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A fundamental question in the theory of discrete and continuous-time population models concerns the conditions for the extinction or persistence of populations – a question that is addressed mathematically by persistence theory. For some time, it has been recognized that if the dynamics of a structured population are mathematically captured by continuous or discrete semiflows and if these semiflows have first-order approximations, the spectral radii of certain bounded linear positive operators (better known as basic reproduction numbers) act as thresholds between population extinction and persistence. *This book combines the theory of discrete-time dynamical systems with applications to population dynamics with an emphasis on spatial structure. The inclusion of two sexes that must mate to produce offspring leads to the study of operators that are (positively) homogeneous (of degree one) and order-preserving rather than linear and positive. *While this book offers an introduction to ordered normed vector spaces, some background in real and functional analysis (including some measure theory for a few chapters) will be helpful. The appendix and selected exercises provide a primer about basic concepts and about relevant topics one may not find in every analysis textbook.

Cover -- Title Page -- Copyright Page -- Contents -- Preface -- Chapter 1. Some General Remarks on Mathematical Modeling -- Bibliographic Remarks -- PART 1. BASIC POPULATION GROWTH MODELS -- Chapter 2. Birth, Death, and Migration -- 2.1 The Fundamental Balance Equation of Population Dynamics -- 2.2 Birth Date Dependent Life Expectancies -- 2.3 The Probability of Lifetime Emigration -- Chapter 3. Unconstrained Population Growth for Single Species -- 3.1 Closed Populations -- 3.1.1 The Average Intrinsic Growth Rate for Periodic Environments -- 3.1.2 The Average Intrinsic Growth Rate for Nonperiodic Environments -- 3.2 Open Populations -- 3.2.1 Nonzero Average Intrinsic Growth Rate -- 3.2.2 Zero Average Intrinsic Growth Rate -- Chapter 4. Von Bertalanffy Growth of Body Size -- Chapter 5. Classic Models of Density-Dependent Population Growth for 37 Single Species -- 5.1 The Bernoulli and the Verhulst Equations -- 5.2 The Beverton-Holt and Smith Differential Equation -- 5.2.1 Derivation from a Resource-Consumer Model -- 5.2.2 Derivation from Cannibalism of Juveniles by Adults -- 5.3 The Ricker Differential Equation -- 5.4 The Gompertz Equation -- 5.5 A First Comparison of the Various Equations -- Chapter 6. Sigmoid Growth -- 6.1 General Conditions for Sigmoid Growth -- 6.2 Fitting Sigmoid Population Data -- Chapter 7. The Allee Effect -- 7.1 First Model Derivation: Search for a Mate -- 7.2 Second Model Derivation: Impact of a Satiating Generalist Predator -- 7.3 Model Analysis -- Chapter 8. Nonautonomous Population Growth:Asymptotic Equality of 75 Population Sizes -- Chapter 9. Discrete-Time Single-Species Models -- 9.1 The Discrete Analog of the Verhulst (Logistic) and the Bernoulli Equation: the Beverton-Holt Difference Equation and Its Generalization -- 9.2 The Ricker Difference Equation -- 9.3 Some Analytic Results for Scalar Difference Equations

Cover -- Title page -- Contents -- Preface -- Introduction -- Semiflows on metric spaces -- Compact attractors -- Uniform weak persistence -- Uniform persistence -- The interplay of attractors, repellers, and persistence -- Existence of nontrivial fixed points via persistence -- Nonlinear matrix models: Main act -- Topological approaches to persistence -- An SI endemic model with variable infectivity -- Semiflows induced by semilinear Cauchy problems -- Microbial growth in a tubular bioreactor -- Dividing cells in a chemostat -- Persistence for nonautonomous dynamical systems -- Forced persistence in linear Cauchy problems -- Persistence via average Lyapunov functions -- Tools from analysis and differential equations -- Tools from functional analysis and integral equations -- Bibliography -- Index -- Back Cover.