Mendelian and Non-Mendelian Quadratic Operators

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.

The paper is 14 pages and will appear in Appl. Math. Inf. Sci. 7, No. 5, 1721-1729 (2013)