Search

2005-01-01

Fagan, William F., Lewis, Mark A., Neubert, Michael G., Aumann, Craig, Apple, Jennifer L., Bishop, John G.

Here we study the spatial dynamics of a coinvading consumer‐resource pair. We present a theoretical treatment with extensive empirical data from a long‐studied field system in which native herbivorous insects attack a population of lupine plants recolonizing a primary successional landscape...

2005-01-01

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

Individuals in streams are constantly subject to predominantly unidirectional flow. The question of how these populations can persist in upper stream reaches is known as the “drift paradox.” We employ a general mechanistic movement-model framework and derive dispersal kernels for this situation....

2005-01-01

Frithjof Lutscher, Elizaveta Pachepsky, Mark A. Lewis

Individuals in streams are constantly subject to predominantly unidirectional flow. The question of how these populations can persist in upper stream reaches is known as the “drift paradox.” We employ a general mechanistic movement-model framework and derive dispersal kernels for this situation....

2005

Kouritzin, Michael, Sun, W.

Herein, we analyze an efficient branching particle method for asymptotic solutions to a class of continuous-discrete filtering problems. Suppose that t→Xt is a Markov process and we wish to calculate the measure-valued process t→μt(⋅)≐P{Xt∈⋅|σ{Ytk, tk≤t}}, where tk=kɛ and Ytk is a distorted,...

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...

2006-01-01

Chad M. Topaz, Andrea L. Bertozzi, Mark A. Lewis

We construct a continuum model for biological aggregations in which individuals experience long-range social attraction and short range dispersal. For the case of one spatial dimension, we study the steady states analytically and numerically. There exist strongly nonlinear states with compact...

2007-01-01

Eftimie, R., Lewis, Mark A., Lutscher, F., de Vries, G.

We construct and analyze a nonlocal continuum model for group formation with application to self-organizing collectives of animals in homogeneous environments. The model consists of a hyperbolic system of conservation laws, describing individual movement as a correlated random walk. The turning...

2007-01-01

Eftimie, R., De Vries, G., Lewis, Mark A.

We present previously undescribed spatial group patterns that emerge in a one-dimensional hyperbolic model for animal group formation and movement. The patterns result from the assumption that the interactions governing movement depend not only on distance between conspecifics, but also on how...

2007-01-01

Nisbet, Roger, Anderson, Kurt E., McCauley, Edward, Lewis, Mark A.

Much ecological research involves identifying connections between abiotic forcing and population densities or distributions. We present theory that describes this relationship for populations in media with strong unidirectional flow (e.g., aquatic organisms in streams and rivers). Typically,...

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...