IDEAS home Printed from https://ideas.repec.org/a/eee/thpobi/v74y2008i3p251-262.html
   My bibliography  Save this article

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

Author

Listed:
  • 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.

Suggested Citation

  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0040580908000786
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.tpb.2008.07.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. David W. Pfennig & William R. Harcombe & Karin S. Pfennig, 2001. "Frequency-dependent Batesian mimicry," Nature, Nature, vol. 410(6826), pages 323-323, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Matessi, Carlo & Schneider, Kristan A., 2009. "Optimization under frequency-dependent selection," Theoretical Population Biology, Elsevier, vol. 76(1), pages 1-12.
    3. Priklopil, Tadeas, 2012. "Chaotic dynamics of allele frequencies in condition-dependent mating systems," Theoretical Population Biology, Elsevier, vol. 82(2), pages 109-116.
    4. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:thpobi:v:74:y:2008:i:3:p:251-262. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/intelligence .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.