A new method for estimating the demographic history from DNA sequences: an importance sampling approach.

The effective population size over time (demographic history) can be retraced from a sample of contemporary DNA sequences. In this paper, we propose a novel methodology based on importance sampling (IS) for exploring such demographic histories. Our starting point is the generalized skyline plot with the main difference being that our procedure, skywis plot, uses a large number of genealogies. The information provided by these genealogies is combined according to the IS weights. Thus, we compute a weighted average of the effective population sizes on specific time intervals (epochs), where the genealogies that agree more with the data are given more weight. We illustrate by a simulation study that the skywis plot correctly reconstructs the recent demographic history under the scenarios most commonly considered in the literature. In particular, our method can capture a change point in the effective population size, and its overall performance is comparable with the one of the bayesian skyline plot. We also introduce the case of serially sampled sequences and illustrate that it is possible to improve the performance of the skywis plot in the case of an exponential expansion of the effective population size.