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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)

We describe a discrete-time, stochastic population model with density dependence, environmental-type process noise, and lognormal observation or sampling error. The model, a stochastic version of the Gompertz model, can be transformed into a linear Gaussian state-space model (Kalman filter) for convenient fitting to time series data. The model has a… (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)

- 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)

- Henk Wolda, Brian Dennis
- Oecologia
- 1993

A large number of time series of abundances of insects and birds from a variety of data sets were submitted to a new density dependence test. The results varied enormously between data sets, but the relation between the frequency of statistically significant density dependence (SSDD) and the length of the series was similar to that of the power curve of the… (More)

- Andrew M. Kramer, Brian Dennis, Andrew M. Liebhold, John M. Drake
- Population Ecology
- 2009

Allee effects are an important dynamic phenomenon believed to be manifested in several population processes, notably extinction and invasion. Though widely cited in these contexts, the evidence for their strength and prevalence has not been critically evaluated. We review results from 91 studies on Allee effects in natural animal populations. We focus on… (More)

- R F Costantino, J M Cushing, B Dennis, R A Desharnais, S M Henson
- Bulletin of mathematical biology
- 1998

Experiments with the flour beetle Tribolium have revealed that animal numbers were larger in cultures grown in a periodically fluctuating volume of medium than in cultures grown in a constant volume of the same average size. In this paper we derive and analyze a discrete stage-structured mathematical model that explains this phenomenon as a kind of… (More)

- S M Henson, R F Costantino, J M Cushing, B Dennis, R A Desharnais
- Bulletin of mathematical biology
- 1999

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)

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)