An operator semigroup in mathematical genetics
The authors first describe some models for population dynamics such as the Cannings model and the Wright-Fisher model. Then, they introduce the Moran model for population genetics, which provides a way to define the master equation. Chapter 4 is devoted to describe mathematical tools for solving and investigating the asymptotic behavior of mild solutions to the master equation via semigroup theory. Here, there are facts about Banach spaces, bounded linear operators, semigroups of linear operators and their generators, the Markov semigroup and the concept of core of generators. Deriving the semigroup related to the master equation and its asymptotic behavior is the topic of the last chapter. This book is a very interesting readable descriptive text in one of the important branches of applied mathematics. It helps readers to gain insight about the application of such deep mathematical tools as the semigroup theory of linear operators in other branches of science.
scientific article; zbMATH DE number 6176759