Mutation and Chaos in Nonlinear Models of Heredity

TL;DR

This paper investigates a nonlinear discrete dynamical system modeling Mendelian inheritance with mutations, revealing chaotic behaviors through numerical simulations, thus enhancing understanding of complex hereditary dynamics.

Contribution

It introduces a new model of hereditary transmission incorporating mutations and analyzes its chaotic dynamics using numerical simulations.

Findings

Chaotic behavior observed in the inheritance model.

Mutations significantly influence the system's dynamics.

Numerical simulations illustrate complex hereditary patterns.

Abstract

In this short communication, we shall explore a nonlinear discrete dynamical system that naturally occurs in population systems to describe a transmission of a trait from parents to their offspring. We consider a Mendelian inheritance for a single gene with three alleles and assume that to form a new generation, each gene has a possibility to mutate, that is, to change into a gene of the other kind. We investigate the derived models. A numerical simulation assists us to get some clear picture about chaotic behaviors of such models.