Unified Framework to Evaluate Panmixia and Migration Direction among Multiple Sampling Locations
Beerli, Peter, Palczewski, Michal, Genetics
For many biological investigations, groups of individuals are genetically sampled from several geographic locations. These sampling locations often do not reflect the genetic population structure. We describe a framework using marginal likelihoods to compare and order structured population models, such as testing whether the sampling locations belong to the same randomly mating population or comparing unidirectional and multidirectional gene flow models. In the context of inferences employing Markov chain Monte Carlo methods, the accuracy of the marginal likelihoods depends heavily on the approximation method used to calculate the marginal likelihood. Two methods, modified thermodynamic integration and a stabilized harmonic mean estimator, are compared. With finite Markov chain Monte Carlo run lengths, the harmonic mean estimator may not be consistent. Thermodynamic integration, in contrast, delivers considerably better estimates of the marginal likelihood. The choice of prior distributions does not influence the order and choice of the better models when the marginal likelihood is estimated using thermodynamic integration, whereas with the harmonic mean estimator the influence of the prior is pronounced and the order of the models changes. The approximation of marginal likelihood using thermodynamic integration in MIGRATE allows the evaluation of complex population genetic models, not only of whether sampling locations belong to a single panmictic population, but also of competing complex structured population models.
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INVESTIGATIONS using genetic samples from individuals taken across a geographic or biological range- for example, water frogs caught at several ponds, blood samples of humans collected in several villages, or viruses collected from different host species that have the same disease-are common. Whether the individuals studied belong to a single population that is longterm randomly mating or to two or more populations that have varying degrees of genetic isolation from each other is an important concern. Because the geographic information about the locations often does not give a clear indication about the degree of genetic isolation of the individuals, we often use the genetic data themselves to calculate test statistics to suggest whether or not the locations belong to the same population. Many programs (Hudson et al. 1992b; Michalakis and Excoffier 1996; Rousset 1996; Neigel 2002; Weir and Hill 2002; Holsinger et al. 2002) use allele frequencies to calculate FST for pairs of locations or use Fisher's exact test to reject panmixia for the whole or subsets of the data (Raymond and Rousset 1995; Rousset 2008).
Several methods test explicitly whether two populations are or are not panmictic (for example, Hudson et al. 1992a; Rousset 1996). These methods are often applied to all pairs of a multiple-population data set. This is problematic, because both Beerli (2004) and Slatkin (2005) have shown that pairwise analyses can inflate the effective population size estimates, thereby confounding estimators of migration that use the effective number of migrants.
Alternatives to tests based on allele frequencies have been implemented, for example, in the programs STRUCTURE (Pritchard et al. 2000), BAPS (Corander et al. 2008), and STRUCTURAMA (Huelsenbeck and Andolfatto 2007). These methods allow the assignment of individuals to groups using the compatibility of their multilocus genotypes. They can thus be used to group locations into panmictic units on the basis of allele profiles and geography; this capability led to many advancements in landscape genetics and phylogeography. If we are interested in directionality of migration, however, this framework is often insufficient because the assignment methods offer only limited insight into population processes, such as migration, mutation, or fluctuation of population size, that underlie and account for the present genetic structure (Palsbøll et al. …