A dynamical system of temperature-dependent sex linked inheritance

TL;DR

This paper models temperature-dependent sex-linked inheritance using dynamical systems derived from gonosomal algebras, analyzing their long-term behavior and limit points.

Contribution

It introduces a reduction of complex sex-linked population dynamics to simpler free population models, enabling analysis of their asymptotic behavior.

Findings

Reduction of sex-linked population dynamics to free population models

Characterization of limit points for the evolution operators

Insights into long-term behavior of temperature-dependent sex determination systems

Abstract

Recently, R.Varro introduced a gonosomal algebra of the temperature-dependent sex determination system which is controlled by three temperature ranges. In this paper we study dynamical systems which are given by quadratic evolution operators of the gonosomal algebras of sex-liked populations. We show that this evolution operator can be reduced to an evolution operator of free population. Then using behavior of the free population we describe the set of limit points for trajectories of several evolution operators of the sex-linked populations.