Research Publications (Mathematical and Statistical Sciences)

2016-01-01

Jonathan R. Potts, Mark A. Lewis

Mechanistic home range analysis (MHRA) is a highly effective tool for understanding spacing patterns of animal populations. It has hitherto focused on populations where animals defend their territories by communicating indirectly, e.g. via scent marks. However, many animal populations defend...

2001-01-01

M. R. OWEN, M. A. LEWIS

Observations on Mount St Helens indicate that the spread of recolonizing lupin plants has been slowed due to the presence of insect herbivores and it is possible that the spread of lupins could be reversed in the future by intense insect herbivory [Fagan, W. F. and J. Bishop (2000). Trophic...

2015-01-01

Esteban M. Paolucci, Marco R. Hernandez, Alexei Potapov, Mark A. Lewis, Hugh J. MacIsaac

2019-05-10

Nathan G. Marculis, Jimmy Garnier, · Roger Lui, Mark A. Lewis

A stage-structured model of integrodifference equations is used to study the asymptotic neutral genetic structure of populations undergoing range expansion. That is, we study the inside dynamics of solutions to stage-structured integrodifference equations. To analyze the genetic consequences for...

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...