On discrete evolutionary dynamics driven by quadratic interactions

TL;DR

This paper explores discrete evolutionary models with quadratic interactions, focusing on genetic algebras to analyze stability and evolution, and also examines cases outside this framework such as bistochastic matrices.

Contribution

It extends the application of genetic algebras to quadratic evolutionary dynamics and investigates stability in models that cannot be addressed by this framework.

Findings

Analysis of stability in genetic algebra models

Identification of models outside genetic algebra framework

Insights into quadratic interactions in diploid populations

Abstract

After an introduction to the general topic of models for a given locus of a diploid population whose quadratic dynamics is determined by a fitness landscape, we consider more specifically the models that can be treated using genetic (or train) algebras. In this setup, any quadratic offspring interaction can produce any type of offspring and after the use of specific changes of basis, we study the evolution and possible stability of some examples. We also consider some examples that cannot be treated using the framework of genetic algebras. Among these are bistochastic matrices.