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The Wright–Fisher model with efficiency

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  • González Casanova, Adrián
  • Miró Pina, Verónica
  • Pardo, Juan Carlos

Abstract

In this article, we propose a Wright–Fisher model with two types of individuals: the inefficient individuals, those who need more resources to reproduce and can have a higher growth rate, and the efficient individuals. In this model, the total amount of resource N is fixed, and the population size varies randomly depending on the number of efficient individuals. We show that, as N increases, the frequency process of efficient individuals converges to a diffusion which is a generalization of the Wright–Fisher diffusion with selection. The genealogy of this model is given by a branching–coalescing process that we call the Ancestral Selection/Efficiency Graph, and that is an extension of the Ancestral Selection Graph (Krone and Neuhauser, 1997a,b). The main contribution of this paper is that, in evolving populations, inefficiency can arise as a promoter of selective advantage and not necessarily as a trade-off.

Suggested Citation

  • González Casanova, Adrián & Miró Pina, Verónica & Pardo, Juan Carlos, 2020. "The Wright–Fisher model with efficiency," Theoretical Population Biology, Elsevier, vol. 132(C), pages 33-46.
    • Handle: RePEc:eee:thpobi:v:132:y:2020:i:c:p:33-46
    DOI: 10.1016/j.tpb.2020.02.003
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    References listed on IDEAS

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    1. Parsons, Todd L. & Quince, Christopher & Plotkin, Joshua B., 2008. "Absorption and fixation times for neutral and quasi-neutral populations with density dependence," Theoretical Population Biology, Elsevier, vol. 74(4), pages 302-310.
    2. Robert E. Beardmore & Ivana Gudelj & David A. Lipson & Laurence D. Hurst, 2011. "Metabolic trade-offs and the maintenance of the fittest and the flattest," Nature, Nature, vol. 472(7343), pages 342-346, April.
    3. Mark J. Fitzpatrick & Elah Feder & Locke Rowe & Marla B. Sokolowski, 2007. "Maintaining a behaviour polymorphism by frequency-dependent selection on a single gene," Nature, Nature, vol. 447(7141), pages 210-212, May.
    4. Baake, Ellen & González Casanova, Adrián & Probst, Sebastian & Wakolbinger, Anton, 2019. "Modelling and simulating Lenski’s long-term evolution experiment," Theoretical Population Biology, Elsevier, vol. 127(C), pages 58-74.
    5. González Casanova, Adrián & Kurt, Noemi & Wakolbinger, Anton & Yuan, Linglong, 2016. "An individual-based model for the Lenski experiment, and the deceleration of the relative fitness," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2211-2252.
    6. Kluth, Sandra & Baake, Ellen, 2013. "The Moran model with selection: Fixation probabilities, ancestral lines, and an alternative particle representation," Theoretical Population Biology, Elsevier, vol. 90(C), pages 104-112.
    7. Mano, Shuhei, 2009. "Duality, ancestral and diffusion processes in models with selection," Theoretical Population Biology, Elsevier, vol. 75(2), pages 164-175.
    8. Lenz, Ute & Kluth, Sandra & Baake, Ellen & Wakolbinger, Anton, 2015. "Looking down in the ancestral selection graph: A probabilistic approach to the common ancestor type distribution," Theoretical Population Biology, Elsevier, vol. 103(C), pages 27-37.
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