Developmental Models and Polygenic Characters

Abstract

A comprehensive understanding of evolution requires an appreciation of the mechanisms by which genes affect phenotypes. It is generally accepted that genetic variation produces phenotypic variation through changes in developmental processes, and a number of investigators have sought ways to introduce developmental information into evolutionary models (Riska 1986; Atchley 1987; Slatkin 1987; Wake and Larson 1987). Nonetheless, a general understanding of how development mediates between the genetic and phenotypic levels of evolution remains elusive. Toward improving this understanding, we have explored the consequences of a simple nonlinear model of development based on the mechanism believed to be responsible for the determination of eyespot patterns on the wings of butterflies (Murray 1989; Nijhout 1991). Models of pattern formation in development (such as positional information, lateral inhibition, reaction-diffusion, diffusion gradient and threshold) make precise predictions about how form will vary with variation in parameters of the model (Meinhardt 1982; Edelstein-Keshet 1988; Murray 1989; Nijhout 1990). Moreover, many models allow us to relate certain parameter values specifically to gene activity. For instance, in ordinary and partial differential equation models, the rate constants can often be directly equated with gene activity, because genes code for enzymes that control reaction rates. Different values of a rate constant can represent different alleles of a gene that code for enzymes with different catalytic efficiencies. Developmental models can, therefore, make certain predictions about the relation between genetic variation and phenotypic variation. Developmental models, however, are always about the individual, whereas evolutionary theory is about populations. Thus, for developmental models to be useful for the study of microevolution, they need to be stated in populational terms (Atchley and Hall 1991). To date, attempts to integrate developmental information into microevolutionary models have been done in the context of quantitative genetics by assuming that developmental parameters such as the growth rate of a tissue and the timing of its growth can be treated as quantitative genetic traits (Atchley 1987, 1990; Slatkin 1987). Atchley (1987) has developed a model that assumes that natural selection can act directly on these developmental