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Homophilic replicator equations.

Bryce Morsky¹, Ross Cressman², C T Bauch³

¹Department of Mathematics and Statistics, University of Guelph, Guelph, Canada. bmorsky@uoguelph.ca.

Journal of Mathematical Biology

|December 21, 2016

Summary

This summary is machine-generated.

Homophilic imitation, where organisms copy others with similar traits, significantly impacts population diversity by influencing tag and strategy evolution. This process affects how novel traits spread and can slow down evolutionary convergence.

Keywords:

Diversity Homophily Imitation Replicator equation Tags Traits

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Area of Science:

Evolutionary Biology
Theoretical Ecology
Behavioral Ecology

Background:

Tags, or conspicuous attributes, influence inter-organism behavior and have been used to study group formation and altruism.
Homophilic imitation, a form of tag-based selection, occurs when individuals imitate others with similar tags.

Purpose of the Study:

To develop homophilic replicator equations to model tag-based selection and homophilic imitation dynamics.
To investigate the impact of homophilic imitation on population diversity, trait evolution, and evolutionary stability.

Main Methods:

Developed homophilic replicator equations modeling imitation dynamics based on tags, strategies, fitness, and tag similarity.
Analyzed fixed manifolds, stability conditions, and the phenomenon of coat-tailing.
Extended the model to include recurrent mutations and invasions to assess their effects on diversity.

Main Results:

Homophilic imitation significantly affects population diversity but not the Evolutionarily Stable Strategy (ESS).
Novel tags introduced by invaders establish more readily with homophilic imitation.
A negative correlation was found between homophily and the rate of convergence.

Conclusions:

Homophilic imitation is a key driver of diversity in populations with tag-based selection.
The model provides insights into how traits spread and how population diversity is maintained or reduced under different invasion scenarios.
Understanding homophily is crucial for predicting evolutionary dynamics and trait diversity in various biological systems.