## Modelling Fluctuating PopulationsIntroduction; Deterministic models; Single-species models with age structure; Modelos of interacting species; The effects of spatial heterogeneity; Sochastic models; Birth and death processes in a static environment; Variable environments; Case studies; Oscillations in Laboratory fly populations; Chemostat populations of unicellular algae; Predator-prey quasi-cycles in a patchy environment. |

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### Contents

SingleSpecies Models | 19 |

SingleSpecies Models with Age Structure | 62 |

Models of Interacting Species | 86 |

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adult amplitude analysis angular frequency assume assumption behaviour birth and death calculate carrying capacity Chapter chemostat constant CPDF death model death rate defined delay demographic stochasticity density-dependent depend deterministic deterministic steady difference equation differential equations diffusion discrete driving fluctuations ecological environment environmental variations equa equation models estimate evaluated example expectation values experimental exponentially extinction fluctuation intensity Fourier transform growth rate Gurney hence individual integral involving large number limit cycle locally linear approximation Lyapunov function mathematical matrix Nisbet non-linear normalized obtain overdamped parameters parasitoids partial differential equation patch occupancy perturbation population density population dynamics population fluctuations population models predator-prey predators predicted prey probability distribution qualitative quantities quasi-cycles random result Section shown in Fig simple single sinusoidal solution spatially species spectral density stationary stochastic differential equations tion transfer function two-species underdamped unstable variable variance white noise zero