Description 
1 online resource (xvii, 856 pages) 
Series 
Lecture notes in mathematics, 16179692 ; 2092 

Lecture notes in mathematics (SpringerVerlag) ; 2092. 00758434

Contents 
Introduction  Emergence and fixation in the FW model with two types  Formulation of the multitype and multiscale model  Formulation of the main results in the general case  A Basic Tool: Dual Representations  Longtime behaviour: ergodicity and nonergodicity  Meanfield emergence and fixation of rare mutants (Phase 1,2)  Methods and proofs for the FW model with two types  Emergence, fixation with M [greater than or equal to] 2 lower order types  Emergence, fixation: The general (M, M)type meanfield model  Neutral evolution on E1 after fixation (Phase 3)  Reequilibration on higher level E1 (Phase 4)  Iteration of the cycle I: Emergence and fixation on E2  Iteration of the cycle  the general multilevel hierarchy  Windingup: Proofs of the Theorems 311  Appendix 1  Tightness  Appendix 2. Nonlinear semigroup perturbations  References  Index of Notation and Tables of Basic Objects  Index 
Summary 
This book constructs a rigorous framework for analysing selected phenomena in evolutionary theory of populations arising due to the combined effects of migration, selection and mutation in a spatial stochastic population model, namely the evolution towards fitter and fitter types through punctuated equilibria. The discussion is based on a number of new methods, in particular multiple scale analysis, nonlinear Markov processes and their entrance laws, atomic measurevalued evolutions and new forms of duality (for statedependent mutation and multitype selection) which are used to prove ergodic theorems in this context and are applicable for many other questions and renormalization analysis for a variety of phenomena (stasis, punctuated equilibrium, failure of naive branching approximations, biodiversity) which occur due to the combination of rare mutation, mutation, resampling, migration and selection and make it necessary to mathematically bridge the gap (in the limit) between time and space scales 
Bibliography 
Includes bibliographical references (pages 847851) and index 
Notes 
English 

Online resource; title from PDF title page (SpringerLink, viewed January 23, 2014) 
Subject 
Population genetics  Mathematical models.


Punctuated equilibrium (Evolution)  Mathematical models


Stochastic models.


Markov processes.


Population genetics.


Genetics, Population


Markov Chains


Markov processes.


Population genetics  Mathematical models.


Stochastic models.

Form 
Electronic book

Author 
Greven, Andreas, 1953 author.

ISBN 
9783319021539 

3319021532 
