LEADER 04387nam 22006735 450 001 9910300252603321 005 20220516173227.0 010 $a3-319-21711-9 024 7 $a10.1007/978-3-319-21711-6 035 $a(CKB)3710000000471391 035 $a(EBL)4178425 035 $a(SSID)ssj0001585574 035 $a(PQKBManifestationID)16265281 035 $a(PQKBTitleCode)TC0001585574 035 $a(PQKBWorkID)14865580 035 $a(PQKB)10270089 035 $a(DE-He213)978-3-319-21711-6 035 $a(MiAaPQ)EBC4178425 035 $a(PPN)190527218 035 $a(EXLCZ)993710000000471391 100 $a20150903d2015 u| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aStochastic models for structured populations $escaling limits and long time behavior /$fby Sylvie Meleard, Vincent Bansaye 205 $a1st ed. 2015. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2015. 215 $a1 online resource (111 p.) 225 1 $aStochastics in Biological Systems,$x2364-2297 ;$v1.4 300 $aDescription based upon print version of record. 311 $a3-319-21710-0 320 $aIncludes bibliographical references. 327 $aIntroduction -- Discrete Monotype Population Models and One-dimensional Stochastic Differential Equations -- Birth and Death Processes -- Scaling Limits for Birth and Death Processes -- Continuous State Branching Processes -- Feller Diffusion with Random Catastrophes -- Structured Populations and Measure-valued Stochastic Differential Equations -- Population Point Measure Processes -- Scaling limits for the individual-based process -- Splitting Feller Diffusion for Cell Division with Parasite Infection -- Markov Processes along Continuous Time Galton-Watson Trees -- Appendix. 330 $aIn this contribution, several probabilistic tools to study population dynamics are developed. The focus is on scaling limits of qualitatively different stochastic individual based models and the long time behavior of some classes of limiting processes. Structured population dynamics are modeled by measure-valued processes describing the individual behaviors and taking into account the demographic and mutational parameters, and possible interactions between individuals. Many quantitative parameters appear in these models and several relevant normalizations are considered, leading to infinite-dimensional deterministic or stochastic large-population approximations. Biologically relevant questions are considered, such as extinction criteria, the effect of large birth events, the impact of environmental catastrophes, the mutation-selection trade-off, recovery criteria in parasite infections, genealogical properties of a sample of individuals. These notes originated from a lecture series on Structured Population Dynamics at Ecole polytechnique (France). Vincent Bansaye and Sylvie Méléard are Professors at Ecole Polytechnique (France). They are a specialists of branching processes and random particle systems in biology. Most of their research concerns the applications of probability to biodiversity, ecology and evolution. 410 0$aStochastics in Biological Systems,$x2364-2297 ;$v1.4 606 $aProbabilities 606 $aBiomathematics 606 $aEcology 606 $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004 606 $aGenetics and Population Dynamics$3https://scigraph.springernature.com/ontologies/product-market-codes/M31010 606 $aTheoretical Ecology/Statistics$3https://scigraph.springernature.com/ontologies/product-market-codes/L19147 615 0$aProbabilities. 615 0$aBiomathematics. 615 0$aEcology. 615 14$aProbability Theory and Stochastic Processes. 615 24$aGenetics and Population Dynamics. 615 24$aTheoretical Ecology/Statistics. 676 $a519.2 700 $aMeleard$b Sylvie$4aut$4http://id.loc.gov/vocabulary/relators/aut$0755635 702 $aBansaye$b Vincent$4aut$4http://id.loc.gov/vocabulary/relators/aut 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910300252603321 996 $aStochastic Models for Structured Populations$92533260 997 $aUNINA