Abstract
Populations of voles, and lemmings of the Northern hemisphere exhibit cyclic fluctuations with a cycle of three to four years. Krebs et al. presented evidence that the cycles are driven by changes in the genotypic structure of the population [9]. Incorporating some of their hypotheses we present a mathematical model of a one locus two allele population with density dependent selection and assuming a slow selection hypothesis, the existence of periodic solutions is proved. These solutions arise by Hopf bifurcation in δ 1/¦β1¦, the ratio of the residual death and birth rates of the density sensitive homozygote.
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Partially supported by NSF Grant # MCS-8005777
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Hunt, F. Regulation of population cycles by genetic feedback: Existence of periodic solutions of a mathematical model. J. Math. Biology 13, 271–282 (1982). https://doi.org/10.1007/BF00276064
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DOI: https://doi.org/10.1007/BF00276064