Joint Inference of Population Assignment and Demographic History

Abstract

A new approach to assigning individuals to populations using genetic data is described. Most existing methods work by maximizing Hardy-Weinberg and linkage equilibrium within populations, neither of which will apply for many demographic histories. By including a demographic model, within a likelihood framework based on coalescent theory, we can jointly study demographic history and population assignment. Genealogies and population assignments are sampled from a posterior distribution using a general isolation-with-migration model for multiple populations. A measure of partition distance between assignments facilitates not only the summary of a posterior sample of assignments, but also the estimation of the posterior density for the demographic history. It is shown that joint estimates of assignment and demographic history are possible, including estimation of population phylogeny for samples from three populations. The new method is compared to results of a widely used assignment method, using simulated and published empirical data sets.T HE assignment of individuals to populations is a common population genetic application (Paetkau et al. 1995;Rannala and Mountain 1997;Pritchard et al. 2000;Dawson and Belkhir 2001;Corander et al. 2003;Baudouin et al. 2004;Guillot et al. 2005;François et al. 2006;Pella and Masuda 2006;Wu et al. 2006;Huelsenbeck and Andolfatto 2007;Zhang 2008;Reeves and Richards 2009). Most methods assume random mating within populations and free recombination between loci to find population assignments that minimize the amount of departure from Hardy-Weinberg equilibrium (HWE) and linkage equilibrium (LE) within populations. The population assignment with the highest likelihood, or highest posterior probability under Bayesian approaches, is taken as the assignment estimate. Generally the true allele frequencies are not known so that methods must either make use of estimated allele frequencies (e.g., Grant et al. 1980) or consider the range of possible allele frequencies (e.g., Pritchard et al. 2000).Methods based on minimizing departure from HWE and LE typically offer little accommodation for the different potential causes of differentiation between populations. They allow populations to differ in allele frequencies, but they do so without including explicit evolutionary models of demography and mutation that cause such differences (Waples and Gaggiotti 2006;Listman et al. 2007). For example, it is possible that a method based on departures from HWE and LE will provide better estimates when divergence arises under an island model than when a similar amount of divergence arises under a phylogenetic branching model or vice versa. To assess such dependencies methods must be run on data simulated under various kinds of demographic histories. Without demographic history as a part of the model implemented in a method, such simulation studies tend to treat the computer program as a "black box" that can reveal interactions between demography and assignment only when observed in operation under ...

Phylogeographic studies of plants in China: Advances in the past and directions in the future

“…Second, new tools have been developed and widely used to measure gene flow between diverging species (Nielsen & Wakeley, 2001; Pinho & Hey, 2010). For example, the isolation and migration (IM) model and the corresponding calculations can be extended to the multiple‐loci data (Hey & Nielsen, 2004) and multiple populations (Hey & Nielsen, 2007; Hey, 2010; Choi & Hey, 2011). In contrast to the likelihood realization, Wegmann & Excoffier (2010) presented a novel attempt to infer demographic history included in the IM model parameters using the approximate Bayesian computation (ABC) procedure.…”

Identifying Loci Under Selection Against Gene Flow in Isolation-with-Migration Models

“…Mean assignment: Although it would not be meaningful to take an arithmetic average of sampled assignments, we can use the idea of "mean assignment", a, which is the vector that minimizes the squared partition distance to all of the sampled vectors (Huelsenbeck and Andolfatto 2007;Choi and Hey 2011;Onogi et al 2011). The partition distance is defined as the minimum number of elements that must be removed to make two assignment vectors identical, over all possible labeling of one of the vectors (Gusfield 2002).…”

“…Because the minimum is taken over possible labelings, the mean assignment is not sensitive to label switching. The mean assignment computation was implemented by adapting the mean partition functions from Onogi et al (2011) and Choi and Hey (2011).…”

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