological settings to make statistical inference about selection and divergence among model organisms, it has not been incorporated into phylogeographic studies that focus on estimating population genetic parameters for nonmodel organisms. Here, we modified a recently developed time-dependent PRF model to independently estimate genetic parameters from a nuclear and mitochondrial DNA data set of 22 sister pairs of birds that have diverged across a biogeographic barrier. We found that species that inhabit humid habitats had more recent divergence times and larger effective population sizes than those that inhabit drier habitats, and divergence time estimated from the PRF model were similar to estimates from a coalescent species-tree approach. Selection coefficients were higher in sister pairs that inhabited drier habitats than in those in humid habitats, but overall the mitochondrial DNA was under weak selection. Our study indicates that PRF models are useful for estimating various population genetic parameters and serve as a framework for incorporating estimates of selection into comparative phylogeographic studies.A range of analytical approaches have been developed to estimate divergence times and effective population sizes from DNA data (Takahata et al. 1995;Yang 1997Yang , 2002Hickerson et al. 2003;Rannala and Yang 2003;Hey and Nielsen 2004;Heled and Drummond 2010). These types of models have been applied to an array of empirical systems and used to reconstruct population history (e.g., Jennings and Edwards 2005;Won and Hey 2005;Lee and Edwards 2008;Hurt et al. 2009;Hailer et al. 2012), but the extension of these analyses to incorporate selection has been limited. A potential means of including selection estimates into studies examining population or phylogeographic history is the implementation of approaches that compare polymorphic and fixed nucleotide patterns within and between species (Hudson et al. 1987). Using this method, McDonald and Kreitman (1991) proposed a statistical test for homogeneity of synonymous and nonsynonymous DNA mutations among closely related species and demonstrated that an excess of nonsynonymous differences among fruit fly species was the result of the fixation of beneficial mutations.The McDonald-Kreitman test was extended and incorporated into a quantitative model used to compare intraspecific polymorphism with interspecific divergence by modeling mutation frequencies as a Poisson random field (PRF) (Sawyer and Hartl 1992). The PRF models the number of synonymous and nonsynonymous fixed differences and polymorphic sites as independent Poisson random varia...

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