http://arxiv.org/abs/1402.2424

Can one hear the shape of a population history?

Junhyong Kim, Elchanan Mossel, Miklós Z. Rácz, Nathan Ross (Submitted on 11 Feb 2014)

Reconstructing past population size from present day genetic data is a major goal of population genetics. Recent empirical studies infer population size history using coalescent-based models applied to a small number of individuals. While it is known that the allelic spectrum is not sufficient to infer the population size history, the distribution of coalescence times is. Here we provide tight bounds on the amount of information needed to recover the population size history at a certain level of accuracy assuming data given either by exact coalescence times, or given blocks of non-recombinant DNA sequences whose loci have approximately equal times to coalescence. Importantly, we prove lower bounds showing that it is impossible to accurately deduce population histories given limited data.