Genetic variability in sensitivity to population density affects the dynamics of simple ecological models

Many 1-dimensional discrete time ecological models contain a sensitivity pa rameter that does not affect the dynamic complexity of these models. We sho w that genetic variability in this parameter can have a strong effect on po pulation dynamics. We incorporate ecological dynamics in two different popu lation genetic models with one locus and two alleles. The first is the clas sical model of a randomly mating population in Hardy-Weinberg equilibrium, and the second is a model of differential selection in males and females. I n populations in Hardy-Weinberg equilibrium, variability in the sensitivity parameter can be maintained by overdominance. In this case, the dynamics o f the polymorphic population tend to be much simpler than those of monomorp hic populations. In the model with different selection in males and females , polymorphisms can be maintained in various ways, e.g., by opposing direct ional selection in males and females. Polymorphism in the sensitivity param eter tends to simplify population dynamics in the model with different sele ction in males and females as well. A number of interesting dynamic effects can be observed, e.g., multiple attractors with complicated basins of attr action. Then the final state of the system after a successful invasion by m utant alleles may depend on the mutation rate and on the distribution of mu tational steps. In addition, there are situations in which genetic variabil ity destabilizes a stable population dynamic equilibrium in the monomorphic model. There is an analogy between genetic variability and variability imp osed by the environment. If differences in sensitivity are caused by the en vironment, dynamic effects similar to those in the genetic models can be ob served. In addition, source-sink structures that are known to occur in spat ially structured models can be seen in the genetic model if one of the geno types is inviable. The results suggest that combining ecological and popula tion genetic models can lead to a number of new insights. More work is need ed, e.g., with fertility models, in which fitnesses are not assigned to ind ividuals, but to mating pairs. (C) 1999 Academic Press.