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Fisher's geometric model with a moving optimum.

Matuszewski S, Hermisson J, Kopp M - Evolution (2014)

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.

View Article: PubMed Central - PubMed

Affiliation: Mathematics and BioSciences Group, Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090, Vienna, Austria. Sebastian.Matuszewski@univie.ac.at.

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The impact of mutational and selectional correlations on the distribution of adaptive substitutions for n = 2 traits. The left-hand column shows the correlation  between step sizes in the direction of the moving optimum (α1) and in an orthogonal direction (α2) for different values of mutational (top row) and selectional (bottom row) correlation ρΣ and ρM, plotted as a function of the rate of environmental change v1. The right-hand column shows , that is, the mean phenotypic lag in the direction orthogonal to the moving optimum, demonstrating the flying- and diving-kite effects (top and bottom, respectively). Lines show results from adaptive-walk simulations, whereas symbols are from individual-based simulations. Remaining parameters: Θ = 1, σ2 = 10, m2 = 1.
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fig05: The impact of mutational and selectional correlations on the distribution of adaptive substitutions for n = 2 traits. The left-hand column shows the correlation between step sizes in the direction of the moving optimum (α1) and in an orthogonal direction (α2) for different values of mutational (top row) and selectional (bottom row) correlation ρΣ and ρM, plotted as a function of the rate of environmental change v1. The right-hand column shows , that is, the mean phenotypic lag in the direction orthogonal to the moving optimum, demonstrating the flying- and diving-kite effects (top and bottom, respectively). Lines show results from adaptive-walk simulations, whereas symbols are from individual-based simulations. Remaining parameters: Θ = 1, σ2 = 10, m2 = 1.

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.


Fisher's geometric model with a moving optimum.

Matuszewski S, Hermisson J, Kopp M - Evolution (2014)

The impact of mutational and selectional correlations on the distribution of adaptive substitutions for n = 2 traits. The left-hand column shows the correlation  between step sizes in the direction of the moving optimum (α1) and in an orthogonal direction (α2) for different values of mutational (top row) and selectional (bottom row) correlation ρΣ and ρM, plotted as a function of the rate of environmental change v1. The right-hand column shows , that is, the mean phenotypic lag in the direction orthogonal to the moving optimum, demonstrating the flying- and diving-kite effects (top and bottom, respectively). Lines show results from adaptive-walk simulations, whereas symbols are from individual-based simulations. Remaining parameters: Θ = 1, σ2 = 10, m2 = 1.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4285815&req=5

fig05: The impact of mutational and selectional correlations on the distribution of adaptive substitutions for n = 2 traits. The left-hand column shows the correlation between step sizes in the direction of the moving optimum (α1) and in an orthogonal direction (α2) for different values of mutational (top row) and selectional (bottom row) correlation ρΣ and ρM, plotted as a function of the rate of environmental change v1. The right-hand column shows , that is, the mean phenotypic lag in the direction orthogonal to the moving optimum, demonstrating the flying- and diving-kite effects (top and bottom, respectively). Lines show results from adaptive-walk simulations, whereas symbols are from individual-based simulations. Remaining parameters: Θ = 1, σ2 = 10, m2 = 1.
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.

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.

View Article: PubMed Central - PubMed

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