Inferring the Demographic History of Inbred Species from Genome-Wide SNP Frequency Data

Abstract

Demographic inference using the site frequency spectrum (SFS) is a common way to understand historical events affecting genetic variation. However, most methods for estimating demography from the SFS assume random mating within populations, precluding these types of analyses in inbred populations. To address this issue, we developed a model for the expected SFS that includes inbreeding by parameterizing individual genotypes using beta-binomial distributions. We then take the convolution of these genotype probabilities to calculate the expected frequency of biallelic variants in the population. Using simulations, we evaluated the model's ability to coestimate demography and inbreeding using one- and two-population models across a range of inbreeding levels. We also applied our method to two empirical examples, American pumas (Puma concolor) and domesticated cabbage (Brassica oleracea var. capitata), inferring models both with and without inbreeding to compare parameter estimates and model fit. Our simulations showed that we are able to accurately coestimate demographic parameters and inbreeding even for highly inbred populations (F = 0.9). In contrast, failing to include inbreeding generally resulted in inaccurate parameter estimates in simulated data and led to poor model fit in our empirical analyses. These results show that inbreeding can have a strong effect on demographic inference, a pattern that was especially noticeable for parameters involving changes in population size. Given the importance of these estimates for informing practices in conservation, agriculture, and elsewhere, our method provides an important advancement for accurately estimating the demographic histories of these species.

Keywords: conservation; demography; domestication; inbreeding; site frequency spectrum.

Fig. 1.

Comparison of expected spectra for F = 0.5, 0.75, and 0.9 between $\partial a\partial i$ (dark gray) and SLiM (light gray) for the equilibrium and bottleneck+growth models.

Fig. 2.

(a) Estimates of F from data generated with SLiM for the bottleneck and growth model (lower) plus an illustration of the model (upper). In this model, N_A is the ancestral population size, ν₀ is the size of the bottleneck (proportion of N_A remaining after population reduction), and T is the amount of time for the population to recover back to a size of N_A. (b) Estimates of F from data generated with SLiM for the divergence with one-way migration model (lower) plus an illustration of the model (upper). N_A in this model is the same as the bottleneck model, ν₂ is the size of the diverging population (again a proportion of N_A), T is the divergence time between populations, and M₂₁ is the one-way migration rate of individuals from population one into population two.

Fig. 3.

The observed joint site frequency spectrum for Puma concolor in Texas and Florida, along with the model fit and residuals, for models with inbreeding (middle) and without inbreeding (right). Residuals for each model are plotted below their expected spectra and a cartoon representation of the proposed demographic model is given in the bottom left.

Fig. 4.

The observed site frequency spectrum for Brassica oleracea var. capitata, along with the model fit (light gray) and residuals (bottom panels), for models with inbreeding (middle) and without inbreeding (right). On the left is a cartoon of the proposed demographic model with parameters labeled.