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

Abstract

Abstract. How phenotypic variances of quantitative traits are influenced by the heterogeneity in environment is an important problem in evolutionary biology. In this study, both genetic and environmental variances in a plastic trait under migration-mutation-stabilizing selection are investigated. For this, a linear reaction norm is used to approximate the mapping from genotype to phenotype, and a population of clonal inheritance is assumed to live in a habitat consisting of many patches in which environmental conditions vary among patches and generations. The life cycle is assumed to be selection-reproduction-mutation-migration. Analysis shows that phenotypic plasticity is adaptive if correlations between the optimal phenotype and environment have become established in both space and/or time, and it is thus possible to maintain environmental variance (V E ) in the plastic trait. Under the special situation of no mutation but maximum migration such that separate patches form an effective single-site habitat, the genotype that maximizes the geometric mean fitness will come to fixation and thus genetic variance (V G ) cannot be maintained. With mutation and/or restricted migration, V G can be maintained and it increases with mutation rate but decreases with migration rate; whereas V E is little affected by them. Temporal variation in environmental quality increases V G while its spatial variance decreases V G . Variation in environmental conditions may decrease the environmental variance in the plastic trait.

Phenotypic Plasticity, Costs of Phenotypes, and Costs of Plasticity

“…This is an essential step required before developing or applying models addressing whether the evolution and maintenance of plasticity depends on the details of the environment. Intuitively, and consistent with many theoretical models, loss of plasticity and greater stability are generally favored in more stable environments, whereas plasticity is generally favored by heterogeneous or fluctuating environments—but outcomes can be complex depending on the reliability of the cue and/or the sensory detection mechanism that organisms use to detect environmental fluctuations, by time lags, by details of the plasticity‐eliciting and selective environments, and by costs associated with plastic phenotypes (van Tienderen 1991; Moran 1992; Scheiner & Callahan 1999; Sultan & Spencer 2002; Zhang 2006; Kingsolver et al 2007).…”

“…Work by Stinchcombe et al (2004), discussed earlier, involved across‐environment selection analyses using simple, unweighted averages of genotypic trait means and genotypic means for fitness. Yet several theoretical and simulation studies have demonstrated that the response to selection depends on the details of both the plasticity‐eliciting and selective environments, which may not be identical (Scheiner & Callahan 1999; Sultan & Spencer 2002; Zhang 2006). Unfortunately, few studies have attempted to characterize the spatiotemporal distribution of selective environments (Feder et al 1997; Huber et al 2004) or the environments known to trigger plastic responses (Sultan et al 1998; Scheiner & Callahan 1999).…”

Condition-dependence, genotype-by-environment interactions and the lek paradox

“…Earlier work (Day 2000;Proulx 2001;Reinhold 2004;McLain 2005) has concluded that GEIs offer a potentially very powerful mechanism that promotes female preference evolution by maintaining variation in male condition, which is then translated to male attractiveness via condition-dependence (see also Zhang 2006). Earlier work (Day 2000;Proulx 2001;Reinhold 2004;McLain 2005) has concluded that GEIs offer a potentially very powerful mechanism that promotes female preference evolution by maintaining variation in male condition, which is then translated to male attractiveness via condition-dependence (see also Zhang 2006).…”

Growth‐mortality tradeoffs and ‘personality traits’ in animals

“…These models also indicate that substantial amounts of genetic and phenotypic variation can be maintained in a population as a result of spatial/temporal variation in environmental factors, coupled with dispersal between habitats with different environmental conditions (e.g. Gavrilets & Scheiner 1993; de Jong & Gavrilets 2000; Zhang 2006). All of these ‘genetic’ models assume that an individual's behavioral phenotype is fixed after it reaches a particular age or life‐stage, and thus can account for inter‐individual variation in behavior, coupled with intra‐individual stability in behavior.…”