Quantitative Ecological Theory: An Introduction to Basic Models

Theoretical Models in Ecology.- Models Covered Here.- 1. Population Growth.- 1.1 Linear Continuous-Time Models.- The "Malthusian" or Density-Independent Model.- The Logistic Model.- 1.2 Nonlinear Continuous-Time Models.- General Autonomous Models.- Density-Independent Nonautonomous Models.- 1.3 Discrete-Time Models.- Density-Independent Model.- Discrete-Time Logistic Model.- General Autonomous Models.- Density-Independent Nonautonomous Models.- Time-Lag Models.- 1.4 Models with Age-Structure.- Discrete-Time: The Leslie Matrix.- Continuous-Time Models.- 1.5 Exercises.- 2. Competition.- 2.1 Lotka-Volterra Models: Special Cases.- No Carrying Capacities.- One Carrying Capacity.- 2.2 Classical Lotka-Volterra Model.- 2.3 General Continuous-Time Models.- 2.4 Discrete-Time Models.- General Two-Species Models.- The Hassell-Comins Model.- 2.5 Symbiosis.- Lotka-Volterra Models.- General Continuous-Time Models.- 2.6 Exercises.- 3. Predation.- 3.1 Lotka-Volterra Models.- Original Lotka-Volterra Model.- An Alternative Lotka-Volterra Model.- 3.2 Generalized Predator-Prey Models.- 3.3 Discrete-Time Models.- Lotka-Volterra Model without Density-Dependence.- Lotka-Volterra Model with Density-Dependence.- Other Discrete-Time Predation Models.- 3.4 Parasitoid Models.- A General Model.- Classical Nicholson-Bailey Model.- Nicholson-Bailey Model with Density-Dependence.- Generalized Nicholson-Bailey Model.- 3.5 Exercises.- 4. Simple Ecosystems.- 4.1 Two Predators and One Prey.- Continuous-Time Models.- Discrete-Time Models: Two Parasitoids.- 4.2 One Predator and Two Prey.- Continuous-Time Models.- Discrete-Time Models: Polyphagous Parasitoids.- 4.3 Three-Species Food Chains.- Continuous-Time Models.- Discrete-Time Models: Parasitoid-Hyperparasitoid Systems.- 4.4 Exercises.- 5. Complex Ecosystems.- 5.1 Local Equilibrium Stability.- Time-Structure and Local Asymptotic Stability.- Arbitrary Complexity and Local Stability.- Ecosystem Model Structure and Local Stability.- 5.2 Global Complex Ecosystem Dynamics.- 6. Migration.- 6.1 Population Growth with Migration.- Recipient Peripheral Populations.- Migrant Pool Model.- Two Habitats.- 6.2 Competition with Migration.- Recipient Peripheral Populations.- Migrant Pool Model.- Two Habitats.- 6.3 Predation with Migration.- Recipient Peripheral Populations.- Migrant Pool Model.- Two Habitats.- 6.4 Ecosystems with Migration.- 6.5 Exercises.