LEADER 04113nam 22006015 450 001 9910299962803321 005 20200630073410.0 010 $a3-319-02153-2 024 7 $a10.1007/978-3-319-02153-9 035 $a(CKB)3710000000078750 035 $a(DE-He213)978-3-319-02153-9 035 $a(SSID)ssj0001091935 035 $a(PQKBManifestationID)11709370 035 $a(PQKBTitleCode)TC0001091935 035 $a(PQKBWorkID)11032298 035 $a(PQKB)10296812 035 $a(MiAaPQ)EBC3107052 035 $a(PPN)176105549 035 $a(EXLCZ)993710000000078750 100 $a20131212d2014 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSpatial Fleming-Viot Models with Selection and Mutation /$fby Donald A. Dawson, Andreas Greven 205 $a1st ed. 2014. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014. 215 $a1 online resource (XVII, 856 p. 1 illus.) 225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v2092 300 $aBibliographic Level Mode of Issuance: Monograph 311 $a3-319-02152-4 327 $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. 330 $aThis book constructs a rigorous framework for analysing selected phenomena in evolutionary theory of populations arising due to the combined effects of migration, selection and mutation in a spatial stochastic population model, namely the evolution towards fitter and fitter types through punctuated equilibria. The discussion is based on a number of new methods, in particular multiple scale analysis, nonlinear Markov processes and their entrance laws, atomic measure-valued evolutions and new forms of duality (for state-dependent mutation and multitype selection) which are used to prove ergodic theorems in this context and are applicable for many other questions and renormalization analysis for a variety of phenomena (stasis, punctuated equilibrium, failure of naive branching approximations, biodiversity) which occur due to the combination of rare mutation, mutation, resampling, migration and selection and make it necessary to mathematically bridge the gap (in the limit) between time and space scales. 410 0$aLecture Notes in Mathematics,$x0075-8434 ;$v2092 606 $aProbabilities 606 $aEvolution (Biology) 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aEvolutionary Biology$3https://scigraph.springernature.com/ontologies/product-market-codes/L21001 615 0$aProbabilities. 615 0$aEvolution (Biology) 615 14$aProbability Theory and Stochastic Processes. 615 24$aEvolutionary Biology. 676 $a575.1 700 $aDawson$b Donald A$4aut$4http://id.loc.gov/vocabulary/relators/aut$0478914 702 $aGreven$b Andreas$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910299962803321 996 $aSpatial Fleming-Viot Models with Selection and Mutation$92356121 997 $aUNINA