Research Publications (Mathematical and Statistical Sciences)

2020-01-14

Nathan G. Marculis, Mark A. Lewis

The method of inside dynamics provides a theory that can track the dynamics of neutral gene fractions in spreading populations. However, the role of mutations has so far been absent in the study of the gene flow of neutral fractions via inside dynamics. Using integrodifference equations, we...

2016-01-01

Avgar, Tal, Potts, Jonathan R., Lewis, Mark A., Boyce, Mark S.

A resource selection function is a model of the likelihood that an available spatial unit will be used by an animal, given its resource value. But how do we appropriately define availability? Step selection analysis deals with this problem at the scale of the observed positional data, by matching...

2018-01-01

Mark A. Lewis, Nathan G. Marculis, Zhongwei Shen

To understand the efects that the climate change has on the evolution of species as well as the genetic consequences, we analyze an integrodifference equation (IDE) models for a reproducing and dispersing population in a spatio-temporal heterogeneous environment described by a shifting...

2015-01-01

Jon Jacobsen, Yu Jin, Mark A. Lewis

To fully understand population persistence in river ecosystems, it is neces- sary to consider the effect of the water flow, which varies tremendously with seasonal fluctuations of water runoff and snow melt. In this paper, we study integrodifference models for growth and dispersal in the presence...

1997

Kouritzin, Michael, Dawson, Donald

A general Hilbert-space-based stochastic averaging theory is brought forth herein for arbitrary-order parabolic equations with (possibly long range dependent) random coefficients. We use regularity conditions onView the MathML sourcewhich are slightly stronger than those required to prove...

2001-01-01

Clark, James S., Lewis, Mark A., Horvath, Lajos

For populations having dispersal described by fat‐tailed kernels (kernels with tails that are not exponentially bounded), asymptotic population spread rates cannot be estimated by traditional models because these models predict continually accelerating (asymptotically infinite) invasion. The...

2016-01-01

Maya L. Groner, Luke A. Rogers, Andrew W. Bateman, Brendan M. Connors, L. Neil Frazer, Sean C. Godwin, Martin Krkosˇek, Mark A. Lewis, Stephanie J. Peacock, Erin E. Rees, Crawford W. Revie, Ulrike E. Schla¨gel

Effective disease management can benefit from mathematical models that identify drivers of epidemiological change and guide decision-making. This is well illustrated in the host–parasite system of sea lice and salmon, which has been modelled extensively due to the economic costs associated...

2024-05-13

Shi, Qingyan, Song, Yongli, Wang, Hao

Abstract taken from the article Spatial memory is key in animal movement modeling, but it has been challenging to explicitly model learning to describe memory acquisition. In this paper, we study novel cognitive consumer-resource models with different consumer learning mechanisms and investigate...

2017-10-29

Stephanie J. Peacock, Juliette Bouhours, Mark A. Lewis, P´eter K. Moln´ar

Spatial variability in host density is a key factor affecting disease dynamics of wildlife, and yet there are few spatially explicit models of host-macroparasite dynamics. This limits our understanding of parasitism in migratory hosts, whose densities change considerably in both space and time....

2019-02-01

Mélodie Kunegel-Lion, Rory L. McIntosh, Mark A. Lewis

Insect epidemics such as the mountain pine beetle (MPB) outbreak have a major impact on forest dynamics. In Cypress Hills, Canada, the Forest Service Branch of the Saskatchewan Ministry of Environment aims to control as many new infested trees as possible by conducting ground-based surveys around...