Mendelian and Non-Mendelian Quadratic Operators

TL;DR

This paper develops mathematical models for Mendelian and Non-Mendelian inheritance in bisexual populations, focusing on Fisher's 1:1 principle, and applies these models to blood group transmission.

Contribution

It introduces new quadratic stochastic operators modeling both Mendelian and Non-Mendelian inheritance, including blood group transmission.

Findings

Mathematical models for Mendelian inheritance under Fisher's principle

Quadratic operators for ABO and Rh blood group inheritance

Analysis of inheritance evolution in bisexual populations

Abstract

In this paper, we attempt to provide mathematical models of Mendelian and Non-Mendelian inheritances of the bisexual population system having Fisher's {\textbf{1:1}} principle. In our model, we always assume that distributions of the same phenotype of female and male populations are equal. We study the evolution of a Mendelian trait. As an application of a non-Mendelian inheritance, we construct a quadratic stochastic operator that describes transmission of {\textbf{ABO}} and Rh blood groups.