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 transferability of demographic histories across populations.

Transpacific coalescent pathways of coconut rhinoceros beetle biotypes: Resistance to biological control catalyses resurgence of an old pest

“…Variance was calculated using the script TreemixVarianceExplained.R ( https://github.com) and graphed in r v. 3.2.2 to evaluate the optimal number of migrations necessary to explain the data. We used moments to explore demographic history, population growth patterns and migration in the two distinct Palau populations (Jouganous, Long, Ragsdale, & Gravel, ). A simple demographic model was constructed in moments which estimates the relative time the two populations diverged (T1), effective population sizes (nu1 and nu2) and relative migration rates between the two populations (m12 and m21).…”

Efficiently Inferring the Demographic History of Many Populations With Allele Count Data

“…For D populations, this involves numerically solving a Ddimensional integral. The initial ∂a∂i method in Gutenkunst et al (2009) could handle up to D = 3 populations; subsequent improvements (Lukić and Hey 2012;Jouganous et al 2017) extended this to D = 4 and then D = 5 populations by using spectral representations or alternative basis functions for solving the PDEs.…”

“…To our knowledge, no other method can infer this demographic model using the full SFS. The moments software package (Jouganous et al 2017) is capable of computing the SFS for up to 5 populations, less than the 8 populations here, though it can scale to more individuals per population than momi2. While the fastsimcoal2 software package (Excoffier et al 2013) is capable of handling demographies of this size and larger, it does not compute the full, exact SFS, and also does not include an option for the ascertainment scheme we use here (excluding mutations private to Neanderthal and MA1).…”

“…The joint sample frequency spectrum (SFS) is the multidimensional histogram of mutant allele counts in a sample of DNA sequences and is a popular summary statistic which lies at the core of hundreds of empirical studies in population genetics (see, e.g., Wakeley and Hey 1997;Griffiths and Tavaré 1998;Nielsen 2000;Gutenkunst et al 2009;Coventry et al 2010;Gazave et al 2014;Gravel et al 2011;Nelson et al 2012;Excoffier et al 2013;Jenkins, Mueller, and Song 2014;Bhaskar, Wang, and Song 2015;Jouganous et al 2017). Recently, progress has also been made on theoretical fronts to characterize statistical properties of SFS-based inference.…”

“…However, natural populations are often related by a more complex history that is not tree-like, as gene flow (the exchange of migrants between populations) adds extra edges to the topology associated with the demographic history. In this case, computing the expected SFS is much more computationally demanding, and existing methods for computing the exact expected SFS can scale to only a handful of populations (Gutenkunst et al 2009;Jouganous et al 2017).…”