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A Wright-Fisher model with indirect selection.
Ludovic Goudenège1, Pierre-André Zitt2
1LAMA, Université de Marne-la-Vallée, 5, boulevard Descartes, Cité Descartes-Champs-sur-Marne, 77454, Marne-la-Vallée Cedex 2, France. goudenege@math.cnrs.fr.
Journal of Mathematical Biology
|March 2, 2015
Summary
This study models spiteful behavior using a generalized Wright-Fisher model. It reveals how harmful actions can evolve due to indirect selective advantages in large populations with skewed sex ratios.
Area of Science:
- Evolutionary biology
- Population genetics
- Mathematical modeling
Background:
- Spiteful behaviors, where individuals harm others without personal gain, are observed in nature.
- Examples include parasitoid wasps where males mate without fertility.
Purpose of the Study:
- To generalize the Wright-Fisher model to include spiteful behavior.
- To analyze the evolutionary dynamics of such behaviors in large populations.
Main Methods:
- A generalized Wright-Fisher model incorporating spiteful traits.
- Mathematical analysis using recurrence relations and partial differential equations (PDEs).
- Derivation of a diffusion approximation for large populations.
Main Results:
- Convergence to a diffusion process with frequency-dependent selection and genetic drift.
- Quantitative comparison of indirect and direct selective advantages.
- Demonstration of spiteful behavior's evolutionary viability under specific conditions.
Conclusions:
- Spiteful behavior can be evolutionarily stable due to indirect selection.
- The generalized model provides a framework for studying altruism and spite in population genetics.
- Mathematical tools offer new insights into evolutionary dynamics.
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