System drift and speciation

Abstract

Even if a species' phenotype does not change over evolutionary time, the underlying mechanism may change, as distinct molecular pathways can realize identical phenotypes. Here we use quantitative genetics and linear system theory to study how a gene network underlying a conserved phenotype evolves, as the genetic drift of small changes to these molecular pathways cause a population to explore the set of mechanisms with identical phenotypes. To do this, we model an organism's internal state as a linear system of differential equations for which the environment provides input and the phenotype is the output, in which context there exists an exact characterization of the set of all mechanisms that give the same input-output relationship. This characterization implies that selectively neutral directions in genotype space should be common and that the evolutionary exploration of these distinct but equivalent mechanisms can lead to the reproductive incompatibility of independently evolving populations. This evolutionary exploration, or system drift, proceeds at a rate proportional to the amount of intrapopulation genetic variation divided by the effective population size (Ne). At biologically reasonable parameter values this process can lead to substantial interpopulation incompatibility, and thus speciation, in fewer than Ne generations. This model also naturally predicts Haldane's rule, thus providing another possible explanation of why heterogametic hybrids tend to be disrupted more often than homogametes during the early stages of speciation.

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

“…Previous authors have noted that Fisher's model predicts this pattern (Barton 2001; Fraïsse et al. 2016b; Schiffman and Ralph 2017), and here, we extend this insight to give formal conditions for Haldane's Rule. We will assume identical selection in both sexes, and that pure‐species individuals of both sexes have the same fitness.…”

“…For example, previous authors have shown that Fisher's model predicts Haldane's Rule: the tendency of sex‐specific breakdown to appear in the heterogametic sex (Haldane 1922; Turelli and Orr 2000; Barton 2001; Fraïsse et al. 2016b; Schiffman and Ralph 2017; see Fig. 1 C).…”

The geometry and genetics of hybridization

“…First, stabilizing selection might maintain the phenotype at a (more-or-less) stationary optimum, while still allowing for divergence at the genomic level, perhaps by nearly neutral evolution. This is sometimes called "system drift" (Barton 1989;Mani and Clarke 1990;Hartl and Taubes 1998;Rosas et al 2010;Schiffman and Ralph 2017), and it is illustrated in Figure 3c. Alternatively, divergence could involve adaptation to a moving optimum, but with a complex pattern of environmental change, e.g., with an optimum that oscillated back and forth; this is illustrated in Figure 3d.…”

“…So far, we have ignored an implausible prediction of Fisher's model. Equation 20, predicts that fully heterozygous hybrids will always be as fit as their parents, because, when p 12 = 1 and h = 1/2, the benefits of heterozygosity exactly cancel the costs of hybridity (Barton 2001;Fraïsse et al 2016;Schiffman and Ralph 2017).…”

“…First, the model assumes that fitness is determined by a few quantitative traits, each with additive genetics. This assumption is less restrictive than it seems, because the "traits" need not be identified with standard quantitative traits (such as height or weight), but might emerge from a variety of more complex underlying phenotypic models (Martin 2014;Schiffman and Ralph 2017;Fraïsse and Welch 2019). Nevertheless, additivity leads to some questionable predictions, especially for the initial F1 cross (Fraïsse et al 2016).…”