Fisher's geometric model with a moving optimum.
Bottom Line: Fisher's geometric model has been widely used to study the effects of pleiotropy and organismic complexity on phenotypic adaptation.We focus on the distribution of adaptive substitutions, that is, the multivariate distribution of the phenotypic effects of fixed beneficial mutations.Our main results are based on an "adaptive-walk approximation," which is checked against individual-based simulations.
Affiliation: Mathematics and BioSciences Group, Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090, Vienna, Austria. Sebastian.Matuszewski@univie.ac.at.Show MeSH
Mentions: Figure 4 shows the multivariate distribution of adaptive substitutions, ϕ(α), for different strengths of selectional and mutational correlations under varying speeds of environmental change for n = 2 traits. As in the isotropic case (Fig. 1), the distribution ϕ(α) is biased toward the direction of the optimum, with pleiotropic side effects of fixed mutations on average being neutral (Figs. S5_6, S5_7). The shape of the distribution, however, critically depends on the interaction between the type and strength of correlations and the rate of environmental change. Mutational correlations tend to align the distribution of adaptive substitutions along the leading eigenvector of M, with stronger mutational correlations leading to stronger correlation in step sizes (Figs.4, 5, and S5_8 top left). This effect is strongest in fast-changing environments and gradually gets weaker as the rate of environmental change decreases (Fig. 5), until becoming almost unnoticeable. Selectional correlations similarly orientate the distribution of adaptive substitutions along to the leading eigenvector of Σ (Figs.4, 5 bottom left, S5_8). In contrast to mutational correlations, however, their impact is strongest if environmental change is slow (for small γ and the first step, the correlation is given by , see eq. S36). Correlations in step sizes remain almost unchanged for a broad range of rates v1, before dropping off sharply once environmental change gets sufficiently fast.
Affiliation: Mathematics and BioSciences Group, Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090, Vienna, Austria. Sebastian.Matuszewski@univie.ac.at.