Elements of Mathematical EcologyElements of Mathematical Ecology provides an introduction to classical and modern mathematical models, methods, and issues in population ecology. The first part of the book is devoted to simple, unstructured population models that ignore much of the variability found in natural populations for the sake of tractability. Topics covered include density dependence, bifurcations, demographic stochasticity, time delays, population interactions (predation, competition, and mutualism), and the application of optimal control theory to the management of renewable resources. The second part of this book is devoted to structured population models, covering spatially-structured population models (with a focus on reaction-diffusion models), age-structured models, and two-sex models. Suitable for upper level students and beginning researchers in ecology, mathematical biology, and applied mathematics, the volume includes numerous clear line diagrams that clarify the mathematics, relevant problems throughout the text that aid understanding, and supplementary mathematical and historical material that enrich the main text. |
Contents
SINGLESPECIES MODELS | 3 |
Harvest models bifurcations and breakpoints | 13 |
Stochastic birth and death processes | 25 |
Discretetime models | 43 |
Delay models | 70 |
Branching processes | 93 |
INTERACTING POPULATIONS | 107 |
To cycle or not to cycle | 116 |
SPATIALLY STRUCTURED MODELS | 267 |
Spatial steady states linear problems | 276 |
Spatial steady states nonlinear problems | 294 |
Models of spread | 311 |
AGESTRUCTURED MODELS | 345 |
The Lotka integral equation | 353 |
The difference equation | 365 |
The Leslie matrix | 377 |
Global bifurcations in predatorprey models | 140 |
Chemostat models | 161 |
Discretetime predatorprey models | 181 |
Competition models | 198 |
Mutualism models | 220 |
DYNAMICS OF EXPLOITED POPULATIONS | 237 |
STRUCTURED POPULATION MODELS | 265 |
The McKendrickvon Foerster PDE | 391 |
Some simple nonlinear models | 401 |
SEXSTRUCTURED MODELS | 413 |
| 425 | |
| 443 | |
| 447 | |
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Common terms and phrases
approach assume asymptotic bifurcation birth boundary conditions carrying capacity Chapter characteristic close competition Consider constant corresponding curve death decreases density dependence derivatives determine difference equation differential equation diffusion distribution dynamics ecology effect eigenvalues equilibrium example exponential extinction females Figure fishing focus follows function given gives grow growth growth rate harvesting implies increase individuals initial condition integral interested introduce lead limit cycle linear logistic look males Mathematical matrix mutualism N₁ negative nonlinear obtain occur orbit origin oscillations parameter periodic perturbations phase plane population positive predator predator-prey prey probability problem produces reduces result roots satisfies side simple solution solve species stable turn unstable variable wave yield zero zero-growth isoclines