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A defining hypothesis of theoretical ecology during the past century has been that population fluctuations might largely be explained by relatively low-dimensional, non-linear ecological interactions, provided such interactions could be correctly identified and modeled. The realization in recent decades that such nonlinear interactions might result in chaos… (More)

- Brian Dennis
- 2002

The Allee effect, or inverse density dependence at low population sizes, could seriously impact preservation and management of biological populations. The mounting evidence for widespread Allee effects has lately inspired theoretical studies of how Allee effects alter population dynamics. However, the recent mathematical models of Allee effects have been… (More)

Animals and many plants are counted in discrete units. The collection of possible values (state space) of population numbers is thus a nonnegative integer lattice. Despite this fact, many mathematical population models assume a continuum of system states. The complex dynamics, such as chaos, often displayed by such continuous-state models have stimulated… (More)

- ZHENG ZENG, ROBERT M. NOWIERSKI, MARK L. TAPER, BRIAN DENNIS, WILLIAM P. KEMP
- 1999

We propose a class of complex population dynamic models that combines new time-varying parameters and second-order time lags for describing univariate ecological time series data. The Kalman filter and likelihood function were used to estimate parameters of all models in the class for 31 data sets, and Schwarz's information criterion (SIC) was used to… (More)

High-resolution data collected over the past 60 years by a single family of Siberian scientists on Lake Baikal reveal significant warming of surface waters and long-term changes in the basal food web of the world's largest, most ancient lake. Attaining depths over 1.6 km, Lake Baikal is the deepest and most voluminous of the world's great lakes. Increases… (More)

Mathematical models predict that a population which oscillates in the absence of time-dependent factors can develop multiple attracting final states in the advent of periodic forcing. A periodically-forced, stage-structured mathematical model predicted the transient and asymptotic behaviors of Tribolium (flour beetle) populations cultured in periodic… (More)

- M A T H E M A T I C A L M O D, Robert A Desharnais, R F Costantino, J M Cushing, Shandelle M Henson, Brian Dennis
- 2001

We used small perturbations in adult numbers to control large fluctuations in the chaotic demographic dynamics of laboratory populations of the flour beetle Tribolium castaneum. A nonlinear mathematical model was used to identify a sensitive region of phase space where the addition of a few adult insects would result in a dampening of the life stage… (More)

A scaling rule of ecological theory, accepted but lacking experimental confirmation, is that the magnitude of fluctuations in population densities due to demographic stochasticity scales inversely with the square root of population numbers. This supposition is based on analyses of models exhibiting exponential growth or stable equilibria. Using two… (More)

Mathematically, chaotic dynamics are not devoid of order but display episodes of near-cyclic temporal patterns. This is illustrated, in interesting ways, in the case of chaotic biological populations. Despite the individual nature of organisms and the noisy nature of biological time series, subtle temporal patterns have been detected. By using data drawn… (More)

Lattice effects in ecological time-series are patterns that arise because of the inherent discreteness of animal numbers. In this paper, we suggest a systematic approach for predicting lattice effects. We also show that an explanation of all the patterns in a population time-series may require more than one deterministic model, especially when the dynamics… (More)