Quadratic stochastic operators as operators describing Fisher's generalized model

Abstract

This article explores the modeling of biological processes using dynamic models. In particular, it highlights the
importance of dynamic models in population genetics. To enable a more precise mathematical analysis, the use
of quadratic stochastic operators (QSO) is introduced. The paper also examines the role of QSO in the
generalized Fisher model and analyzes their mathematical properties. It is demonstrated that QSO serve as a
well-founded tool for the stable mathematical modeling of genetic processes within populations. Special
attention is given to the fundamental definitions of QSO, their properties, and their application within the model.