CONSTRAINTS FOR THE EVOLUTION OF FUNCTIONALLY COUPLED CHARACTERS: A NONLINEAR ANALYSIS OF A PHENOTYPIC MODEL

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Abstract
On the basis of a phenotypic model of R. Lande a nonlinear analysis is performed to investigate the evolutionary dynamics of functionally coupled quantitative traits. The underlying fitness topography has multiple peaks with a ridge and two hills adjacent to a saddle. Evolution of a complex of functionally constrained characters corresponds precisely to moving uphill along a ridge. For modelling the topology of the ridge, I follow ideas of Rechenberg and Wagner and use a so-called corridor model. The analysis reveals certain population-genetic constraints for the evolutionary emergence of a selectively favored complex of functionally constrained characters. Due to the population-genetic structure, as reflected in the pattern of variation and covariation, a population will often not be allowed to become adapted to existing physiological requirements, such as functional coupling of characters. Instead, within the present model where extinction cannot occur, it will evolve in some other direction toward an optimum that may be physiologically rather remote. In particular, there exists an optimal pattern of genetic and phenotypic variances and covariances in the following sense: on the one hand an increasing deviation from this pattern imposes increasing restrictions on the set of initial conditions enabling a population to move uphill along the ridge; on the other hand, an increasing deviation leads to a decreasing rate of adaptation along the ridge. Finally, some consequences of these constraints for possible interpretations of certain empirical results are discussed.