title: Inferring the demographic history from DNA sequences: An importance sampling approach based on non-homogeneous processes.
abstract: In Ait Kaci Azzou et al. (2015) we introduced an Importance Sampling (IS) approach for estimating the demographic history of a sample of DNA sequences, the skywis plot. More precisely, we proposed a new nonparametric estimate of a population size that changes over time. We showed on simulated data that the skywis plot can work well in typical situations where the effective population size does not undergo very steep changes. In this paper, we introduce an iterative procedure which extends the previous method and gives good estimates under such rapid variations. In the iterative calibrated skywis plot we approximate the effective population size by a piecewise constant function, whose values are re-estimated at each step. These piecewise constant functions are used to generate the waiting times of non homogeneous Poisson processes related to a coalescent process with mutation under a variable population size model. Moreover, the present IS procedure is based on a modified version of the Stephens and Donnelly (2000) proposal distribution. Finally, we apply the iterative calibrated skywis plot method to a simulated data set from a rapidly expanding exponential model, and we show that the method based on this new IS strategy correctly reconstructs the demographic history.
authors.affiliation: ÉMoStA, Département de Mathématiques, Université du Québec à Montréal, Canada. Electronic address: ait_kaci_azzou.sadoune@uqam.ca.
authors.forename: S
authors.initials: S
authors.lastname: Ait Kaci Azzou
authors.affiliation: ÉMoStA, Département de Mathématiques, Université du Québec à Montréal, Canada. Electronic address: larribe.fabrice@uqam.ca.
authors.forename: F
authors.initials: F
authors.lastname: Larribe
authors.affiliation: ÉMoStA, Département de Mathématiques, Université du Québec à Montréal, Canada. Electronic address: froda.sorana@uqam.ca.
authors.forename: S
authors.initials: S
authors.lastname: Froda
mesh_terms: D001483:Base Sequence; D004247:DNA / Q000235:genetics*; D008957:Models, Genetic; D009154:Mutation; D011156:Population Density
chemical_list: D004247:DNA
keywords: Calibrated skywis plot; Coalescent process; Effective population size; Importance sampling; Non-homogeneous processes