Theoretical expectations of the Isolation–Migration model of population evolution for inferring demographic parameters

Abstract

Summary1. The Bayesian inference of demographic parameters under an Isolation-Migration (IM) model of population evolution offers a major improvement over previously available approaches. This method is implemented in a popular program, IMa, widely used in population genetic studies. 2. While the robustness of the method to deviations of the IM model has previously been evaluated, we assess the performance of the program with two populations when the model used to generate the analysed data meets the assumptions of the IM model completely; the goal is to identify the conditions under which the method works best. Overall, we test eighteen sets of conditions and analyse AE 500 simulated data sets, for a total of over 200,000 hours of analyses using a large computer cluster. 3. Although we find clear differences in quality estimates among models, the best ranges of demographic parameter values to infer accurate estimates differ among parameters. Divergence time is best estimated in the absence of gene flow and when population sizes are large compared to divergence time. In contrast, the classic population parameter ϑ (= 4Nl) is best estimated, for the two current populations, when divergence time is large compared to population size, with or without migration. The parameter is always poorly estimated in the case of the ancestral population. While it is possible to distinguish between scenarios with or without gene flow, estimating the extent of gene flow, when different from 0, is associated with relatively high error rates. In general, increasing the number of loci or the sample size reduces the variance and credible interval of the estimates, and only for the migration rate, it slightly improves the accuracy of the estimate as well. Increasing the prior distribution range of a parameter can dramatically increase that of its posterior distribution. Surprisingly, differences are highlighted among the estimates inferred from sequences generated by different simulation programs, especially for the simulation program SIMDIV. 4. Overall, the performances of the method shown here probably reflect the limitation of the method in general and/or of the historical information contained in DNA sequence data.

Demographic and genetic approaches to study dispersal in wild animal populations: A methodological review

“…Violations of these assumptions have been shown to bias estimates of gene flow (Becquet & Przeworski, ; Strasburg & Rieseberg, ). False‐positive rates were found when testing for the presence of migration using likelihood ratio tests in small data set (~5–50 loci of 2,500 bp) and low divergence time (Cruickshank & Hahn, ) or small number of sample sites (Quinzin, Mayer, Elvinger, & Mardulyn, ). Two other important limitations of IM model are the assumption of a constant effective deme size and the inability to fit more complex and realistic models, including those with secondary contacts.…”

Population divergence time estimation using individual lineage label switching

“… Strasburg and Rieseberg (2010) highlighted that assumption misspecification can lead the program IM ( Hey 2010 ) to deliver biased answers. Recently, Quinzin et al (2015) evaluated the program IM and observed that divergence time estimates are more accurate if migration is low and if the populations are large compared to the divergence time. We find similar patterns with Migrate and IMa2p .…”

Inter-glacial isolation caused divergence of cold-adapted species: the case of the snow partridge

“…Because either model is not flawless, we integrated the divergence time calculated by the 2 models. In the IM model, the divergence time is best estimated in the scenario of gene flow equals to zero ( Quinzin et al 2015 ), and in the gene flow case the coalescent time of the samples predate the divergence time ( Wilkinson-Herbots 2008 ), so we put the divergence time estimated by IM as the right boundary. The “complete isolation” model does not consider gene flow, the divergence time estimated by *Beast may posterior to the divergence time ( Wilkinson-Herbots 2008 ), so we put it as the left boundary.…”