AvR. F. Costantino,Brian Dennis
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Complex Population Dynamics: Theory and Data brings together over two decades of research and reflection on experimental nonlinear population dynamics. The broad theme of the book is the interface of population data and mathematical models. The authors establish a cornerstone example of a low-dimensional mathematical population model for which quantitative predictions, often unexpected, were borne out in controlled and replicated experiments. Central messages include the importance of low-dimensional, mechanistic models that serve as testable hypotheses; the importance of model validation on independent data; the prediction of novel outcomes in response to parameter manipulation; the interaction of nonlinearity and stochasticity—and how stochasticity illuminates, rather than obscures, deterministic forces; abrupt transitions in dynamic regimes in response to interventions; and how chaotic dynamics are expressed in discrete-state, noisy population systems. The book explores nonlinear phenomena in experimental data, including equilibria, cycles, bifurcations, invariant loops, multiple attractors, resonance and attenuance, saddles, stable and unstable manifolds, basins of attraction, basin boundaries, and chaos, and shows how these dynamics manifest in real data in both time series and state space plots.
The book offers an invaluable resource to professional ecologists and applied mathematicians. Although primarily a reference text, it is written to be accessible and engaging to a student audience and could be used as supplementary reading in an advanced ecological modeling class.
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