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Fisher's geometric model of adaptation meets the functional synthesis: data on pairwise epistasis for fitness yields insights into the shape and size of phenotype space.

Weinreich DM, Knies JL - Evolution (2013)

Bottom Line: We present an analytic framework for classifying pairs of mutations with respect to similarity of underlying mechanism on this basis, and also show that these data can yield an estimate of the number of mutationally labile phenotypes underlying fitness effects.We use computer simulations to explore the robustness of our approach to violations of analytic assumptions and analyze several recently published datasets.This work provides a theoretical complement to the functional synthesis as well as a novel test of Fisher's geometric model.

View Article: PubMed Central - PubMed

Affiliation: Department of Ecology and Evolutionary Biology, and Center for Computational Molecular Biology, Brown University, Providence, Rhode Island, 02912. Daniel_Weinreich@Brown.edu.

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Estimation of θFGM in computer simulations allowing experimental error in fitness assay. Equation 5 can return real and imaginary values. Heavy lines represent mean ±1 SD of real values of θFGM (eq. 4) for a given θtrue (computed with eq. 3) in a sliding window 10° wide; heavy dashed line represents θFGM = θtrue. (Scale on left y-axis.) Light lines represent fraction of imaginary values of θFGM's in the same sliding window (solid: frequency of imaginary θFGM with real part = 0°; dashed: frequency of imaginary θFGM's with real part = 180°; scale on right y-axis). All parameter values as shown (phenotypic dimensionality n, experimental noise σnoise, experimental replicates R). Phenotypic epistasis (σepistasis) equal to 0, z0 = zopt, and S = I.
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fig04: Estimation of θFGM in computer simulations allowing experimental error in fitness assay. Equation 5 can return real and imaginary values. Heavy lines represent mean ±1 SD of real values of θFGM (eq. 4) for a given θtrue (computed with eq. 3) in a sliding window 10° wide; heavy dashed line represents θFGM = θtrue. (Scale on left y-axis.) Light lines represent fraction of imaginary values of θFGM's in the same sliding window (solid: frequency of imaginary θFGM with real part = 0°; dashed: frequency of imaginary θFGM's with real part = 180°; scale on right y-axis). All parameter values as shown (phenotypic dimensionality n, experimental noise σnoise, experimental replicates R). Phenotypic epistasis (σepistasis) equal to 0, z0 = zopt, and S = I.

Mentions: Under analytic assumptions (i.e., setting σnoise = σepistasis = 0, z0 = zopt and random positive semidefinite S) simulation results were precisely concordant with equation 5 for all parameter values examined (not shown). Figures 4 and 5 present simulation results that explore sensitivity of equation 5 to experimental noise and to relaxing model assumptions, respectively. Each panel displays the mean real θFGM values (± 1 SD) across a sliding window of θtrue values 10° wide. In addition, we show the frequency of each of the two classes of imaginary values of θFGM observed each in each sliding window. Finally, in each panel, we report the r2 value for a linear regression of real estimates of θ forced through the origin (see Discussion).


Fisher's geometric model of adaptation meets the functional synthesis: data on pairwise epistasis for fitness yields insights into the shape and size of phenotype space.

Weinreich DM, Knies JL - Evolution (2013)

Estimation of θFGM in computer simulations allowing experimental error in fitness assay. Equation 5 can return real and imaginary values. Heavy lines represent mean ±1 SD of real values of θFGM (eq. 4) for a given θtrue (computed with eq. 3) in a sliding window 10° wide; heavy dashed line represents θFGM = θtrue. (Scale on left y-axis.) Light lines represent fraction of imaginary values of θFGM's in the same sliding window (solid: frequency of imaginary θFGM with real part = 0°; dashed: frequency of imaginary θFGM's with real part = 180°; scale on right y-axis). All parameter values as shown (phenotypic dimensionality n, experimental noise σnoise, experimental replicates R). Phenotypic epistasis (σepistasis) equal to 0, z0 = zopt, and S = I.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4282100&req=5

fig04: Estimation of θFGM in computer simulations allowing experimental error in fitness assay. Equation 5 can return real and imaginary values. Heavy lines represent mean ±1 SD of real values of θFGM (eq. 4) for a given θtrue (computed with eq. 3) in a sliding window 10° wide; heavy dashed line represents θFGM = θtrue. (Scale on left y-axis.) Light lines represent fraction of imaginary values of θFGM's in the same sliding window (solid: frequency of imaginary θFGM with real part = 0°; dashed: frequency of imaginary θFGM's with real part = 180°; scale on right y-axis). All parameter values as shown (phenotypic dimensionality n, experimental noise σnoise, experimental replicates R). Phenotypic epistasis (σepistasis) equal to 0, z0 = zopt, and S = I.
Mentions: Under analytic assumptions (i.e., setting σnoise = σepistasis = 0, z0 = zopt and random positive semidefinite S) simulation results were precisely concordant with equation 5 for all parameter values examined (not shown). Figures 4 and 5 present simulation results that explore sensitivity of equation 5 to experimental noise and to relaxing model assumptions, respectively. Each panel displays the mean real θFGM values (± 1 SD) across a sliding window of θtrue values 10° wide. In addition, we show the frequency of each of the two classes of imaginary values of θFGM observed each in each sliding window. Finally, in each panel, we report the r2 value for a linear regression of real estimates of θ forced through the origin (see Discussion).

Bottom Line: We present an analytic framework for classifying pairs of mutations with respect to similarity of underlying mechanism on this basis, and also show that these data can yield an estimate of the number of mutationally labile phenotypes underlying fitness effects.We use computer simulations to explore the robustness of our approach to violations of analytic assumptions and analyze several recently published datasets.This work provides a theoretical complement to the functional synthesis as well as a novel test of Fisher's geometric model.

View Article: PubMed Central - PubMed

Affiliation: Department of Ecology and Evolutionary Biology, and Center for Computational Molecular Biology, Brown University, Providence, Rhode Island, 02912. Daniel_Weinreich@Brown.edu.

Show MeSH