Robust demographic inference from genomic and SNP data

Abstract

We introduce a flexible and robust simulation-based framework to infer demographic parameters from the site frequency spectrum (SFS) computed on large genomic datasets. We show that our composite-likelihood approach allows one to study evolutionary models of arbitrary complexity, which cannot be tackled by other current likelihood-based methods. For simple scenarios, our approach compares favorably in terms of accuracy and speed with ∂a∂i, the current reference in the field, while showing better convergence properties for complex models. We first apply our methodology to non-coding genomic SNP data from four human populations. To infer their demographic history, we compare neutral evolutionary models of increasing complexity, including unsampled populations. We further show the versatility of our framework by extending it to the inference of demographic parameters from SNP chips with known ascertainment, such as that recently released by Affymetrix to study human origins. Whereas previous ways of handling ascertained SNPs were either restricted to a single population or only allowed the inference of divergence time between a pair of populations, our framework can correctly infer parameters of more complex models including the divergence of several populations, bottlenecks and migration. We apply this approach to the reconstruction of African demography using two distinct ascertained human SNP panels studied under two evolutionary models. The two SNP panels lead to globally very similar estimates and confidence intervals, and suggest an ancient divergence (>110 Ky) between Yoruba and San populations. Our methodology appears well suited to the study of complex scenarios from large genomic data sets.

Figure 1. Tested demographic models.

A) One population with bottleneck B) Isolation of two populations with asymmetric migration C) Three population divergence with migration and bottleneck. This model corresponds roughly to a model of human differentiation, where N₁ would be the size of an African population, and T_DIV would correspond to the exit of a population diverging into Asian and European populations growing exponentially and still exchanging migrants at rate m. We assume that the current size of the expanding population is known and equal to 1 million diploids. D) Divergence of two continent-islands. We assume that two Continent-Island systems were created T _CI1 and T _CI2 generations ago, with the youngest continent stemming from one of the island of Continent 2. The parameters of interest are the per generation number of migrant genes (M = 2Nm) from each continent to each island, the age of the continents and the ancestral population size N _A. The island population sizes were set to 500 diploids and M changed due to immigration rates m that could differ for each island.

Figure 2. Three population divergence and growth model.

fastsimcoal2 results are in black and 's results (8/10) are in blue. True parameters values are shown as red dots. fastsimcoal2 required 4–5 h for a single estimation based on 40 ECM cycles over parameters, whereas a run of requires on average 34 hours on a similar CPU.

Figure 3. Hierarchical islands model.

Boxplots showing the distribution parameters estimated from 10 data sets simulated under the same scenario. True parameter values are shown as red dots. fastsimcoal2 required 35–40 hours for a single estimation based on 30 ECM cycles over parameters, using 50 thousand simulations to estimate the expected SFS under a given set of parameters.

Figure 4. Demographic models of four human populations.

A: Simple model of African American (ASW) admixture supposed to have occurred 16 generations ago, with contributions from 3 potential sources (Europeans : CEU; Yoruba: YRI; Luhya: LWK. The European population is assumed to have diverged 2000 generations ago (50 Kya, [28]) from Africa. B1: More realistic demographic scenario (dark grey) of African American admixture and population differentiation, based on continent-island models used to depict spatially arranged populations after range expansions [see e.g. 47]. B2: same as B1 but with an additional possible admixture of Luhya from an unsampled (possibly East African) population. The extra parameters and population of model B2 are shown with a lighter shade of gray and with dashed arrows, respectively. The models and their parameters are further described in the Material and Methods section.

Figure 5. Alternative demographic models for two African populations.

A) Simple model of population divergence. The San and Yoruba populations are assumed to have split from an ancestral African population and to have gone through a recent populations size increase. They also had a single pulse of asymmetrical gene flow (admixture) T_a generations ago. B) More complex scenario, where the San and Yoruba demes belong to two distinct continent-island structures, which have also admixed asymmetrically T_a generations ago. The ancestral Yoruba and San populations would have gone through exponential growth at different times, and have exchanged genes just after their divergence until T_EY generations ago. In both models, we assumed that the Denisova population diverged from the ancestral human population 16,000 generations ago, as estimated in based on an ancestral population size of 10,000 diploids (see Table S11.2 in Suppl. Mat. of ref. [58]). This date would correspond to ≈400,000 years assuming a generation time of 25 y. The models and their parameters are further described in the Material and Methods section.