The impact of population demography and selection on the genetic architecture of complex traits

Abstract

Population genetic studies have found evidence for dramatic population growth in recent human history. It is unclear how this recent population growth, combined with the effects of negative natural selection, has affected patterns of deleterious variation, as well as the number, frequency, and effect sizes of mutations that contribute risk to complex traits. Because researchers are performing exome sequencing studies aimed at uncovering the role of low-frequency variants in the risk of complex traits, this topic is of critical importance. Here I use simulations under population genetic models where a proportion of the heritability of the trait is accounted for by mutations in a subset of the exome. I show that recent population growth increases the proportion of nonsynonymous variants segregating in the population, but does not affect the genetic load relative to a population that did not expand. Under a model where a mutation's effect on a trait is correlated with its effect on fitness, rare variants explain a greater portion of the additive genetic variance of the trait in a population that has recently expanded than in a population that did not recently expand. Further, when using a single-marker test, for a given false-positive rate and sample size, recent population growth decreases the expected number of significant associations with the trait relative to the number detected in a population that did not expand. However, in a model where there is no correlation between a mutation's effect on fitness and the effect on the trait, common variants account for much of the additive genetic variance, regardless of demography. Moreover, here demography does not affect the number of significant associations detected. These findings suggest recent population history may be an important factor influencing the power of association tests and in accounting for the missing heritability of certain complex traits.

Figure 1. Models of population size changes over time.

(A) A model of European population history with a severe bottleneck starting 2000 generations ago (BN). (B) A similar model of European population history as shown in (A), except that here the population instantaneously expanded 100-fold 80 generations ago (BN+growth). (C) A model with a 2-fold ancient expansion (Old growth). This is a possible model for African population history.

Figure 2. Changes in genetic variation over time as a function of population size.

Solid orange lines denote the bottlenecked population that did not recently expand (BN). Dashed green lines denote a population that expanded 80 generations ago (BN+growth). Note that the lines from the two populations overlap except in the last 80 generations. Dashed purple lines denote the population that underwent an ancient expansion (Old growth). (A) Number of synonymous SNPs segregating in the sample. (B) Number of nonsynonymous SNPs segregating in the sample. (C) Proportion of SNPs segregating in the sample that are nonsynonymous. (D) Absolute value of the average fitness effect of nonsynonymous SNPs segregating in the sample. Samples of 1000 chromosomes were taken at different time points throughout the simulation. Results are averaged over 1000 simulation replicates.

Figure 3. Effect of recent population growth on the heritability attributable to mutations of different ages when τ = 0.5.

Orange boxes denote the bottlenecked population that did not recently expand (BN). Green boxes denote a population that expanded 80 generations ago (BN+growth). “Before bottleneck” refers to mutations that arose more than 1960 generations ago (before or during the bottleneck). “After bottleneck” refers to mutations that arose after the population recovered from the bottleneck, but earlier than 80 generations ago. “After growth” refers to mutations that arose within the last 80 generations (after the population expanded). (A) Heritability attributed to mutations of different ages. Note that recent population growth does not affect the median heritability attributable to mutations of different ages. (B) Number of SNPs segregating in the present-day that arose during the different time intervals. (C) Mean allele frequency of SNPs that are segregating in the present-day that arose during the different time intervals. (D) Mean effect size of SNPs that are segregating in the present-day that arose during the different time intervals. Here and M = 70 kb.

Figure 4. Cumulative distribution of the amount of the additive genetic variance of a trait (V_A; y-axis) explained by SNPs segregating below a given frequency in the population (x-axis).

(A) A SNP's effect on the trait is correlated with its effect on fitness (τ = 0.5). Note that the population that experienced recent growth (green; BN+growth) has a higher proportion of V_A accounted for by low-frequency SNPs (<0.1% frequency) than the populations that did not recently expand (orange and purple; BN and Old growth). (B) A SNP's effect on the trait is independent of its effect on fitness (τ = 0). Note that less of V_A is accounted for by low-frequency variants than when the trait is correlated with fitness (A). Here and M = 70 kb.

Figure 5. The number of causal variants in a sample of 1000 cases from each simulated population.

(A) A SNP's effect on the trait is correlated with its effect on fitness (τ = 0.5). Note that the population that experienced recent growth (green; BN+growth) has a higher number of causal variants than the population that did not recently expand (orange; BN). (B) A SNP's effect on the trait is independent of its effect on fitness (τ = 0). Here and M = 70 kb.

Figure 6. Cumulative distribution of the amount of the phenotypic variance of a trait (V_P; y-axis) explained by the SNPs that explain the most variance (x-axis).

(A) A SNP's effect on the trait is correlated with its effect on fitness (τ = 0.5). Note that the top SNPs that account for the most variance explain less of it in the population that experienced recent growth (green; BN+growth) than in the populations that did not recently expand (orange and purple; BN and Old growth). (B) A SNP's effect on the trait is independent of its effect on fitness (τ = 0). Here and M = 70 kb.

Figure 7. The number of causal SNPs with a significant P-value (<1×10⁻⁵) in the single-marker association test for different models of population history.

(A) A SNP's effect on the trait is correlated with its effect on fitness (τ = 0.5). (B) A SNP's effect on the trait is independent of its effect on fitness (τ = 0). Here and M = 70 kb.

Figure 8. Cumulative distribution of the amount of the additive genetic variance of a trait (V_A; y-axis) explained by SNPs with a single-marker association test P-value less than a given threshold (x-axis).

(A) A SNP's effect on the trait is correlated with its effect on fitness (τ = 0.5). Note that the population that experienced recent growth (green line; BN+growth) has a lower proportion of V_A accounted for by SNPs at any P-value threshold than the populations that did not recently expand (orange and purple lines; BN and Old growth). (B) A SNP's effect on the trait is independent of its effect on fitness (τ = 0). Here note that the SNPs with low P-values (<0.05) account for most of the V_A regardless of the demographic history of the population. Here and M = 70 kb.