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Maximization principles for frequency-dependent selection I: the one-locus two-allele case

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  • Schneider, Kristan A.

Abstract

In this article we study the one-locus two-allele version of the pairwise-interaction model of frequency-dependent selection in discrete and continuous time. Our main aim is to provide necessary and sufficient conditions for the validity of maximization principles. We provide a systematic approach that covers all possible facets of the dynamical behavior of the model, and we illustrate our results by concrete examples. We show that the mean fitness of the population is nondecreasing if the interaction coefficients are symmetric and positive. Moreover, monotonic convergence to the set of equilibria always occurs, which is not true if we also consider negative interaction coefficients. For asymmetric interaction, we provide necessary conditions when the mean fitness is nondecreasing and sufficient conditions when it is not. Furthermore, in discrete time, we show that limit cycles cannot occur, unless some interaction coefficients are negative.

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  • Schneider, Kristan A., 2008. "Maximization principles for frequency-dependent selection I: the one-locus two-allele case," Theoretical Population Biology, Elsevier, vol. 74(3), pages 251-262.
    • Handle: RePEc:eee:thpobi:v:74:y:2008:i:3:p:251-262
    DOI: 10.1016/j.tpb.2008.07.006
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    References listed on IDEAS

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    1. David W. Pfennig & William R. Harcombe & Karin S. Pfennig, 2001. "Frequency-dependent Batesian mimicry," Nature, Nature, vol. 410(6826), pages 323-323, March.
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    Cited by:

    1. Priklopil, Tadeas, 2012. "Chaotic dynamics of allele frequencies in condition-dependent mating systems," Theoretical Population Biology, Elsevier, vol. 82(2), pages 109-116.
    2. Yasuhiro Sato & Rie Shimizu-Inatsugi & Kazuya Takeda & Bernhard Schmid & Atsushi J. Nagano & Kentaro K. Shimizu, 2024. "Reducing herbivory in mixed planting by genomic prediction of neighbor effects in the field," Nature Communications, Nature, vol. 15(1), pages 1-14, December.
    3. Trotter, Meredith V. & Spencer, Hamish G., 2009. "Complex dynamics occur in a single-locus, multiallelic model of general frequency-dependent selection," Theoretical Population Biology, Elsevier, vol. 76(4), pages 292-298.
    4. Matessi, Carlo & Schneider, Kristan A., 2009. "Optimization under frequency-dependent selection," Theoretical Population Biology, Elsevier, vol. 76(1), pages 1-12.

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