Research Publications (Mathematical and Statistical Sciences)

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...

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,...

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...

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...

2017-11-25

Juliana M. Berbert, Mark A. Lewis

Animal search patterns are governed by the various movement strategies undertaken when animals encounter stimuli. The stimuli caused by resource growth and depletion can modify search patterns due to the need to finding resources. In this paper, we investigate the influence of resource depletion...

2016-01-01

Qihua Huang, Hao Wang, Anthony Ricciardi, Mark A. Lewis

We develop a staged-structured population model that describes the competitive 7 dynamics of two functionally similar, congeneric invasive species: zebra mussels and quagga 8 mussels. The model assumes that the population survival rates are functions of temperature 9 and turbidity, and that the...

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...