F(ST) and Q(ST) under neutrality

Abstract

A commonly used test for natural selection has been to compare population differentiation for neutral molecular loci estimated by F(ST) and for the additive genetic component of quantitative traits estimated by Q(ST). Past analytical and empirical studies have led to the conclusion that when averaged over replicate evolutionary histories, Q(ST) = F(ST) under neutrality. We used analytical and simulation techniques to study the impact of stochastic fluctuation among replicate outcomes of an evolutionary process, or the evolutionary variance, of Q(ST) and F(ST) for a neutral quantitative trait determined by n unlinked diallelic loci with additive gene action. We studied analytical models of two scenarios. In one, a pair of demes has recently been formed through subdivision of a panmictic population; in the other, a pair of demes has been evolving in allopatry for a long time. A rigorous analysis of these two models showed that in general, it is not necessarily true that mean Q(ST) = F(ST) (across evolutionary replicates) for a neutral, additive quantitative trait. In addition, we used finite-island model simulations to show there is a strong positive correlation between Q(ST) and the difference Q(ST) - F(ST) because the evolutionary variance of Q(ST) is much larger than that of F(ST). If traits with relatively large Q(ST) values are preferentially sampled for study, the difference between Q(ST) and F(ST) will also be large and positive because of this correlation. Many recent studies have used tests of the null hypothesis Q(ST) = F(ST) to identify diversifying or uniform selection among subpopulations for quantitative traits. Our findings suggest that the distributions of Q(ST) and F(ST) under the null hypothesis of neutrality will depend on species-specific biology such as the number of subpopulations and the history of subpopulation divergence. In addition, the manner in which researchers select quantitative traits for study may introduce bias into the tests. As a result, researchers must be cautious before concluding that selection is occurring when Q(ST) not equal F(ST).

Figure 1.—

Mean Q_ST − F_ST across replicate populations in groups 10 and 11 from Table 1, together with their equivalents after exchanging the effect sizes a_A and a_B. These values assume uniform distributions of allele frequencies (across replicates) at loci where segregation persists. The value of mean Q_ST − F_ST depends only on the ratio ; because of the symmetry induced by exchanging a_A and a_B, including ratios <1 would simply reflect the graph across the vertical line .

Figure 2.—

G_ST (calculated using four markers) vs. Q_ST (for a neutral trait determined additively by two QTL) after 100 generations for 100 runs of an individual-based simulation with d = 2 initially identical demes of N = 100 individuals each, with a mean of Nm = 0.1 migrants per deme per generation.

Figure 3.—

G_ST (using 10 markers) vs. Q_ST (for a trait determined by 10 QTL) after 1000 generations for 24 runs of a simulation as in Figure 2 but with d = 20, N = 500, and Nm = 1.0.

Figure 4.—

The joint distribution of differentiation at the quantitative trait (Q_ST) and individual loci (F_ST) from finite-island model simulations carried out over a range of values for the product of the effective population size of each deme (N) and the rate of gene flow into each deme per generation (m). Q_ST shows more variation than F_ST for a given value of Nm. Q_ST and F_ST are each based on 10 independent diallelic loci, the quantitative trait loci had equal phenotypic effects, 100 replicate simulations were carried out for each Nm value, and the total population was 20 demes. Values at the 10,000th generation are shown for Nm = 0.002 and at the 1000th generation for all other Nm values.

Figure 5.—

The joint distribution of differentiation at the quantitative trait (Q_ST) by the difference between differentiation at the quantitative trait and individual loci (Q_ST − F_ST). The difference between Q_ST and F_ST is positively correlated with Q_ST. Q_ST and F_ST are each based on 10 independent diallelic loci, the quantitative trait loci had equal phenotypic effects, 100 replicate simulations were carried out for each Nm value, and the total population was 20 demes. Values at the 10,000th generation are shown for Nm = 0.002 and at the 1000th generation for all other Nm values. These graphs use the same simulation data sets as Figure 4.

Figure 6.—

Mean difference between differentiation at the quantitative trait and individual loci (Q_ST − F_ST) over 100 replicate simulations along with two standard deviations above and below the mean. Q_ST and F_ST are each based on 10 independent diallelic loci, the quantitative trait loci had equal phenotypic effects, 100 replicate simulations were carried out for each Nm value, and the total population was 20 demes. These graphs use the same simulation data sets as Figures 4 and 5.