Blockbuster meets the theoretical limit of genome-wide SFS-based inference of recent demography

1 The molecular diversity of a sample of DNA sequences from the same species is traditionally summarized by the so-called Site Frequency Spectrum (SFS). Past variations in population size leave a trace in the shape of this histogram that several popular programs leverage to infer demography. The ability of inference methods using genome-wide SFS to document recent demography for conservation purposes needs to be evaluated both theoretically and practically. Assuming population size is piecewise constant, we predict analytically that the date of the most recent demographic change that leaves a statistically detectable trace in the SFS is on the order of generations, where n is the sample size and N is the effective population size before the change. We further show that robust parameter estimation is achieved at N 3 / 4 /n generations for both the date and intensity of the most recent change. We release Blockbuster , a deterministic program that reliably infers a demographic scenario with piecewise-constant population size through time from a genome-wide SFS. Blockbuster consistently outperforms recent similar programs in accuracy, robustness, and computational time. More importantly, it reaches the theoretical limit on the most recent demographic changes. Finally, we propose a simple yet efficient method to circumvent the presence of population structure, a well-known and pervasive complication that prevents reliable inference of demographic history.