Summary
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 ageclasses, or within the first age-class only. Excluding age-class 1 mating within one age-class only results in periodical change of genetic compositions.
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References
Crow, J. F., Kimura, K.: An introduction of population genetics theory. Harper and Row 1970.
Demetrius, L.: Primitivity conditions for growth matrices. Math. Biosc. 12, 53–58 (1971).
Girault, M.: Stochastic processes. Berlin-Heidelberg-New York: Springer 1966.
Jacquard, A.: The genetic structure of populations. Berlin-Heidelberg-New York: Springer 1974.
Karlin, S.: Equilibrium behaviour of population genetic models with non-random mating. New York- London-Paris: Gordon and Breach 1969.
Leslie, P. H.: On the use of matrices in certain population mathematics. Biometrika 33, 183–212 (1945).
Moran, P. A. P.: The statistical processes of evolutionary theory. Oxford: Clarendon Press 1962.
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Gregorius, H.R. Convergence of genetic compositions assuming infinite population-size and overlapping generations. J. Math. Biology 3, 179–186 (1976). https://doi.org/10.1007/BF00276204
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DOI: https://doi.org/10.1007/BF00276204