The genetics of speciation: Insights from Fisher's geometric model

Abstract

Research in speciation genetics has uncovered many robust patterns in intrinsic reproductive isolation, and fitness landscape models have been useful in interpreting these patterns. Here, we examine fitness landscapes based on Fisher's geometric model. Such landscapes are analogous to models of optimizing selection acting on quantitative traits, and have been widely used to study adaptation and the distribution of mutational effects. We show that, with a few modifications, Fisher's model can generate all of the major findings of introgression studies (including "speciation genes" with strong deleterious effects, complex epistasis and asymmetry), and the major patterns in overall hybrid fitnesses (including Haldane's Rule, the speciation clock, heterosis, hybrid breakdown, and male-female asymmetry in the F1). We compare our approach to alternative modeling frameworks that assign fitnesses to genotypes by identifying combinations of incompatible alleles. In some cases, the predictions are importantly different. For example, Fisher's model can explain conflicting empirical results about the rate at which incompatibilities accumulate with genetic divergence. In other cases, the predictions are identical. For example, the quality of reproductive isolation is little affected by the manner in which populations diverge.

Coadapted genomes and selection on hybrids: Fisher's geometric model explains a variety of empirical patterns

“…This pattern of F1 hybrid vigor (high F1 fitness) followed by breakdown in later crosses, has widespread empirical support (see references in Table S1 of Fraïsse et al. 2016b and Rosas et al. 2010).…”

“…2007; Fraïsse et al. 2016b), and so these can vary independently of other results. We now define the key quantity f , as the expected value of S for a given class of hybrid, scaled by the expected value for an unfit reference class.…”

“…Finally, we moved the phenotypic optima during the simulation, so that much of the divergence took place by positive selection (see Fraïsse et al. 2016b; Fig. S3f).…”

“…This prediction agrees with the widespread finding of heterosis (Crow 1952; Table S1 of Fraïsse et al. 2016b). Indeed, by rearranging equation (6) it is clear that hybrids will tend to be fitter than parental line P1 (such that $f<f_{\mathrm{P}1}$) on the condition that $p_{12}>{\beta }_{1}hfalse(1-{\beta }_{2}hfalse)$.…”

“…The full simulation procedure is described in Fraïsse et al. (2016b), but all simulations assumed allopatric divergence between P1 and P2, haploid genomics, and a low mutation rate, such that fixation or loss events could be tracked one mutation at a time. In the simulations shown in Figure S3, we began with a core set of parameters (Fig.…”