Research Publications (Mathematical and Statistical Sciences)

2014-01-01

Schlägel, Ulrike E, Lewis, Mark A.

Animals of many species demonstrate movement behaviour in which decisions are based on a variety of information. Effects of resources have been studied widely, often under the assumption that the environment is constant over the course of the study. Much less understood is the role of dynamic...

1996-01-01

Lewis, Mark A., Veit, R.R.

Since about 1940, when they were first released in the new York City area, house finches (Carpodacus mexicanus) have multiplied explosively and colonized much of eastern North America. We take advantage of the richly detailed documentation of this biological invasion to construct a mathematical...

1995-01-01

Sherratt, J. A., Lewis, Mark A., Fowler, A. C.

Irregularities in observed population densities have traditionally been attributed to discretization of the underlying dynamics. We propose an alternative explanation by demonstrating the evolution of spatiotemporal chaos in reaction-diffusion models for predator-prey interactions. The chaos is...

2006-01-01

McCauley, E., Lewis, Mark A., Lutscher, F.

The question how aquatic populations persist in rivers when individuals are constantly lost due to downstream drift has been termed the “drift paradox.” Recent modeling approaches have revealed diffusion-mediated persistence as a solution. We study logistically growing populations with and...

2015-01-01

Potapov, Alex, Merrill, Evelyn, Pybus, Margo, Lewis, Mark A.

We consider the problem of estimating the basic reproduction number R0 from data on prevalence dynamics at the beginning of a disease outbreak. We derive discrete and continuous time models, some coefficients of which are to be fitted from data. We show that prevalence of the disease is...

2015-01-01

Bateman, Andrew W., Neubert, Michael G., Krkošek, Martin, Lewis, Mark A.

Some of the most fundamental quantities in population ecology describe the growth and spread of populations. Population dynamics are often characterized by the annual rate of increase, λ, or the generational rate of increase, R0. Analyses involving R0 have deepened our understanding of disease...

2014-01-01

Potts, Jonathan R., Lewis, Mark A.

Territory formation is ubiquitous throughout the animal kingdom. At the individual level, various behaviours attempt to exclude conspecifics from regions of space. At the population level, animals often segregate into distinct territorial areas. Consequently, it should be possible to derive...

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...

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...

2005-01-01

Lewis, Mark A., Wonham, Marjorie J., MacIsaac, Hugh J.

Biological invasions are a major and increasing agent of global biodiversity change. Theory and practice indicate that invasion risk can be diminished by reducing propagule pressure, or the quantity, quality, and frequency of introduced individuals. For aquatic invasions, the primary global...