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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)

A defining hypothesis of theoretical ecology during the past century has been that population fluctuations might largely be explained by relatively low-dimensional, nonlinear 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)

- Subhash R Lele, Brian Dennis, Frithjof Lutscher
- Ecology letters
- 2007

We introduce a new statistical computing method, called data cloning, to calculate maximum likelihood estimates and their standard errors for complex ecological models. Although the method uses the Bayesian framework and exploits the computational simplicity of the Markov chain Monte Carlo (MCMC) algorithms, it provides valid frequentist inferences such as… (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)

- 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)

- 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)

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)

- 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)

- S M Henson, R F Costantino, J M Cushing, R A Desharnais, B Dennis, A A King
- Science
- 2001

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)

- Brian Dennis
- 2001