Inferring the Joint Demographic History of Multiple Populations: Beyond the Diffusion Approximation

Abstract

Understanding variation in allele frequencies across populations is a central goal of population genetics. Classical models for the distribution of allele frequencies, using forward simulation, coalescent theory, or the diffusion approximation, have been applied extensively for demographic inference, medical study design, and evolutionary studies. Here we propose a tractable model of ordinary differential equations for the evolution of allele frequencies that is closely related to the diffusion approximation but avoids many of its limitations and approximations. We show that the approach is typically faster, more numerically stable, and more easily generalizable than the state-of-the-art software implementation of the diffusion approximation. We present a number of applications to human sequence data, including demographic inference with a five-population joint frequency spectrum and a discussion of the robustness of the out-of-Africa model inference to the choice of modern population.

Model‐based detection and analysis of introgressed Neanderthal ancestry in modern humans

“…The size of the population ancestral to modern humans after the expansion and the size of the African population are set to N = 23,000. These sizes are consistent with the estimates provided by Jouganous, Long, Ragsdale, and Gravel (). The size of the non‐African population after the split is set to N = 2,000.…”

“…The more recent small size will have a stronger impact on genetic variation than the larger ancestral size. Several studies (Jouganous et al, 2017) report a strong population bottleneck in European and Asian populations after the out-of-Africa event, followed by rapid exponential population growth, and Sankararaman et al (2014) incorporate this into their demographic model. As we will detail later, our method considers each non-African haplotype one at a time.…”

“…Following Pr€ ufer et al (2014), we set the time of divergence between modern humans and Neanderthals, T nean , to 26,000 generations ago, which corresponds to 650 kya, assuming a generation time of 25 years, and the time that the population ancestral to modern humans expands is set to 12,000 generations ago (Jouganous et al, 2017). The split between African and Non-African T div is set to 4,000 generations ago, or 100 kya (Scally & Durbin, 2012), and the time of the introgression or admixture event T admix is set to 2,000 generations ago (Sankararaman, Patterson, Li, P€ a€ abo, & Reich, 2012), which corresponds to 50 kya (Pr€ ufer et al, 2014).…”

Genomic signatures of sympatric speciation with historical and contemporary gene flow in a tropical anthozoan (Hexacorallia: Actiniaria)

“…We used the allele frequency spectrum (AFS), coalescent simulations, and ordinary differential equations to provide empirical support that the pattern of cryptic species-level diversity we detect using our ddRADseq data set most probably arose in sympatry. We used two approaches: (a) A coalescent approach using the program fastsimcoal2 (FSC2; Excoffier, Dupanloup, Huerta-Sánchez, Sousa, & Foll, 2013), and (b) an ordinary differential equations approach using Moments (Jouganous, Long, Ragsdale, & Gravel, 2017). Both approaches calculate the composite likelihood of arbitrarily complex demographic models under a given AFS.…”

Speciation and gene flow across an elevational gradient in New Guinea kingfishers

“…We inferred the demographic history of diverging lineages using moments v.1.0.0, which uses ordinary differential equations to model the evolution of allele frequencies (Jouganous et al, 2017). We used moments to calculate a folded joint site frequency spectrum (JSFS) using a SNP dataset that included only whole genome sequencing data, a minimum minor allele count of 1, no more than 10% missing data per site, a minimum depth of 6x per individual, and a minimum quality score of 30.…”