Multiple-merger coalescents - suitable models for gene genealogies in real populations?

• Applicant: Dr. Fabian Freund
• Subject Area: Mathematics
• Term: from 2015 to 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 284099193

To assess which evolutionary forces have acted on a real population, one can compare the observed genetic diversity in a sample with its distribution under one or several theoretical models for possible evolutionary histories of the population. Such models include a model of the sample's genealogy. For a single selectively neutral genetic locus without recombination, the standard genealogy model is Kingman's n-coalescent if the sample of size n is taken form a randomly mating population with fixed size, much higher than the sample size. Kingman's n-coalescent is a random bifurcating tree with n leaves. This genealogy model can be extended e.g. to account for population size fluctuations in the past or for population subdivision while still being a bifurcating tree. However, theoretical models for populations with properties like reproduction sweepstakes or rapid selection will lead to multifurcating random trees as genealogies of a sample called multiple-merger n-coalescents.The main goal of this project is to assess whether samples from real populations which have properties where theoretical models predict multiple-merger n-coalescents genealogies are actually fitting better to these models than to extended Kingman's n-coalescents based on the observed genetic diversity. Several statistical methods have been proposed to distinguish between multiple-merger n-coalescents and the (extended) Kingman's n-coalescent (gene tree maximum likelihood, approximate Bayesian computation (ABC), approximate likelihood and an approach using a minimum-distance statistic, the latter three based on the site frequency spectrum of the sample). Further aims of this project are to refine and extend the ABC inference method and to investigate whether using statistics based on other genetic information than the site frequency spectrum can improve inference capacity. The inference capacity of the available inference methods will be compared via simulation for different genealogy model comparisons to identify the best method for a given comparison of different n-coalescents as genealogy models. To assess the main goal, first populations that might be linked to multiple-merger genealogies are identified. For these, specific multiple-merger n-coalescents and (extended) Kingman's n-coalescents (biologically reasonable alternative models) are used as potential genealogy models. For these models, inference for the best model is performed following the inference protocol established before. The inference results are then discussed in the light of known properties of the populations.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1590: Probabilistic Structures in Evolution