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New & Forthcoming Titles | An Operator Semigroup in Mathematical Genetics - Lyapunov Equation Model of Drift and Mutation:

An Operator Semigroup in Mathematical Genetics

Lyapunov Equation Model of Drift and Mutation: Population Dependence and Asymptotic Behavior

Bobrowski, Adam, Kimmel, Marek

2015, 80 p. 20 illus.

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  • About this book

  • Combines genetic models with advanced mathematics
  • Contains examples based on human evolution data
  • Written by leading experts in the field
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 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. 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.

Content Level » Research

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

Related subjects » Analysis - Animal Sciences - Biomedical Engineering - Probability Theory and Stochastic Processes

Table of contents 

1 Introduction.- 2 Genetic background.- 3 Motivating example.- 4 Mathematical tools.- 5 Master Equation.- 6 Epilogue.

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