An Operator Semigroup in Mathematical Genetics

This authored monograph presents a mathematical description of the time evolution of neutral genomic regions in terms of the differential Lyapunov equation. The qualitative behavior of its solutions, with respect to different mutation models and demographic patterns, can be characterized using operator semi group theory.

Mutation and drift are two of the main genetic forces, which act on genes of individuals in populations. Their effects are influenced by population dynamics. This book covers the application to two mutation models: single step mutation for microsatellite loci and single-base substitutions. The effects of demographic change to the asymptotic of the distribution are also covered. The target audience primarily covers researchers and experts in the field but the book may also be beneficial for graduate students.

• Differential Lyapunov Equation
• Microsatellite Loci
• Mutation Models
• Mutation and Drift
• Single-base Substitions
• Time Evolution of Neutral Genomic Regions

“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.” (Ruhollah Jahanipur, zbMATH 1335.92002, 2016)

• Faculty of Electrical Engineering and Computer Science, Department of Mathematics, Lublin University of Technology, Nadbystrzycka 38A, Lublin, Poland

  Adam Bobrowski

• Systems Engineering group, Silesian University of Technology, Gliwice, Poland, Department of Statistics, Rice University, Houston, USA

  Marek Kimmel

Policies and ethics