Skin deep: The decoupling of genetic admixture levels from phenotypes that differed between source populations

Abstract

Objectives: In genetic admixture processes, source groups for an admixed population possess distinct patterns of genotype and phenotype at the onset of admixture. Particularly in the context of recent and ongoing admixture, such differences are sometimes taken to serve as markers of ancestry for individuals-that is, phenotypes initially associated with the ancestral background in one source population are assumed to continue to reflect ancestry in that population. Such phenotypes might possess ongoing significance in social categorizations of individuals, owing in part to perceived continuing correlations with ancestry. However, genotypes or phenotypes initially associated with ancestry in one specific source population have been seen to decouple from overall admixture levels, so that they no longer serve as proxies for genetic ancestry. Here, we aim to develop an understanding of the joint dynamics of admixture levels and phenotype distributions in an admixed population.

Methods: We devise a mechanistic model, consisting of an admixture model, a quantitative trait model, and a mating model. We analyze the behavior of the mechanistic model in relation to the model parameters.

Results: We find that it is possible for the decoupling of genetic ancestry and phenotype to proceed quickly, and that it occurs faster if the phenotype is driven by fewer loci. Positive assortative mating attenuates the process of dissociation relative to a scenario in which mating is random with respect to genetic admixture and with respect to phenotype.

Conclusions: The mechanistic framework suggests that in an admixed population, a trait that initially differed between source populations might serve as a reliable proxy for ancestry for only a short time, especially if the trait is determined by few loci. It follows that a social categorization based on such a trait is increasingly uninformative about genetic ancestry and about other traits that differed between source populations at the onset of admixture.

Keywords: admixture; assortative mating; mechanistic model; population genetics.

Figure 1:

A schematic of an admixture process with positive assortative mating by a phenotype initially correlated with admixture levels. In generation 0, an admixture process begins with females from one population (source 1, left) and males from another (source 2, right). For a quantitative phenotype, source population 1 begins with a high trait value of 6 and source population 2 has a low trait value of 0. Three loci contribute additively to the genetic architecture of the phenotype; each allele derived from source population 1 contributes a value of 1 to the phenotype. The phenotype is represented by the shading of a box. Individuals are depicted as pairs of chromosomes with the ancestral sources of those chromosomes; short vertical lines along the chromosome indicate the three loci that contribute to the phenotype. After generation 1, positive assortative mating by phenotype proceeds in the admixed population. Lines connecting generations are displayed in four colors, representing four mating pairs. Initially, in generation 2, a strong correlation exists between admixture and phenotype $\left(r=0.96\right)$. By generation 4, however, owing to recombination events that stochastically dissociate the trait loci from the overall genetic admixture, the genetic admixture has been decoupled from the phenotype, so that some of the individuals with the highest trait values have among the lowest admixture coefficients for source population 1, and the correlation between phenotype and overall genetic admixture has dissipated $\left(r=-0.09\right)$.

Figure 2:

A schematic diagram of the admixture process. At the founding of the population $\left(g=0\right)$, two isolated source populations produce the first generation of an admixed population $\left(H_1\right)$. In the subsequent generations $\left(g\ge 1\right)$, populations from $S_1$, $S_2$, and $H_g$ provide a parental pool $H_g^{\text{par}}$ at generation $g$ from which the admixed population $H_{g+1}$ at generation $g+1$ is produced. Fractional contributions from three populations in forming the parental pool are $s_{1,g}$, $s_{2,g}$, and $h_g$, respectively. Individuals in the parental pool mate based on mating models described in the “Mating Model” section.

Figure 3:

An example of the quantitative trait model. Here, a diploid individual with $k=8$ trait loci is shown. At each locus i, an allele $L_{ij}$ contributes to the overall trait value if and only if $L_{ij}=X_i$, where $X_i$ is a variable indicating which of two alleles, “0” or “1,” increases the trait value. The total trait value of an individual equals the number of alleles satisfying $L_{ij}=X_i$ across the $k$ trait loci. In this example, the individual has $T=6$.

Figure 4:

Correlation between admixture fraction and quantitative trait value $\left(\text{Cor}\left[H_A,T\right]\right)$ as a function of time. All parameter values in panel (E) follow the base case; the number of quantitative trait loci $k$ and the assortative mating strength $c$ vary across panels. In each panel, for a given $\left(k,c\right)$ pair, for each mating scheme, the mean of 100 simulated trajectories is plotted. The red, blue, and green curves represent results from random mating, assortative mating by admixture fraction, and assortative mating by phenotype, respectively. (A) $k=1$, $c=0.1$. (B) $k=1$, $c=0.5$. (C) $k=1$, $c=1.0$. (D) $k=10$, $c=0.1$. (E) $k=10$, $c=0.5$. (F) $k=10$, $c=1.0$. (G) $k=100$, $c=0.1$. (H) $k=100$, $c=0.5$. (I) k = 100, $c=1.0$.

Figure 5:

Variance of admixture fraction $\left(\text{Var}\left[H_A\right]\right)$ as a function of time. The simulations shown are the same ones from Figure 4. (A) $k=1$, $c=0.1$. (B) $k=1$, $c=0.5$. (C) $k=1$, $c=1.0$. (D) $k=10$, $c=0.1$. (E) $k=10$, $c=0.5$. (F) $k=10$, $c=1.0$. (G) $k=100$, $c=0.1$. (H) $k=100$, $c=0.5$. (I) $k=100$, $c=1.0$. Colors and symbols follow Figure 4. The y-axis is plotted on a logarithmic scale.

Figure 6:

Variance of the phenotype $\left(\text{Var}\left[T\right]\right)$ as a function of time. The simulations shown are the same ones from Figure 4. (A) $k=1$, $c=0.1$. (B) $k=1$, $c=0.5$. (C) $k=1$, c = 1.0. (D) $k=10$, $c=0.1$. (E) $k=10$, $c=0.5$. (F) k = 10, $c=1.0$. (G) $k=100$, $c=0.1$. (H) $k=100$, $c=0.5$. (I) $k=100$, $c=1.0$. Colors and symbols follow Figure 4. The y-axis is plotted on a logarithmic scale.