The IICR (inverse instantaneous coalescence rate) as a summary of genomic diversity: insights into demographic inference and model choice

The availability of complete human genome sequences from populations across the world has given rise to new population genetic inference methods that explicitly model their ancestral relationship under recombination and mutation. So far, application of these methods to evolutionary history more recent than 20-30 thousand years ago and to population separations has been limited. Here we present a new method that overcomes these shortcomings. The Multiple Sequentially Markovian Coalescent (MSMC) analyses the observed pattern of mutations in multiple individuals, focusing on the first coalescence between any two individuals. Results from applying MSMC to genome sequences from nine populations across the world suggest that the genetic separation of non-African ancestors from African Yoruban ancestors started long before 50,000 years ago, and give information about human population history as recently as 2,000 years ago, including the bottleneck in the peopling of the Americas, and separations within Africa, East Asia and Europe.

We consider the distribution of pairwise sequence differences of mitochondrial DNA or of other nonrecombining portions of the genome in a population that has been of constant size and in a population that has been growing in size exponentially for a long time. We show that, in a population of constant size, the sample distribution of pairwise differences will typically deviate substantially from the geometric distribution expected, because the history of coalescent events in a single sample of genes imposes a substantial correlation on pairwise differences. Consequently, a goodness-of-fit test of observed pairwise differences to the geometric distribution, which assumes that each pairwise comparison is independent, is not a valid test of the hypothesis that the genes were sampled from a panmictic population of constant size. In an exponentially growing population in which the product of the current population size and the growth rate is substantially larger than one, our analytical and simulation results show that most coalescent events occur relatively early and in a restricted range of times. Hence, the "gene tree" will be nearly a "star phylogeny" and the distribution of pairwise differences will be nearly a Poisson distribution. In that case, it is possible to estimate r, the population growth rate, if the mutation rate, mu, and current population size, N0, are assumed known. The estimate of r is the solution to ri/mu = ln(N0r) - gamma, where i is the average pairwise difference and gamma approximately 0.577 is Euler's constant.

Many coalescent-based methods aiming to infer the demographic history of populations assume a single, isolated and panmictic population (i.e. a Wright-Fisher model). While this assumption may be reasonable under many conditions, several recent studies have shown that the results can be misleading when it is violated. Among the most widely applied demographic inference methods are Bayesian skyline plots (BSPs), which are used across a range of biological fields. Violations of the panmixia assumption are to be expected in many biological systems, but the consequences for skyline plot inferences have so far not been addressed and quantified. We simulated DNA sequence data under a variety of scenarios involving structured populations with variable levels of gene flow and analysed them using BSPs as implemented in the software package BEAST. Results revealed that BSPs can show false signals of population decline under biologically plausible combinations of population structure and sampling strategy, suggesting that the interpretation of several previous studies may need to be re-evaluated. We found that a balanced sampling strategy whereby samples are distributed on several populations provides the best scheme for inferring demographic change over a typical time scale. Analyses of data from a structured African buffalo population demonstrate how BSP results can be strengthened by simulations. We recommend that sample selection should be carefully considered in relation to population structure previous to BSP analyses, and that alternative scenarios should be evaluated when interpreting signals of population size change.