Population paths implied by the mean number of pairwise nucleotide differences among mitochondrial DNA sequences

Scenarios, such as populations experiencing a bottleneck or an exponential growth, have been suggested as candidates for explaining the observed differences among mitochondrial DNA sequences in a sample of a given population closed to migrations. Here, population size is considered as capable of varying, and the set of the at least 95% most probable population paths capable of producing the observed mean number of pairwise nucleotide differences is delineated. To do this, the mean and the variance of coalescence times of two genes taken in an n-genes sample with varying population size are expressed. The observed mean coalescence time already echoed a set of population paths due to the variance associated to the coalescent process, but only specific scenarios have been studied, such as the bottleneck or the exponential function. However, mitochondrial DNA data does not reflect a single scenario, after the effect of the variance. These scenarios implied by pairwise nucleotide differences are described through a set-valued function, the 'regulation map', a convenient way to represent temporal population paths.