Environmental Tolerance

A theory for the expression of a population's response to density-independent gradients of environmental factors is derived for the case of asexuality. It is shown that the environmental tolerance of a genotype is a function of at least four parameters: g₁ and VE1, the environmental optimum and its developmental variance between individuals, and g₂ and VE2, the expected genetic contribution to the breadth of adaptation and its developmental variance. The realized breadth of adaptation of a genotype (V1/2) is a complex function of g₂, VE1, and VE2, but we argue that, with an appropriate scale transformation, the tolerance curve of a genotype is approximately normal, with mean g₁ and standard deviation V1/2. It is shown that temporal heterogeneity in the environment selects for more-broadly-adapted genotypes but that the within-generation component (V_) plays a more prominent role than the between-generation component (V_). Spatial heterogeneity selects for higher V1/2 only when it occurs in conjunction with temporal variance within generations and only if V_ is small relative to V_. We argue that since g₂ is expected to evolve subject to the constraint that V1/2 is optimized, species exposed to conditions favoring identical V1/2 may evolve different g₂ if pronounced interspecific differences exist for VE1 and VE2. A maximum-likelihood method is shown to be capable of generating accurate estimates of the genotypic parameters g₁, g₂, VE1, and VE2 with moderately large samples. We suggest how this procedure may be used to estimate analogous parameters for a population of mixed genotypes and to obtain estimates of the genetic variance for the environmental optimum and breadth of adaptation. The potential utility of this methodology for the analysis of data routinely generated in programs for environmental assessment and plant breeding is pointed out.