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2011-01-01

Jin, Yu, Lewis, Mark A.

The critical domain size problem determines the size of the region of habitat needed to ensure population persistence. In this paper we address the critical domain size problem for seasonally fluctuating stream environments and determine how large a reach of suitable stream habitat is needed to...

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...

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...

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...

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....

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...

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...

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...

2016-01-01

Peacock, Stephanie J., Krkošek, Martin, Lewis, Mark A., Lele, Subhash

The statistical tools available to ecologists are becoming increasingly sophisticated, allowing more complex, mechanistic models to be fit to ecological data. Such models have the potential to provide new insights into the processes underlying ecological patterns, but the inferences made are...

2011-01-01

Young, J. D., Yan, N. D., Lewis, Mark A., Wittmann, M. J.

Whether the invasive freshwater cladoceran Bythotrephes longimanus can establish after introduction into a water body depends on several biotic and abiotic factors. Among these, water temperature is important because both development rates and mode of reproduction (parthenogenetic or sexual) in...