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Abstract

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: g$_1$ and V$_{E1}$, the environmental optimum and its developmental variance between individuals, and g$_2$ and V$_{E2}$, the expected genetic contribution to the breadth of adaptation and its developmental variance. The realized breadth of adaptation of a genotype (V$^{1/2}$) is a complex function of g$_2$, V$_{E1}$, and V$_{E2}$, but we argue that, with an appropriate scale transformation, the tolerance curve of a genotype is approximately normal, with mean g$_1$ and standard deviation V$^{1/2}$. It is shown that temporal heterogeneity in the environment selects for more-broadly-adapted genotypes but that the within-generation component (V$_{\phitw}$) plays a more prominent role than the between-generation component (V$_{\phitb}$). Spatial heterogeneity selects for higher V$^{1/2}$ only when it occurs in conjunction with temporal variance within generations and only if V$_{\phitb}$ is small relative to V$_{\phitw}$. We argue that since g$_2$ is expected to evolve subject to the constraint that V$^{1/2}$ is optimized, species exposed to conditions favoring identical V$^{1/2}$ may evolve different g$_2$ if pronounced interspecific differences exist for V$_{E1}$ and V$_{E2}$. A maximum-likelihood method is shown to be capable of generating accurate estimates of the genotypic parameters g$_1$, g$_2$, V$_{E1}$, and V$_{E2}$ 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.