LEADER 04223nam 2200589 450 001 9910796029403321 005 20220523053353.0 010 $a0-8218-9511-7 035 $a(CKB)3780000000000125 035 $a(EBL)3114412 035 $a(SSID)ssj0000889084 035 $a(PQKBManifestationID)11566325 035 $a(PQKBTitleCode)TC0000889084 035 $a(PQKBWorkID)10881939 035 $a(PQKB)10694146 035 $a(MiAaPQ)EBC3114412 035 $a(RPAM)17588081 035 $a(PPN)195408284 035 $a(EXLCZ)993780000000000125 100 $a20150416h20122012 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 12$aA mutation-selection model with recombination for general genotypes /$fSteven N. Evans, David Steinsaltz, Kenneth W. Wachter 210 1$aProvidence, Rhode Island :$cAmerican Mathematical Society,$d2012. 210 4$dİ2012 215 $a1 online resource (128 p.) 225 1 $aMemoirs of the American Mathematical Society,$x1947-6221 ;$vVolume 222, Number 1044 300 $a"March 2013, Volume 222, Number 1044 (third of 5 numbers)." 311 $a0-8218-7569-8 320 $aIncludes bibliographical references and index. 327 $aContents -- Abstract -- Chapter 1. Introduction -- 1.1. Informal description of the limit model -- 1.2. Example I: Mutation counting -- 1.3. Example II: Polynomial selective costs -- 1.4. Example III: Demographic selective costs -- 1.5. Comments on the literature -- 1.6. Overview of the remainder of the work -- Chapter 2. Definition, Existence, and Uniqueness of the Dynamical System -- 2.1. Spaces of measures -- 2.2. Definition of the dynamical system -- 2.3. Existence and uniqueness of solutions -- 2.4. Lemmas used in the proof of existence and uniqueness -- Chapter 3. Equilibria -- 3.1. Introductory example: One-dimensional systems -- 3.2. Introductory example: Multiplicative selective costs -- 3.3. Frechet derivatives -- 3.4. Existence of equilibria via perturbation -- 3.5. Concave selective costs -- 3.6. Concave selective costs: Existence and stability of equilibria -- 3.7. Iterative computation of the minimal equilibrium -- 3.8. Stable equilibria in the concave setting via perturbation -- 3.9. Equilibria for demographic selective costs -- Chapter 4. Mutation, Selection, and Recombination in Discrete Time -- 4.1. Mutation and selection in discrete time -- 4.2. Recombination in discrete time -- 4.3. Recombination trees and annealed recombination -- 4.4. Vintages -- Chapter 5. Shattering and the Formulation of the Convergence Result -- 5.1. Shattering of random measures -- 5.2. Consequences of shattering -- 5.3. Convergence to Poisson of iterated recombination -- 5.4. Atoms in the initial intensity -- 5.5. Preview of the main convergence result -- Chapter 6. Convergence with Complete Poissonization -- Chapter 7. Supporting Lemmas for the Main Convergence Result -- 7.1. Estimates for Radon-Nikodym derivatives -- 7.2. Comparisons with complete Poissonization -- Chapter 8. Convergence of the Discrete Generation System -- 8.1. Outline of the proof -- 8.2. The convergence theorem -- Appendix A. Results Cited in the Text -- A.1. Gronwall's Inequality -- A.2. Two expectation approximations -- A.3. Identities for Poisson random measures -- A.4. Bounds for Poisson random measures -- A.5. Bounds for Radon-Nikodym derivatives -- Bibliography -- Index -- Glossary of Notation. 410 0$aMemoirs of the American Mathematical Society ;$vVolume 222, Number 1044. 606 $aEvolutionary genetics 606 $aMutation (Biology) 606 $aGenetic recombination 615 0$aEvolutionary genetics. 615 0$aMutation (Biology) 615 0$aGenetic recombination. 676 $a572.8/38 700 $aEvans$b Steven N$g(Steven Neil),$0314671 702 $aSteinsaltz$b David$f1966- 702 $aWachter$b Kenneth W. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910796029403321 996 $aA mutation-selection model with recombination for general genotypes$93757614 997 $aUNINA