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Evolutionary dynamics with fluctuating population sizes and strong mutualism.

Thiparat Chotibut1, David R Nelson1

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Summary

This study introduces a Lotka-Volterra model that incorporates natural population growth, offering a more realistic evolutionary game theory framework. It reveals how population size fluctuations significantly impact evolutionary dynamics, especially in mutualism scenarios.

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Area of Science:

  • Evolutionary Biology
  • Theoretical Ecology
  • Mathematical Biology

Background:

  • Game theory is a standard framework for studying evolutionary dynamics in well-mixed populations.
  • Traditional models often assume a fixed population size, neglecting natural growth and fluctuations.
  • This simplification can limit the applicability of game theory to real-world evolutionary scenarios.

Purpose of the Study:

  • To develop and analyze a competitive Lotka-Volterra model that includes natural population growth and number fluctuations.
  • To investigate how varying population sizes influence evolutionary dynamics, particularly in scenarios not well-described by standard evolutionary game theory.
  • To determine fixation probabilities and mean fixation times in systems with population size fluctuations.

Main Methods:

  • Developed a competitive Lotka-Volterra model incorporating population growth and stochastic fluctuations.
  • Analyzed the model in an appropriate limit to connect with standard evolutionary game theory.
  • Employed matched asymptotic expansions for analytical and numerical determination of fixation probabilities and mean fixation times.
  • Focused on strong mutualism scenarios to highlight deviations from standard models.

Main Results:

  • The model reproduces standard evolutionary games with genetic drift and population size fluctuations in a specific limit.
  • Significant deviations from standard evolutionary game theory predictions were observed in regimes with varying population sizes, especially in strong mutualism.
  • Analytical and numerical results for fixation probabilities and mean fixation times were obtained, accounting for population size dynamics.

Conclusions:

  • Varying population size is a crucial factor that can strongly influence evolutionary dynamics beyond standard game theory predictions.
  • The developed Lotka-Volterm model provides a more comprehensive framework for understanding evolutionary processes in systems with natural population growth.
  • This research elucidates the critical interplay between population dynamics and evolutionary dynamics in well-mixed ecological systems.