Convergence of genetic compositions assuming infinite population-size and overlapping generations

The assumptions for the model treated in this paper are based on a population of hypothetically infinite size, which has reached its optimum density within a limited habitat. The aim has been to derive sufficient conditions for the genetic composition of a population to converge to a limit if generations overlap and time is measured in discrete intervals. Trivially the genetic composition does not change if at the starting point of time the compositions within all age-classes are the same; otherwise global convergence of the age-class distributions implies uniform convergence of the genetic compositions within the single age-classes if mating takes place between at least two age-classes, or within the first age-class only. Excluding age-class 1 mating within one age-class only results in periodical change of genetic compositions.