The Evolution of Variance Control

Abstract

Genetically identical individuals can be phenotypically variable, even in constant environmental conditions. The ubiquity of this phenomenon, known as 'intra-genotypic variability', is increasingly evident and the relevant mechanistic underpinnings are beginning to be understood. In parallel, theory has delineated a number of formal expectations for contexts in which such a feature would be adaptive. Here, we review empirical evidence across biological systems and theoretical expectations, including nonlinear averaging and bet hedging. We synthesize existing results to illustrate the dependence of selection outcomes both on trait characteristics, features of environmental variability, and species' demographic context. We conclude by discussing ways to bridge the gap between empirical evidence of intra-genotypic variability, studies demonstrating its genetic component, and evidence that it is adaptive.

Keywords: bet hedging; intra-genotypic variability; micro-environmental plasticity; nonlinear averaging; phenotypic variance; vQTL.

Figure 1.

Long-term adaptive landscapes for different combinations of a mean phenotypic trait and variance in that trait to illustrate the conditions that might selection for intra-genotypic variability (Appendix S1–S3 for more information on how these landscapes were obtained). Upper row shows results for a stable environment, bottom row shows results for a fluctuating environment. Different columns show results for different relationships between the phenotypic trait and reproduction, as depicted in the small graphs. The environment modulates the relation between phenotype and fitness, illustrated by the solid and dotted lines. In a-c and e-g fitness landscapes for continuous phenotypic traits are shown. In d,h results for a discrete phenotypic trait are shown. Here, the x-axis shows the proportion of individuals expressing one trait, and is plotted against long-term fitness (y-axis). Red colors indicate higher long-term fitness, blue colors indicate lower values, and values are scaled for each graph separately. Variance has no effect in the case of the linear relation between phenotypic trait and fitness (a,e), while it results in a higher long-term fitness in the case of a convex relation, due to nonlinear averaging (b,f). When there is a phenotypic optimum that changes through time, for either a continuous (g) or discrete (h) trait, a bet hedging strategy results in the highest long-term fitness.

Figure 2.

Two conditions that can result in selection favoring intra-genotypic variability: a) nonlinear averaging and b) bet hedging. a) The graph shows fitness (y) as a function of phenotype (x). If the relation is convex, an increase in the variance in x (indicated by the grey shading) results in a higher expected fitness value (E[y(x)]) (orange) than the fitness value of the average phenotype (y(E[x])) (blue), as a result of Jensen’s inequality. b) A bet hedging strategy (orange) reduces variance in fitness across generations compared to a non bet hedging strategy (blue). Despite a decrease in arithmetic mean fitness, bet hedging leads to an increase in geometric mean fitness, and is thus expected to be favored by natural selection.

Figure 3.

Graphs depict the optimal variance in a phenotypic trait affecting reproduction, as a function of survival probability per time-step (x-axis) and environmental variance (y-axis). Here we vary it between 0 and 2 while in Fig. 1, we set environmental variance at 0 (stable environment) and at 1 (fluctuating environment). We do so to further explore how environmental variance affects the optimal phenotypic variance for two phenotype-reproduction relations, where selection favored intermediate phenotypic variance (left: continuous, Fig. 1g; right: discrete, Fig. 1h). Like in Fig. 1, the environment modulates the relationship between phenotype and fitness, illustrated by the solid and dotted lines (Appendix S4 for more details on these simulations). The graphs show that higher environmental variance favors higher phenotypic variance. For example, when survival probability is set at 0.5, increasing the environmental variance from 0 to 2, increases the optimal phenotypic variance from 0 to 0.4 (left) and from 0 to 0.23 (right). Higher survival probabilities favor lower phenotypic variance. For example, when the environmental variance is set at 1, increasing survival from 0 to 1, decreases the optimal variance from 0.77 to 0 (left), and from 0.28 to 0 (right).

Figure I.

Evolutionary trajectories of the mean and variance in a trait. Contour lines depict the fitness landscape, corresponding to Fig. 1g (see main text). For clarity, we only show contour lines here. Green dots indicate the trait combination resulting in the highest fitness. Starting from a population with a low mean trait value and no variance (black dots), trajectories towards the fitness optimum (green dots) are shown, for varying genetic variances and covariances, using the multivariate breeder’s equation [99]. Additive genetic variances for the mean (V_A-mean) and variance (V_A-variance) in phenotypic trait were both set at 0.1, and their covariance (cov_A(mean, variance)) at 0. We then, one by one, varied these variance components, while keeping the rest of the G-matrix constant. We assessed how the phenotypic mean and variance evolve over the course of 200 time steps. Graph on the left shows the effect of varying values for V_A-mean′ middle graph shows the effect of varying V_{A-variance′} and graph on the right the effect of changes in cov_A)(mean,variable). Different colors correspond to the range of values for the variable (see legend). Note that we considered a constant genetic variance-covariance matrix within each scenario, an assumption which might be often violated in natural population [100,101] and/or when environmental conditions change through time [102]

Figure II.

Proposed workflow to study the evolution of intra-genotypic variability, focusing on both the fitness consequences as well as on the genetics underlying the traits. 1–2) By using a demographic model (Appendices S1–3) to define the adaptive landscape, partial selection gradients at a given point in the landscape can be obtained. 3) The additive genetic variance462 covariance matrix (G) can be estimated using linear mixed effects models, based on knowledge on phenotypic similarities between relatives [7,15,16,19]. 4) The evolutionary change in multiple traits ($\Delta \overline{z}$), in this case phenotype mean and variance, can be written as the multivariate breeder’s equation [99], as the product of the genetic variance-covariance matrix (G) and the partial selection gradients for each trait (β).

Figure II.

Proposed workflow to study the evolution of intra-genotypic variability, focusing on both the fitness consequences as well as on the genetics underlying the traits. 1–2) By using a demographic model (Appendices S1–3) to define the adaptive landscape, partial selection gradients at a given point in the landscape can be obtained. 3) The additive genetic variance462 covariance matrix (G) can be estimated using linear mixed effects models, based on knowledge on phenotypic similarities between relatives [7,15,16,19]. 4) The evolutionary change in multiple traits ($\Delta \overline{z}$), in this case phenotype mean and variance, can be written as the multivariate breeder’s equation [99], as the product of the genetic variance-covariance matrix (G) and the partial selection gradients for each trait (β).