Genetic Variability in Sensitivity to Population Density Affects the Dynamics of Simple Ecological Models

Abstract

Many 1-dimensional discrete time ecological models contain a sensitivity parameter that does not affect the dynamic complexity of these models. We show that genetic variability in this parameter can have a strong effect on population dynamics. We incorporate ecological dynamics in two different population genetic models with one locus and two alleles. The first is the classical model of a randomly mating population in Hardy–Weinberg equilibrium, and the second is a model of differential selection in males and females. In populations in Hardy–Weinberg equilibrium, variability in the sensitivity parameter can be maintained by overdominance. In this case, the dynamics of the polymorphic population tend to be much simpler than those of monomorphic populations. In the model with different selection in males and females, polymorphisms can be maintained in various ways, e.g., by opposing directional selection in males and females. Polymorphism in the sensitivity parameter tends to simplify population dynamics in the model with different selection in males and females as well. A number of interesting dynamic effects can be observed, e.g., multiple attractors with complicated basins of attraction. Then the final state of the system after a successful invasion by mutant alleles may depend on the mutation rate and on the distribution of mutational steps. In addition, there are situations in which genetic variability destabilizes a stable population dynamic equilibrium in the monomorphic model. There is an analogy between genetic variability and variability imposed by the environment. If differences in sensitivity are caused by the environment, dynamic effects similar to those in the genetic models can be observed. In addition, source-sink structures that are known to occur in spatially structured models can be seen in the genetic model if one of the genotypes is inviable. The results suggest that combining ecological and population genetic models can lead to a number of new insights. More work is needed, e.g., with fertility models, in which fitnesses are not assigned to individuals, but to mating pairs.