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020 _a9783319021539
_9978-3-319-02153-9
024 7 _a10.1007/978-3-319-02153-9
_2doi
050 4 _aQA273.A1-274.9
050 4 _aQA274-274.9
072 7 _aPBT
_2bicssc
072 7 _aPBWL
_2bicssc
072 7 _aMAT029000
_2bisacsh
082 0 4 _a519.2
_223
100 1 _aDawson, Donald A.
_eauthor.
245 1 0 _aSpatial Fleming-Viot Models with Selection and Mutation
_h[electronic resource] /
_cby Donald A. Dawson, Andreas Greven.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2014.
300 _aXVII, 856 p. 1 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2092
505 0 _aIntroduction -- Emergence and fixation in the F-W 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 -- Long-time behaviour: ergodicity and non-ergodicity -- Mean-field emergence and fixation of rare mutants (Phase 1,2) -- Methods and proofs for the F-W model with two types -- Emergence, fixation with M ≥ 2 lower order types -- Emergence, fixation: The general (M, M)-type mean-field model -- Neutral evolution on E1 after fixation (Phase 3) -- Re-equilibration on higher level E1 (Phase 4) -- Iteration of the cycle I: Emergence and fixation on E2 -- Iteration of the cycle – the general multilevel hierarchy -- Winding-up: Proofs of the Theorems 3-11 -- Appendix 1 – Tightness -- Appendix 2. Nonlinear semigroup perturbations -- References -- Index of Notation and Tables of Basic Objects -- Index.
520 _aThis 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.
650 0 _aMathematics.
650 0 _aEvolution (Biology).
650 0 _aDistribution (Probability theory).
650 1 4 _aMathematics.
650 2 4 _aProbability Theory and Stochastic Processes.
650 2 4 _aEvolutionary Biology.
700 1 _aGreven, Andreas.
_eauthor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783319021522
830 0 _aLecture Notes in Mathematics,
_x0075-8434 ;
_v2092
856 4 0 _uhttp://dx.doi.org/10.1007/978-3-319-02153-9
912 _aZDB-2-SMA
912 _aZDB-2-LNM
999 _c92819
_d92819