An operator semigroup in mathematical genetics : Lyapunov equation model of drift and mutation : population dependence and asymptotic behavior

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. Front Matter....Pages i-vi Introduction....Pages 1-2 Genetic Background....Pages 3-18 Motivating Example: Population Bottlenecks in the History of Modern Humans, Use of the Imbalance Index....Pages 19-22 Mathematical Tools....Pages 23-65 Master Equation and Asymptotic Behavior of Its Solutions....Pages 67-83 Epilogue....Pages 85-85 Back Matter....Pages 87-88