Detecting selection with a genetic cross

Abstract

Distinguishing which traits have evolved under natural selection, as opposed to neutral evolution, is a major goal of evolutionary biology. Several tests have been proposed to accomplish this, but these either rely on false assumptions or suffer from low power. Here, I introduce an approach to detecting selection that makes minimal assumptions and only requires phenotypic data from ∼10 individuals. The test compares the phenotypic difference between two populations to what would be expected by chance under neutral evolution, which can be estimated from the phenotypic distribution of an F₂ cross between those populations. Simulations show that the test is robust to variation in the number of loci affecting the trait, the distribution of locus effect sizes, heritability, dominance, and epistasis. Comparing its performance to the QTL sign test-an existing test of selection that requires both genotype and phenotype data-the new test achieves comparable power with 50- to 100-fold fewer individuals (and no genotype data). Applying the test to empirical data spanning over a century shows strong directional selection in many crops, as well as on naturally selected traits such as head shape in Hawaiian Drosophila and skin color in humans. Applied to gene expression data, the test reveals that the strength of stabilizing selection acting on mRNA levels in a species is strongly associated with that species' effective population size. In sum, this test is applicable to phenotypic data from almost any genetic cross, allowing selection to be detected more easily and powerfully than previously possible.

Keywords: evolution; genetic cross; natural selection; variance.

Fig. 1.

The sign test and the v test. (A) Illustration of the sign test applied to the trait of mouse size. (Left) Two mice from separate populations that have had no selection acting on size are expected to have approximately equal numbers of QTL (or QTN) alleles increasing size (binomially distributed with expected frequency = 1/2; stabilizing selection on size would result in a similar pattern, but with a smaller expected parental trait divergence). (Right) In contrast, two populations that have experienced lineage-specific directional selection on size will show greater phenotypic divergence and a preponderance of QTL alleles increasing size in the larger strain. A significant deviation from the binomial expectation indicates rejection of the null hypothesis of neutral evolution. (B) Simulation of trait divergence under a simple model of three selection regimes. One exponentially distributed QTL (or QTN) is added per time step, and the number and effect sizes of QTL are identical in each selection regime; the only difference is their directionality. Under directional selection, all QTL increase the trait value (as in Fig. 1 A, Right); under neutral evolution, their directionalities are random; and under stabilizing selection, their directionalities are whatever will bring the trait closer to the optimum (e.g., if the trait is above the optimum, the next QTL will be negative). Each selection regime has 100 lineages simulated for 100 time steps. (C) Illustration of the v test. Under a simple model, the variance of a neutral trait in two populations is expected to be approximately equal to that of their F₂ progeny (Eq. 1). Lineage-specific directional selection will result in higher parental variance, whereas stabilizing selection will lead to lower parental variance (transgressive segregation).

Fig. 2.

Neutral simulations. Each panel shows 20 quantile–quantile (QQ) plots, each with 10⁴ simulated genetic crosses between two lineages where the trait in question has been evolving neutrally (i.e., QTL directions in each parent are random; Fig. 1 A and B). The x axis shows expected P value quantiles (uniform between zero and 1), and the y axis shows observed P-values of v (Eq. 2). For each panel, one parameter is varied from the baseline model (exponential distribution of QTL effect sizes, RI = 50, number of parental replicates = 10, n_F2 = 100, H² = 1, diploid, no epistasis or dominance), except for the Upper Right panel, which is the baseline model. (A) Effects of varying QTL effect sizes. (B) Effects of varying RI. (C) Effects of varying the number of F₂ individuals. (D) Effects of varying H², with or without the correction in Eq. 2. (E) Effects of varying epistasis and dominance. Bidirectional dominance means all loci are fully dominant but with ∼50% of loci being dominant toward one parent, and ∼50% toward the other. Unidirectional means all loci are fully dominant in the same direction (i.e., the F₁ phenotype is identical to one of the parents).

Fig. 3.

Directional selection simulations. All panels show scatter plots where every point is an independent simulation of a genetic cross between two lineages where the trait in question has been evolving under directional selection (i.e., all QTL are in the same direction; Fig. 1 A and B). The x axis shows sign test log P values, and the y axis shows v-test log P values. For each panel, two key parameters (H² and n_F2) are set to the values shown and a third is varied within the panel (RI, which takes on all integer values from 5 to 100). For each value of RI, 10 simulations are shown, each with an independent set of QTL effect sizes; this results in 960 simulations (data points) per panel. All other parameters are kept constant throughout the figure (exponential distribution of QTL effect sizes, n_par = 10, diploid, no epistasis or dominance).

Fig. 4.

Empirical analysis. (A) Results for artificially selected traits in crops, livestock, and laboratory selection experiments. Inset shows the six most significant traits. (B) Results for naturally selected traits in plants and animals. Inset shows the three most significant traits. (C) Results for gene expression (mRNA levels) and metabolite levels measured in the same mouse RIL panel (BXD). Note that any selection detected between the two parental lineages could involve divergence of their wild ancestors (mostly M. musculus domesticus) and/or artificial selection during their inbreeding in the laboratory. The t-test P values are shown for each comparison. (D, Center) The strength of stabilizing selection vs. heterozygosity (π) in six species (in order of decreasing π: Brassica rapa, Arabidopsis thaliana, Caenorhabditis elegans, Oryza sativa, Mus musculus, Saccharomyces cerevisiae). Side panels: the full distribution of P_nut values for the species with the highest (Right) and lowest (Left) π.