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A stochastic field theory for the evolution of quantitative traits in finite populations

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  • Bhat, Ananda Shikhara

Abstract

Infinitely many distinct trait values may arise in populations bearing quantitative traits, and modeling their population dynamics is thus a formidable task. While classical models assume fixed or infinite population size, models in which the total population size fluctuates due to demographic noise in births and deaths can behave qualitatively differently from constant or infinite population models due to density-dependent dynamics. In this paper, I present a stochastic field theory for the eco-evolutionary dynamics of finite populations bearing one-dimensional quantitative traits. I derive stochastic field equations that describe the evolution of population densities, trait frequencies, and the mean value of any trait in the population. These equations recover well-known results such as the replicator-mutator equation, Price equation, and gradient dynamics in the infinite population limit. For finite populations, the equations describe the intricate interplay between natural selection, noise-induced selection, eco-evolutionary feedback, and neutral genetic drift in determining evolutionary trajectories. My work uses ideas from statistical physics, calculus of variations, and SPDEs, providing alternative methods that complement the measure-theoretic martingale approach that is more common in the literature.

Suggested Citation

  • Bhat, Ananda Shikhara, 2025. "A stochastic field theory for the evolution of quantitative traits in finite populations," Theoretical Population Biology, Elsevier, vol. 161(C), pages 1-12.
    • Handle: RePEc:eee:thpobi:v:161:y:2025:i:c:p:1-12
    DOI: 10.1016/j.tpb.2024.10.003
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    References listed on IDEAS

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    1. Débarre, Florence & Otto, Sarah P., 2016. "Evolutionary dynamics of a quantitative trait in a finite asexual population," Theoretical Population Biology, Elsevier, vol. 108(C), pages 75-88.
    2. Avila, Piret & Mullon, Charles, 2023. "Evolutionary Game Theory and the Adaptive Dynamics Approach: Adaptation where Individuals Interact," IAST Working Papers 23-150, Institute for Advanced Study in Toulouse (IAST).
    3. Piret Avila & Charles Mullon, 2023. "Evolutionary Game Theory and the Adaptive Dynamics Approach: Adaptation where Individuals Interact," Post-Print hal-04067694, HAL.
    4. David V McLeod & Troy Day, 2019. "Social evolution under demographic stochasticity," PLOS Computational Biology, Public Library of Science, vol. 15(2), pages 1-13, February.
    5. Doering, Charles R. & Mueller, Carl & Smereka, Peter, 2003. "Interacting particles, the stochastic Fisher–Kolmogorov–Petrovsky–Piscounov equation, and duality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 325(1), pages 243-259.
    6. Schraiber, Joshua G., 2014. "A path integral formulation of the Wright–Fisher process with genic selection," Theoretical Population Biology, Elsevier, vol. 92(C), pages 30-35.
    7. U. Dieckmann & R. Law, 1996. "The Dynamical Theory of Coevolution: A Derivation from Stochastic Ecological Processes," Working Papers wp96001, International Institute for Applied Systems Analysis.
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