[Modelling of selection acting upon the pleioptropic locus in an asynchronous population]

We created and examined a mathematical model describing the size and genetic composition dynamics in a population with two age classes, where the survival of both zygotes and adult individuals is determined by one pleioptropic locus. Even under present limitations, as the outside effects of a complex multigenic system are reduced to the case of single locus, our model demonstrates a wide range of different evolutionary scenarios for possible changes in the population dynamics. An increase in the reproductive potential and survival is accompanied by a transition from stable to oscillating population numbers. However, the evolutionary growth of these parameters may be nonmonotonic and may fluctuate significantly. In the case of antagonistic pleioptropy, an increase in one of these parameters usually leads to a predictable decrease in the other. This, in turn, may even stabilize the numbers and genetic compositions of the age groups. We demonstrated that selection acting on later stages of the life cycle is accompanied by destabilization of the Hardy-Weinberg equilibriums that link allele and genotype frequencies. We obtained a balance ratio, which allowed us to compare the combined fitness of the genotypes and to demonstrate that selection leads to the exclusion of the least adapted genotypes. Initial conditionsmay in some cases determine the genetic composition and pattern of population size dynamics.