The evolution of hybrid fitness during speciation

Abstract

The evolution of postzygotic reproductive isolation is an important component of speciation. But before isolation is complete there is sometimes a phase of heterosis in which hybrid fitness exceeds that of the two parental species. The genetics and evolution of heterosis and postzygotic isolation have typically been studied in isolation, precluding the development of a unified theory of speciation. Here, we develop a model that incorporates both positive and negative gene interactions, and accounts for the evolution of both heterosis and postzygotic isolation. We parameterize the model with recent data on the fitness effects of 10,000 mutations in yeast, singly and in pairwise epistatic combinations. The model makes novel predictions about the types of interactions that contribute to declining hybrid fitness. We reproduce patterns familiar from earlier models of speciation (e.g. Haldane's Rule and Darwin's Corollary) and identify new mechanisms that may underlie these patterns. Our approach provides a general framework for integrating experimental data from gene interaction networks into speciation theory and makes new predictions about the genetic mechanisms of speciation.

Fig 1. Gene interactions determine parental and hybrid fitness.

Parents P₁ and P₂ cross to produce a hybrid F₁ offspring. Each individual carries two loci (circle and square). The ancestral allele is white and derived mutations that have fixed in the two parental species are shaded. If one mutation is fixed in each species (top panels), negative epistasis causes decreased hybrid fitness (top left), while positive epistasis causes heterosis (top right). If two mutations are fixed in one species and none in the other (bottom panels), both negative epistasis and positive epistasis cause the hybrid to have intermediate fitness. Depending on the dominance of epistasis, hybrid fitness may be higher or lower than the average of the parents.

Fig 2. Relative hybrid fitness through time in the analytic model.

Results from Eq (2) are shown for three sets of parameters. Heterosis occurs during the first four fixed substitutions with set (A). Parameters values in (A) are ${\overline{\mathit{\epsilon }}}_{\mathit{w}}$ = 0.02 and ${\overline{\mathit{\epsilon }}}_{\mathit{b}}$ = 0.01; in (B) are ${\overline{\mathit{\epsilon }}}_{\mathit{w}}$ = 0.01 and ${\overline{\mathit{\epsilon }}}_{\mathit{b}}$ = -0.01; and in (C) are ${\overline{\mathit{\epsilon }}}_{\mathit{w}}$ = 0.05 and ${\overline{\mathit{\epsilon }}}_{\mathit{b}}$ = -0.01. In all cases the populations are diverging symmetrically (v = 1/4) and epistatic dominance is additive (α₁ = 1/4). See S2 Fig for an exploration of a wider range of parameters.

Fig 3. Average epistatic effects of substitutions.

Stochastic simulations of the full model show that the average within-population epistasis is positive at all times. It increases during the first few generations of divergence and then stabilizes. The average between-population epistasis is negative and nearly constant, and has a much smaller absolute size than within-population epistasis. The shaded regions represent 95% confidence intervals.

Fig 4. Relative hybrid fitness through time from the stochastic simulations.

The solid black curve shows the mean hybrid fitness over 10,000 simulations, the grey lines show a sample of 100 simulations, and the shaded area gives the 95% confidence interval. Heterosis (w_H > 1) occurs in some simulations early in divergence, but then rapidly disappears as populations continue to diverge.