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2014

Kouritzin, Michael, Ren, Y.-X.

Let ℓ be Lebesgue measure and X=(Xt,t≥0;Pμ) be a supercritical, super-stable process corresponding to the operator −(−Δ)α/2u+βu−ηu2 on Rd with constants β,η>0 and α∈(0,2]. Put View the MathML source, which for each smallθ is an a.s. convergent complex-valued martingale with limit View the MathML...

2010-01-01

MARK A. LEWIS, WILLIAM NELSON, CAILIN XU

A vigor-structured model for mountain pine beetle outbreak dy- namics within a forest stand is proposed and analyzed. This model explicitly tracks the changing vigor structure in the stand. All model parameters, other than beetle vigor preference, were determined by tting model components to...

2014-01-01

Jonathan R. Potts, Karl Mokross, Mark A. Lewis

Collective phenomena, whereby agent –agent interactions determine spatial patterns, are ubiquitous in the animal kingdom. On the other hand, movement and space use are also greatly influenced by the interactions between animals and their environment. Despite both types of interaction...

2020-05-19

Stephanie J. Peacock, Martin Krkošek, Mark A. Lewis, Péter K. Molnár

Migrations allow animals to track seasonal changes in resources, find mates, and avoid harsh climates, but these regular, longdistance movements also have implications for parasite dynamics and animal health. Migratory animals have been dubbed “superspreaders” of infection, but migration can also...

2008-01-01

Potapov, A. B., Lewis, Mark A.

We consider the model of invasion prevention in a system of lakes that are connected via traffic of recreational boats. It is shown that, in presence of an Allee effect, the general optimal control problem can be reduced to a significantly simpler stationary optimization problem of optimal...

2013-01-01

Krkošek, M., Ashander, J., Lewis, Mark A., Frazer, N.

The exchange of native pathogens between wild and domesticated animals can lead to novel disease threats to wildlife. However, the dynamics of wild host-parasite systems exposed to a reservoir of domesticated hosts are not well understood. A simple mathematical model reveals that the spill-back...

2012-01-01

Poulin, R., Connors, B. M., Krkosek, M., Lewis, Mark A.

Allee effects are thought to mediate the dynamics of population colonization, particularly for invasive species. However, Allee effects acting on parasites have rarely been considered in the analogous process of infectious disease establishment and spread. We studied the colonization of...

2001-01-01

Holt, R. D., Lewis, Mark A., Keitt, T. H.

All species’ ranges are the result of successful past invasions. Thus, models of species’ invasions and their failure can provide insight into the formation of a species’ geographic range. Here, we study the properties of invasion models when a species cannot persist below a critical population...

2014-06-05

Kouritzin, Michael

The classical particle filter, introduced in 1993, approximates the normalized filter directly. It has two defiencies, over resampling and the inability to distinguish models, the former of which was overcome but the later is fundamental. Conversely, the weighted particle filter, motivated by the...

2002-01-01

Lewis, Mark A., Weinberger, H.F., Li, B.T.

The discrete-time recursion system \un+1=Q[\un] with \un(x) a vector of population distributions of species and Q an operator which models the growth, interaction, and migration of the species is considered. Previously known results are extended so that one can treat the local invasion of an...