Abstract
We describe the — unexpected — occurrence of stable limit cycles in the two locus, two allele model. No frequency dependence is involved. The cycles are due to the interaction between recombination and natural selection.
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Akin, E.: The geometry of population genetics. Lecture notes in biomathematics. Vol. 31. Berlin-Heidelberg-New York: Springer 1979
Akin, E.: Domination or equilibrium. Math. Biosci. 50, 239–250 (1980)
Akin, E.: Cycling in the two locus system (Manuscript 1981)
Crow, J. F., Kimura, M.: An introduction to population genetics theory. New York: Harper and Row Publishers, Inc. 1970
Ewens, W. J.: With additive fitness, the mean fitness increases. Nature 221, 1076 (1969a)
Ewens, W. J.: Population genetics. London: Methuen and Co. 1969b
Hastings, A.: Disequilibrium, selection, and recombination: Limits in two-locus two-allele models. Genetics (in press)
Hastings, A.: Induced underdominance at a stable equilibrium (Two locus models) (to appear)
Hirsch, M. W., Pugh, C. C., Shub, M.: Invariant manifolds. Lecture notes in mathematics. Vol. 583. Berlin-Heidelberg-New York: Springer 1977
Hoppensteadt, F. C.: A slow selection analysis of two-locus, two-allele traits. Theoret. Population Biology 9, 68–81 (1976)
Karlin, S., Feldman, M. W.: Linkage and selection: Two locus symmetric viability models. Theoret. Population Biology 1, 39–71 (1970)
Kimura, M.: On the change of population fitness by natural selection. Heredity 12, 145–167 (1958)
Marsden, J. E., McCracken, M.: The Hopf bifurcation and its applications. Berlin-Heidelberg-New York: Springer 1976
Moran, P. A. P.: On the nonexistence of adaptive topographies. Ann. Hum. Genet. 27, 338–393 (1964)
Nagylaki, T.: The evolution of one-and two-locus systems: I. Genetics 83, 583–600 (1976)
Nagylaki, T.: Selection in one-and two-locus systems. Lecture notes in biomathematics. Vol. 15. Berlin-Heidelberg-New York: Springer 1977
Nagylaki, T., Crow, J. F.: Continuous selection models. Theoret. Population Biology 5, 257–283 (1974)
Shahshahani, S.: A new mathematical framework for the study of linkage and selection. Memoirs AMS 211, (1979)
Taylor, P. D., Jonker, L. B.: Evolutionarily stable strategies and game dynamics. Math. Biosci. 40, 145–156 (1978)
Wright, S.: Surfaces of selective value. PNAS 58, 165–172 (1967)
Zeeman, E. C.: Population dynamics from game theory. In: Proc. Int. Conf. Global Theory of Dynamical Systems, Northwestern, Evanston, Illinois 1979
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This work received support from the National Science Foundation and the Research Foundation of the City University of New York
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Akin, E. Cycling in simple genetic systems. J. Math. Biology 13, 305–324 (1982). https://doi.org/10.1007/BF00276066
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DOI: https://doi.org/10.1007/BF00276066