Simultaneous inference of parental admixture proportions and admixture times from unphased local ancestry calls

Abstract

Population genetic analyses of local ancestry tracts routinely assume that the ancestral admixture process is identical for both parents of an individual, an assumption that may be invalid when considering recent admixture. Here, we present Parental Admixture Proportion Inference (PAPI), a Bayesian tool for inferring the admixture proportions and admixture times for each parent of a single admixed individual. PAPI analyzes unphased local ancestry tracts and has two components: a binomial model that leverages genome-wide ancestry fractions to infer parental admixture proportions and a hidden Markov model (HMM) that infers admixture times from tract lengths. Crucially, the HMM accounts for unobserved within-ancestry recombination by approximating the pedigree crossover dynamics, enabling inference of parental admixture times. In simulations, we find that PAPI's admixture proportion estimates deviate from the truth by 0.047 on average, outperforming ANCESTOR and PedMix by 46.0% and 57.6%, respectively. Moreover, PAPI's admixture time estimates were strongly correlated with the truth (R=0.76) but have an average downward bias of 1.01 generations that is partly attributable to inaccuracies in local ancestry inference. As an illustration of its utility, we ran PAPI on African American genotypes from the PAGE study (N = 5,786) and found strong evidence of assortative mating by ancestry proportion: couples' ancestry proportions are highly correlated (R = 0.87) and are closer to each other than expected under random mating (p < 10^-6). We anticipate that PAPI will be useful in studying the population dynamics of admixture and will also be of interest to individuals seeking to learn about their personal genealogies.

Keywords: admixture; assortative mating; local ancestry.

Figure 1

Example pedigree and local ancestry data (A) Pedigree with vertical bars next to each individual representing two of their chromosomes, each colored to represent local ancestry from two populations, blue and green. t_A and t_B are the number of generations to the unadmixed ancestors for parents A and B, respectively; this is the generation in which at least one couple contains individuals of different ancestries. (B) PAPI takes in unphased local ancestry tracts denoted by x_i = (l_i, a_i). The image depicts a particular phasing of the data with labels that correspond to the observed unphased data.

Figure 2

Markovian approximation to an individual’s full pedigree Example pedigree for an admixed individual (left). Viewing the unadmixed ancestors as a pool of founder haplotypes (right), one for each parent, and further viewing recombinations as a Markovian switching process in this pool motivates the use of a single-pulse migration model to capture the effect of t_j and p_j on the observed between-ancestry Poisson switch rates ${\lambda }_{\mathit{j}}^0$ and ${\lambda }_{\mathit{j}}^1$.

Figure 3

Deviance statistics in simulated data for inferred parent ancestry proportions $\left({\mathit{p}}_{\mathit{A}},{\mathit{p}}_{\mathit{B}}\right)$ from PedMix, ANCESTOR, and PAPI (A) Average absolute deviances (d_abs,p) on all scenario 1 and 2 data. (B and C) Absolute deviances for data points where (B) t_A = t_B = 5 and (C) t_A = 9 and t_B = 5. (D and E) Average absolute deviance on all scenario 3 data. (D) PAPI estimates the ground truth near perfectly when $\mathit{E}\left[\left({\mathit{p}}_{\mathit{A}},{\mathit{p}}_{\mathit{B}}\right)\right]\in \left\{\left(1,0\right),\left(0,0\right),\left(1,1\right)\right\}$ and (E) ANCESTOR and PedMix outperform PAPI when $\mathit{E}\left[\left({\mathit{p}}_{\mathit{A}},{\mathit{p}}_{\mathit{B}}\right)\right]=\left(0.5,0.5\right)$ but PAPI’s deviance is low when $\mathit{E}\left[\left({\mathit{p}}_{\mathit{A}},{\mathit{p}}_{\mathit{B}}\right)\right]=\left(0,0.5\right)$.

Figure 4

PAPI and ANCESTOR’s parent ancestry proportion estimates for the HapMap ASW trio children Scatter plots of estimated versus true parent ancestry proportions for (A) PAPI’s full model and (B) ANCESTOR.

Figure 5

PAPI’s estimated time since admixture in simulated individuals (A and B) Box plots of estimated times based on HAPMIX local ancestry tracts for (A) scenario 1 samples (where ${\mathit{t}}_{\mathit{A}}>{\mathit{t}}_{\mathit{B}}$) and (B) scenario 2 data (where t_A = t_B). (C and D) Estimated times based on exact local ancestry tracts for (C) scenario 1 and (D) scenario 2 individuals. In (A) and (C), the x-axis gives the true t_B since t_A is held fixed in these cases. Blue and orange dashed lines represent the simulation ground truths for t_A and t_B, respectively in (A) and (C), while the red dashed lines in (B) and (D) represent the simulation ground truths for t_A and t_B.

Figure 6

PAPI’s estimated time since admixture with two migrant pulses Plots show estimated time since admixture versus q (the proportion of couples in the ${\mathit{t}}_{\mathit{j}}^{\mathit{e}}$ generation with unadmixed individuals of different ancestries) when ${\mathit{t}}_{\mathit{j}}^{\mathit{e}}=9$ and ${\mathit{t}}_{\mathit{j}}^{\mathit{l}}=7$ for (A) $\mathit{E}\left[{\mathit{p}}_{\mathit{j}}\right]=0.25$ and (B) $\mathit{E}\left[{\mathit{p}}_{\mathit{j}}\right]=0.5$. The blue lines depict the least-squares regressions on the plotted data points.

Figure 7

PAPI analyses from African Americans in the BioMe Biobank subset of PAGE (A) Distribution of the parent ancestry estimates (both p_A and p_B plotted separately) in these African Americans. (B) Distribution of time since admixture estimates (t_A and t_B plotted separately). (C) Heatmap of the ancestry proportions of couples (p_A, p_B) ordered as (p_max, p_min). (D) Distribution of $\left|{\mathit{p}}_{\mathit{A}}-{\mathit{p}}_{\mathit{B}}\right|$ estimates from the real couples along with a permuted distribution.