Nonlinear demographic dynamics: mathematical models, statistical methods, and biological experiments'
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TLDR
This study documents the nonlinear prediction of periodic 2-cycles in laboratory cultures of Tribolium and represents a new interdisciplinary approach to un- derstanding nonlinear ecological dynamics.Abstract:
Our approach to testing nonlinear population theory is to connect rigorously mathematical models with data by means of statistical methods for nonlinear time series. We begin by deriving a biologically based demographic model. The mathematical analysis identifies boundaries in parameter space where stable equilibria bifurcate to periodic 2-cy- cles and aperiodic motion on invariant loops. The statistical analysis, based on a stochastic version of the demographic model, provides procedures for parameter estimation, hypothesis testing, and model evaluation. Experiments using the flour beetle Tribolium yield the time series data. A three-dimensional map of larval, pupal, and adult numbers forecasts four possible population behaviors: extinction, equilibria, periodicities, and aperiodic motion including chaos. This study documents the nonlinear prediction of periodic 2-cycles in laboratory cultures of Tribolium and represents a new interdisciplinary approach to un- derstanding nonlinear ecological dynamics.read more
Citations
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Journal ArticleDOI
Pollen limitation of plant reproduction: Ecological and evolutionary causes and consequences
Tia-Lynn Ashman,Tiffany M. Knight,Janette A. Steets,Priyanga Amarasekare,Martin Burd,Diane R. Campbell,Michele R. Dudash,Mark O. Johnston,Susan J. Mazer,Randall J. Mitchell,Martin Morgan,William G. Wilson +11 more
TL;DR: A change in approach is needed to determine whether pollen limitation reflects random fluctuations around a pollen–resource equilibrium, an adaptation to stochastic pollination environments, or a chronic syndrome caused by an environmental perturbation.
Journal ArticleDOI
Estimating community stability and ecological interactions from time‐series data
Anthony R. Ives,Anthony R. Ives,Brian Dennis,Brian Dennis,Kathryn L. Cottingham,Kathryn L. Cottingham,Stephen R. Carpenter,Stephen R. Carpenter +7 more
TL;DR: In this article, the authors derived three properties of stochastic multispecies communities that measure different characteristics associated with community stability using first-order multivariate autoregressive (MAR(1)) models.
Journal ArticleDOI
Fitting population models incorporating process noise and observation error
Perry de Valpine,Alan Hastings +1 more
TL;DR: The numerically integrated state-space (NISS) method as mentioned in this paper was proposed to fit models to time series of population abun- dances that incorporate both process noise and observation error in a likelihood framework.
Journal ArticleDOI
Estimating density dependence, process noise, and observation error
TL;DR: In this paper, the authors describe a discrete-time, stochastic population model with density dependence, environmental-type process noise, and lognormal observation or sampling error.
Journal ArticleDOI
Chaotic Dynamics in an Insect Population
TL;DR: A nonlinear demographic model was used to predict the population dynamics of the flour beetle Tribolium under laboratory conditions and to establish the experimental protocol that would reveal chaotic behavior.
References
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Book
Generalized Linear Models
Peter McCullagh,John A. Nelder +1 more
TL;DR: In this paper, a generalization of the analysis of variance is given for these models using log- likelihoods, illustrated by examples relating to four distributions; the Normal, Binomial (probit analysis, etc.), Poisson (contingency tables), and gamma (variance components).
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Numerical Recipes, The Art of Scientific Computing
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