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Following the Dynamics of Structural Variants in Experimentally Evolved Populations

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Evolutionary Stability for Interactions among Kin under Quantitative Inheritance.

¹Present address: Box 654, 1916 Pike Place #12, Seattle, Washington 98101.

|April 1, 1989

Summary

Evolutionarily stable strategy (ESS) analysis accurately predicts equilibria in models of quantitative inheritance, even with related individuals and environmental variance. This validates ESS predictions for pairwise interactions in evolutionary biology.

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Area of Science:

Evolutionary biology
Quantitative genetics
Game theory

Background:

The theory of evolutionarily stable strategies (ESS) is a powerful tool for predicting evolutionary outcomes under frequency-dependent selection.
However, ESS analysis relies on simplifying assumptions regarding the genetic basis of inheritance, which may not always hold true.

Purpose of the Study:

To analyze the outcomes of interactions between related individuals using a symmetrized multilocus model of quantitative inheritance.
To compare the equilibria predicted by this model with those derived from ESS analysis.
To investigate the impact of environmental variance on evolutionary equilibria.

Main Methods:

A symmetrized multilocus model of quantitative inheritance without mutation was employed.
Fitness changes due to interactions were approximated by the exponential of a quadratic surface.
The stability conditions for equilibria were analyzed and compared between the quantitative genetics model and ESS analysis.

Main Results:

Phenotypes identified as evolutionarily stable by ESS analysis were consistently found as equilibria in the quantitative genetics model.
A difference in one stability condition emerged when relatives interacted, attributable to a modified inclusive fitness function for quantitative traits.
Environmental variance generally altered equilibrium phenotypes but affected ESS-derived equilibria to a similar extent.
A class of genetically polymorphic equilibria were identified but found to be unstable within this model.

Conclusions:

The study validates the use of ESS analysis for predicting the evolution of pairwise interactions under a broader range of conditions.
The findings highlight the importance of considering quantitative inheritance and relatedness in evolutionary game theory.
The results expand the theoretical framework for understanding evolutionary dynamics in complex genetic systems.