LEADER 05597nam 22007334a 450 001 9911019480803321 005 20200520144314.0 010 $a9786610273959 010 $a9781280273957 010 $a128027395X 010 $a9780470322376 010 $a0470322373 010 $a9780470871287 010 $a0470871288 010 $a9780470871294 010 $a0470871296 035 $a(CKB)111087027140056 035 $a(EBL)219699 035 $a(OCoLC)53899023 035 $a(SSID)ssj0000249375 035 $a(PQKBManifestationID)11221961 035 $a(PQKBTitleCode)TC0000249375 035 $a(PQKBWorkID)10205964 035 $a(PQKB)10977075 035 $a(MiAaPQ)EBC219699 035 $a(PPN)19690174X 035 $a(Perlego)2775670 035 $a(EXLCZ)99111087027140056 100 $a20030604d2003 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSpatial ecology via reaction-diffusion equations /$fRobert Stephen Cantrell and Chris Cosner 210 $aChichester, West Sussex, England ;$aHoboken, NJ $cJ. Wiley$dc2003 215 $a1 online resource (429 p.) 225 1 $aWiley series in mathematical and computational biology 300 $aDescription based upon print version of record. 311 08$a9780471493013 311 08$a0471493015 320 $aIncludes bibliographical references (p. [395]-408). 327 $aSpatial Ecology via Reaction-Diffusion Equations; Contents; Preface; Series Preface; 1 Introduction; 1.1 Introductory Remarks; 1.2 Nonspatial Models for a Single Species; 1.3 Nonspatial Models For Interacting Species; 1.3.1 Mass-Action and Lotka-Volterra Models; 1.3.2 Beyond Mass-Action: The Functional Response; 1.4 Spatial Models: A General Overview; 1.5 Reaction-Diffusion Models; 1.5.1 Deriving Diffusion Models; 1.5.2 Diffusion Models Via Interacting Particle Systems: The Importance of Being Smooth; 1.5.3 What Can Reaction-Diffusion Models Tell Us? 327 $a1.5.4 Edges, Boundary Conditions, and Environmental Heterogeneity1.6 Mathematical Background; 1.6.1 Dynamical Systems; 1.6.2 Basic Concepts in Partial Differential Equations: An Example; 1.6.3 Modern Approaches to Partial Differential Equations: Analogies with Linear Algebra and Matrix Theory; 1.6.4 Elliptic Operators: Weak Solutions, State Spaces, and Mapping Properties; 1.6.5 Reaction-Diffusion Models as Dynamical Systems; 1.6.6 Classical Regularity Theory for Parabolic Equations; 1.6.7 Maximum Principles and Monotonicity 327 $a2 Linear Growth Models for a Single Species: Averaging Spatial Effects Via Eigenvalues2.1 Eigenvalues, Persistence, and Scaling in Simple Models; 2.1.1 An Application: Species-Area Relations; 2.2 Variational Formulations of Eigenvalues: Accounting for Heterogeneity; 2.3 Effects of Fragmentation and Advection/Taxis in Simple Linear Models; 2.3.1 Fragmentation; 2.3.2 Advection/Taxis; 2.4 Graphical Analysis in One Space Dimension; 2.4.1 The Best Location for a Favorable Habitat Patch; 2.4.2 Effects of Buffer Zones and Boundary Behavior; 2.5 Eigenvalues and Positivity; 2.5.1 Advective Models 327 $a2.5.2 Time Periodicity2.5.3 Additional Results on Eigenvalues and Positivity; 2.6 Connections with Other Topics and Models; 2.6.1 Eigenvalues, Solvability, and Multiplicity; 2.6.2 Other Model Types: Discrete Space and Time; Appendix; 3 Density Dependent Single-Species Models; 3.1 The Importance of Equilibria in Single Species Models; 3.2 Equilibria and Stability: Sub- and Supersolutions; 3.2.1 Persistence and Extinction; 3.2.2 Minimal Patch Sizes; 3.2.3 Uniqueness of Equilibria; 3.3 Equilibria and Scaling: One Space Dimension; 3.3.1 Minimum Patch Size Revisited 327 $a3.4 Continuation and Bifurcation of Equilibria3.4.1 Continuation; 3.4.2 Bifurcation Results; 3.4.3 Discussion and Conclusions; 3.5 Applications and Properties of Single Species Models; 3.5.1 How Predator Incursions Affect Critical Patch Size; 3.5.2 Diffusion and Allee Effects; 3.5.3 Properties of Equilibria; 3.6 More General Single Species Models; Appendix; 4 Permanence; 4.1 Introduction; 4.1.1 Ecological Overview; 4.1.2 ODE Models as Examples; 4.1.3 A Little Historical Perspective; 4.2 Definition of Permanence; 4.2.1 Ecological Permanence; 4.2.2 Abstract Permanence 327 $a4.3 Techniques for Establishing Permanence 330 $aMany ecological phenomena may be modelled using apparently random processes involving space (and possibly time). Such phenomena are classified as spatial in their nature and include all aspects of pollution. This book addresses the problem of modelling spatial effects in ecology and population dynamics using reaction-diffusion models.* Rapidly expanding area of research for biologists and applied mathematicians* Provides a unified and coherent account of methods developed to study spatial ecology via reaction-diffusion models* Provides the reader with the tools needed to construct 410 0$aWiley series in mathematical and computational biology. 606 $aSpatial ecology$xMathematical models 606 $aReaction-diffusion equations 615 0$aSpatial ecology$xMathematical models. 615 0$aReaction-diffusion equations. 676 $a577/.015/1 700 $aCantrell$b Robert Stephen$01840042 701 $aCosner$b Chris$01751779 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911019480803321 996 $aSpatial ecology via reaction-diffusion equations$94419512 997 $aUNINA