Global dynamics of a selection model for the growth of a population with genotypic fertility differences |
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Authors: | G. J. Butler H. I. Freedman Paul Waltman |
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Affiliation: | (1) Department of Mathematics, University of Alberta, T6G 2G1 Edmonton, Canada;(2) Department of Mathematics, University of Iowa, 52242 Iowa City, IA, USA |
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Abstract: | A population growth model is considered for a one locus two allele problem with selection based entirely on fertility differences. A local stability analysis is carried out for the critical points — which include possible polymorphic states — of the resulting nonlinear differential equations. The methods of dynamical systems theory are applied to obtain limiting genotypic proportions for every initial state. Thus the results are global and there are no periodic solutions.Research for this paper was partially supported by the National Science and Engineering Research Council of Canada Grant NSERC A-8130Research for this paper was partially supported by the National Science and Engineering Research Council of Canada Grant NSERC A-4823Research supported by NSF Grant MCS 7901069. A portion of the work was carried out while the author was a Visiting Professor at the University of Utah, Salt Lake City, Utah |
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Keywords: | Selection Fertility Dynamics |
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