Summary
This investigation studies the dynamic behaviour of a population in which there is a geographic variation in fitness of a one-locus, two allele trait. The results derived here complement certain results by W. H. Fleming who described the existence of a stable polymorphism when the ratio of selection intensity to dispersion rate exceeds a critical value. Here an approximation to the polymorphic state is obtained, and the evolution of other initial states to it is studied.
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References
Fisher, R. A.: Gene Frequencies in a cline determined by selection and diffusion. Biometrics 6, 353–361 (1950).
Fleming, W. H.: A selection-migration model in population genetics. J. of Math. Biol. 2, 219–233 (1975).
Hoppensteadt, F, C., Gordon, N.: Nonlinear Stability Analysis of Static States which arise through bifurcation. Comm. Pure Appl. Math. XXVIII (1975).
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This research was partially supported by the National Science Foundation under grant number GP-32996 X.
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Hoppensteadt, F.C. Analysis of a stable polymorphism arising in a selection-migration model in population genetics. J. Math. Biology 2, 235–240 (1975). https://doi.org/10.1007/BF00277152
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DOI: https://doi.org/10.1007/BF00277152