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1994

Heunis, A. J., Kouritzin, Michael

In this note we consider the almost sure convergence (as ϵ→0) of solution Xϵ(·), defined over the interval 0 ≤ τ ≤ 1, of the random ordinary differential equation View the MathML source Here {F(x, t, ω), t ≥ 0} is a strong mixing process for each x and (x, t) → F(x, t, ω) is subject to regularity...

1995

Kouritzin, Michael

Suppose {εk, −∞ < k < ∞} is an independent, not necessarily identically distributed sequence of random variables, and {cj}∞j=0, {dj}∞j=0 are sequences of real numbers such that Σjc2j < ∞, Σjd2j < ∞. Then, under appropriate moment conditions on {εk, −∞ < k < ∞}, View the MathML source, View the...

2024-06-01

Wang, Tianxu, Wang, Hao

Abstract (description taken from this, pre-print version of the article) Evidence shows that resource quality can determine the costs and benefits of fear effect on consumer dynamics. However, mechanistic modeling and analysis are lacking. This paper formulates a tri-trophic level food chain...

2024-03-01

Wang, Tianxu, Wang, Hao

Abstract (description taken from article) Microplastics pose a severe threat to marine ecosystems; however, relevant mathematical modeling and analysis are lacking. This paper formulates two stoichiometric producer-grazer models to investigate the interactive effects of microplastics, nutrients,...

2014-01-01

Potts, Jonathan R., Mokross, Karl, Stouffer, Philip C., Lewis, Mark A.

Understanding the behavioral decisions behind animal movement and space use patterns is a key challenge for behavioral ecology. Tools to quantify these patterns from movement and animal–habitat interactions are vital for transforming ecology into a predictive science. This is particularly...

2016-01-01

Auger-Méthé, Marie, Field, Chris, Albertsen, Christopher M., Derocher, Andrew E., Lewis, Mark A., Jonsen, Ian D., Mills Flemming, Joanna

State-space models (SSMs) are increasingly used in ecology to model time-series such as animal movement paths and population dynamics. This type of hierarchical model is often structured to account for two levels of variability: biological stochasticity and measurement error. SSMs are flexible....

2012-01-01

Mark A. Lewis, Bingtuan Li

How growth, mortality, and dispersal in a species affect the species' spread and persistence constitutes a central problem in spatial ecology. We propose impulsive reaction-diffusion equation models for species with distinct repro- ductive and dispersal stages. These models can describe a...

2002-01-01

Lewis, Mark A., Bingtuan Li, Hans F. Weinberger

 One crucial measure of a species' invasiveness is the rate at which it spreads into a competitor's environment. A heuristic spread rate formula for a spatially explicit, two-species competition model relies on `linear determinacy' which equates spread rate in the full nonlinear model with spread...

2004-01-01

Lewis, Mark A., Lutscher, F.

This paper is concerned with mathematical analysis of the ‘critical domain-size’ problem for structured populations. Space is introduced explicitly into matrix models for stage-structured populations. Movement of individuals is described by means of a dispersal kernel. The mathematical analysis...

2017-04-01

Guillaume Bastille-Rousseau, Dennis L. Murray, James A. Schaefer, Mark A. Lewis, Shane P. Mahoney, Jonathan R. Potts

Movement influences a myriad of ecological processes operating at multiple spatial and temporal scales. Yet our understanding of animal movement is limited by the resolution of data that can be obtained from individuals. Traditional approaches implicitly assume that movement decisions are made at...