On the importance of being structured: instantaneous coalescence rates and human evolution--lessons for ancestral population size inference?

Most species are structured and influenced by processes that either increased or reduced gene flow between populations. However, most population genetic inference methods assume panmixia and reconstruct a history characterized by population size changes. This is potentially problematic as population structure can generate spurious signals of population size change through time. Moreover, when the model assumed for demographic inference is misspecified, genomic data will likely increase the precision of misleading if not meaningless parameters. For instance, if data were generated under an n-island model (characterized by the number of islands and migrants exchanged) inference based on a model of population size change would produce precise estimates of a bottleneck that would be meaningless. In addition, archaeological or climatic events around the bottleneck's timing might provide a reasonable but potentially misleading scenario. In a context of model uncertainty (panmixia versus structure) genomic data may thus not necessarily lead to improved statistical inference. We consider two haploid genomes and develop a theory that explains why any demographic model with structure will necessarily be interpreted as a series of changes in population size by inference methods ignoring structure. We formalize a parameter, the inverse instantaneous coalescence rate, and show that it is equivalent to a population size only in panmictic models, and is mostly misleading for structured models. We argue that this issue affects all population genetics methods ignoring population structure which may thus infer population size changes that never took place. We apply our approach to human genomic data.

Compound Poisson approximation and testing for gene clusters with multigene families.

We present in this article a compound Poisson approximation for computing probabilities involved in significance tests for conserved genomic regions between different species. We consider the case when the conserved genomic regions are found by the reference region approach. An important aspect of our computations is the fact that we are taking into account the existence of multigene families. We obtain convergence results for the error of our approximation by using the Stein-Chen method for compound Poisson approximation.