Spatial Fleming-Viot Models with Selection and Mutation

Beschreibung

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 measure-valued evolutions and new forms of duality (for state-dependent 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.
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 measure-valued evolutions and new forms of duality (for state-dependent 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.
Develops a class of spatial models of a population undergoing mutation, selection and migration Develops new duality methods for multitype population models Develops the McKean-Vlasov limit of exchangeable population models and their entrance laws Identifies mutation-selection equilibria Offers valuable insights into the role of migration in the emergence of rare mutants in spatial Fleming-Viot models Sheds new light on the role of migration in sustaining biodiversity in evolution Includes supplementary material: sn.pub/extras

Autor*in

Donald A. Dawson

Themen in »Spatial Fleming-Viot Models with Selection and Mutation«

60J70,92D15,92D25,60J80,60J85. Dual processes Emergence of rare mutants Fleming-Viot processes Mutation-selection Spatial migration

Stimmen zu »Spatial Fleming-Viot Models with Selection and Mutation«

Details

Link teilen