Evolution of the Environmental Component of the Phenotypic Variance: Stabilizing Selection in Changing Environments and the Cost of Homogeneity

Abstract

Quantitative traits show abundant genetic, environmental, and phenotypic variance, yet if they are subject to stabilizing selection for an optimal phenotype, both the genetic and environmental components are expected to decline. The mechanisms that determine the level and maintenance of phenotypic variance are not yet fully understood. While there has been extensive study of mechanisms maintaining genetic variability, it has generally been assumed that environmental variance is not dependent on the genotype and therefore not subject to change. However, accumulating data suggest that the environmental variance is under some degree of genetic control. In this study, it is assumed accordingly that both the genotypic value (i.e., mean phenotypic value) and the variance of phenotypic value given genotypic value depend on the genotype. Two models are investigated as potentially able to explain the protected maintenance of environmental variance of quantitative traits under stabilizing selection. One is varying environment among generations, such that both the optimal phenotype and the strength of the stabilizing selection vary between generations. The other is the cost of homogeneity, which is based on an assumption of an engineering cost of minimizing variability in development. It is shown that a small homogeneity cost is enough to maintain the observed levels of environmental variance, whereas a large amount of temporal variation in the optimal phenotype and the strength of selection would be necessary.

Prediction of Breeding Values and Selection Responses With Genetic Heterogeneity of Environmental Variance

“…Methodology: Comparison of genetic models: Different genetic models to account for genetic heterogeneity of environmental variance appear in the literature, basically either additive effects both at the level of the mean and at the level of the environmental variance Zhang and Hill 2005; this study) or additive effects on the mean and an exponential model for the environmental variance (SanCristobal-Gaudy et al 1998Sorensen and Waagepetersen 2003;Ros et al 2004). In the exponential model…”

Genetic parameters related to environmental variability of weight traits in a selection experiment for weight gain in mice; signs of correlated canalised response

“…However, Ibáñez-Escriche et al [20] found no correlation for slaughter weight at 175 days in pigs while Gutiérrez et al [14] found extreme positive and negative correlations depending on the trait, and Damgaard et al [4] and Huby et al [17] found positive genetic correlations between mean and variability for weight in pigs. Moreover, Zhang et al [36] found in the literature a wide range of values for correlations between mean and variability. The negative correlation between mean and environmental variance (−0.19) for WG, means that we should expect the environmental variance for this trait to decrease in an experiment conducted to increase the mean of the trait.…”

“…Our results suggest that before implementing such a selection index, further studies are required to understand the functional relationship between mean and variance and their influence on the expected correlated response. Thus, it would be desirable to explore other models [36] with different relationships between mean and variance. Another possibility would be to validate the models by comparing their expected response to selection with a selection experiment for variability.…”

The Phenotypic Variance Within Plastic Traits Under Migration-Mutation-Selection Balance

“…The clonal frequency change due to mutation and selection follows equation (14). As in Zhang and Hill (2005b), the squared mean phenotype 2 is used as a unit to measure the variance, and thus the average values are V E ϭ 0.005 2 , 2 ϭ 0.1 2 , and ϭ 2V M / ഠ (10 Ϫ5 /) 2 (V M is the mutational variance, of 2 the order of 10 Ϫ3 of the environmental variance (Lynch and Walsh 1998)). Because no direct knowledge of the relevant parameter of slope is available, values of the intrinsic mean m and variance of slope will be assigned arbitrarily.…”

“…Accumulating evidence suggests that environmental variance is under genetic control (Whitlock and Fowler 1999;Sorensen and Waagepetersen 2003;Ros et al 2004;Rowe et al 2005;Mackay and Lyman 2005). Although much theoretical attention has been paid to the maintenance of genetic variation (Bü rger 2000; Barton and Keightley 2002;Zhang and Hill 2005a), and a little to environmental variance within quantitative traits (Bull 1987;Zhang and Hill 2005b), no comprehensive model has been described for both variances together. However, genetic models that ignore gene-environment interactions do not explain the robust patterns of genetic and environmental variances.…”