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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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Fisher's geometric model of adaptation for n = 2 phenotypes. (A) All combinations of phenotype values are represented in n-dimensional space (here, the plane); the optimal value is represented by the point labeled zopt and an individual-labeled z is displaced from this optimum (as perhaps following an environmental perturbation). To be beneficial, a mutation dz on wild-type z must yield a phenotype z + dz lying within the circle passing through z and centered at zopt. Inset: y represents another organism with fitness equal to that of z. Note, however, that mutation dz is seen to exhibit epistasis: it is beneficial on z but deleterious on y. (B) Mutational interactions in TEM-1 β-lactamase between catalytic activity and thermodynamic stability in determining cefotaxime resistance (see Fig. 1), represented qualitatively in Fisher's geometric model. Figure adapted from Weinreich (2010).
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fig02: Fisher's geometric model of adaptation for n = 2 phenotypes. (A) All combinations of phenotype values are represented in n-dimensional space (here, the plane); the optimal value is represented by the point labeled zopt and an individual-labeled z is displaced from this optimum (as perhaps following an environmental perturbation). To be beneficial, a mutation dz on wild-type z must yield a phenotype z + dz lying within the circle passing through z and centered at zopt. Inset: y represents another organism with fitness equal to that of z. Note, however, that mutation dz is seen to exhibit epistasis: it is beneficial on z but deleterious on y. (B) Mutational interactions in TEM-1 β-lactamase between catalytic activity and thermodynamic stability in determining cefotaxime resistance (see Fig. 1), represented qualitatively in Fisher's geometric model. Figure adapted from Weinreich (2010).

Mentions: Fisher's geometric model (Fig. 2A) begins from the premise that the fundamental attribute of adaptation are the many simultaneous “features of conformity” (Fisher 1930, p. 38), both within an organism and between the organism and its environment. Fisher first imagined a continuous, multidimensional phenotype space; any organism can be represented by some point in this space. The biologically optimal combination of phenotypes is at the origin, and fitness elsewhere is a declining function of the distance to the origin. Thus, stabilizing selection acts simultaneously on multiple phenotypes. Second, Fisher assumed that mutations displace an organism in an arbitrary direction in phenotype space; i.e., mutations usually act pleiotropically. Thus, the FGM captures the essential elements of protein evolution outlined above (Weinreich 2010), and this point is illustrated qualitatively in Figure 2B for the G238S and M182T mutations of the TEM-1 allele of β-lactamase. The FGM is one of the few phenotypic models of evolution (reviewed in Orr 2005a) and has received extensive theoretical (Kimura 1983; Hartl and Taubes 1996; Hartl and Taubes 1998; Orr 1998, 1999, 2005b; 2006; Poon and Otto 2000; Welch and Waxman 2003; Waxman and Welch 2005; Martin and Lenormand 2006; Waxman 2006; Sella 2009; Chevin et al. 2010; Le Nagard et al. 2011; Sellis et al. 2011) and experimental (Burch and Chao 1999; Martin et al. 2007; Tenaillon et al. 2007; MacLean et al. 2010; Rokyta et al. 2011) attention.


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)

Fisher's geometric model of adaptation for n = 2 phenotypes. (A) All combinations of phenotype values are represented in n-dimensional space (here, the plane); the optimal value is represented by the point labeled zopt and an individual-labeled z is displaced from this optimum (as perhaps following an environmental perturbation). To be beneficial, a mutation dz on wild-type z must yield a phenotype z + dz lying within the circle passing through z and centered at zopt. Inset: y represents another organism with fitness equal to that of z. Note, however, that mutation dz is seen to exhibit epistasis: it is beneficial on z but deleterious on y. (B) Mutational interactions in TEM-1 β-lactamase between catalytic activity and thermodynamic stability in determining cefotaxime resistance (see Fig. 1), represented qualitatively in Fisher's geometric model. Figure adapted from Weinreich (2010).
© Copyright Policy - open-access
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4282100&req=5

fig02: Fisher's geometric model of adaptation for n = 2 phenotypes. (A) All combinations of phenotype values are represented in n-dimensional space (here, the plane); the optimal value is represented by the point labeled zopt and an individual-labeled z is displaced from this optimum (as perhaps following an environmental perturbation). To be beneficial, a mutation dz on wild-type z must yield a phenotype z + dz lying within the circle passing through z and centered at zopt. Inset: y represents another organism with fitness equal to that of z. Note, however, that mutation dz is seen to exhibit epistasis: it is beneficial on z but deleterious on y. (B) Mutational interactions in TEM-1 β-lactamase between catalytic activity and thermodynamic stability in determining cefotaxime resistance (see Fig. 1), represented qualitatively in Fisher's geometric model. Figure adapted from Weinreich (2010).
Mentions: Fisher's geometric model (Fig. 2A) begins from the premise that the fundamental attribute of adaptation are the many simultaneous “features of conformity” (Fisher 1930, p. 38), both within an organism and between the organism and its environment. Fisher first imagined a continuous, multidimensional phenotype space; any organism can be represented by some point in this space. The biologically optimal combination of phenotypes is at the origin, and fitness elsewhere is a declining function of the distance to the origin. Thus, stabilizing selection acts simultaneously on multiple phenotypes. Second, Fisher assumed that mutations displace an organism in an arbitrary direction in phenotype space; i.e., mutations usually act pleiotropically. Thus, the FGM captures the essential elements of protein evolution outlined above (Weinreich 2010), and this point is illustrated qualitatively in Figure 2B for the G238S and M182T mutations of the TEM-1 allele of β-lactamase. The FGM is one of the few phenotypic models of evolution (reviewed in Orr 2005a) and has received extensive theoretical (Kimura 1983; Hartl and Taubes 1996; Hartl and Taubes 1998; Orr 1998, 1999, 2005b; 2006; Poon and Otto 2000; Welch and Waxman 2003; Waxman and Welch 2005; Martin and Lenormand 2006; Waxman 2006; Sella 2009; Chevin et al. 2010; Le Nagard et al. 2011; Sellis et al. 2011) and experimental (Burch and Chao 1999; Martin et al. 2007; Tenaillon et al. 2007; MacLean et al. 2010; Rokyta et al. 2011) attention.

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