Dispersal and Pattern Formation in a Discrete-Time Predator-Prey Model

Neubert, Michael G.; Kot, Mark; Lewis, Mark A.

doi:10.1006/tpbi.1995.1020

Cited by 270 publications

(282 citation statements)

References 0 publications

Supporting

Mentioning

271

Contrasting

Unclassified

Order By: Relevance

“…Furthermore, one supposes that growth may be density-dependent but dispersal is not. The growth phase is described by some nonnegative function f , and the dispersal phase by a dispersal kernel, k(x, y), where the product k(x, y)∆x gives the probability that an individual who started its dispersal process at y will settle in [x, x + ∆x) (Neubert et al, 1995). The population density in the next generation is obtained by tallying arrivals at location x from all possible locations y, or mathematically as the integral operator where N t (x) denotes the density of the population at time or generation t at location x, and Ω is a biological region of interest (Kot and Schaffer, 1986).…”

Section: Integrodifference Equationsmentioning

confidence: 99%

“…However, as pointed out by Lutscher (2007), an important feature of IDEs that has not received much attention is their ability to model short-distance dispersal with much more detail than reaction-diffusion equations. Indeed, as first shown by Neubert et al (1995) in homogeneous landscapes, dispersal kernels can be derived from mechanistic movement models in the form of reaction-diffusion equations. In this work, we generalize their approach to patchy landscapes and show that the resulting dispersal kernel is, in general, discontinuous.…”

Section: Outline Of the Thesismentioning

confidence: 99%

“…The work in this chapter is based on the pioneering results of Neubert et al (1995), who considered a random walk model with constant diffusion and settling times, and derived corresponding dispersal kernels. VanKirk (1995) extended the results of Neubert et al (1995) by showing how dispersal kernels can be characterized as the Green's function of a second-order differential operator.…”

Section: Individual Dispersalmentioning

confidence: 99%

“…VanKirk (1995) extended the results of Neubert et al (1995) by showing how dispersal kernels can be characterized as the Green's function of a second-order differential operator. VanKirk and Lewis (1999) derived kernels on a single patch with a semi-permeable boundary from a random walk.…”

Section: Individual Dispersalmentioning

confidence: 99%

“…In this dissertation, we choose the mechanistic derivation of dispersal kernels as pioneered by Neubert et al (1995) in a homogeneous landscape and generalize it to heterogeneous landscapes. This approach allows us to explicitly include movement behavior at interfaces between different landscape types by employing recent results from Ovaskainen and Cornell (2003).…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Integrodifference equations in patchy landscapes

Musgrave

Lutscher

2013

J. Math. Biol.

View full text Add to dashboard Cite

In this dissertation, we study integrodifference equations in patchy landscapes. Specifically, we provide a framework for linking individual dispersal behavior with populationlevel dynamics in patchy landscapes by integrating recent advances in modeling dispersal into an integrodifference equation.First, we formulate a random-walk model in a patchy landscape with patchdependent diffusion, settling, and mortality rates. We incorporate mechanisms for individual behavior at an interface which, in general, results in the probability-density function of the random walker being discontinuous at an interface. We show that the dispersal kernel can be characterized as the Green's function of a second-order differential operator and illustrate the kind of (discontinuous) dispersal kernels that arise from our approach. We examine the dependence of obtained kernels on model parameters.Secondly, we analyze integrodifference equations in patchy landscapes equipped with discontinuous kernels. We obtain explicit formulae for the critical-domain-size problem, as well as explicit formulae for the analogous critical size of good patches on an infinite, periodic, patchy landscape. We examine the dependence of obtained formulae on individual behavior at an interface. Through numerical simulations, we observe that, if the population can persist on an infinite, periodic, patchy landscape, its spatial profile can evolve into a discontinuous traveling periodic wave. We derive a dispersion relation for the speed of the wave and illustrate how interface behavior ii

show abstract

Section: Integrodifference Equationsmentioning

confidence: 99%

Section: Outline Of the Thesismentioning

confidence: 99%

Section: Individual Dispersalmentioning

confidence: 99%

Section: Individual Dispersalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Integrodifference equations in patchy landscapes

Musgrave

Lutscher

2013

J. Math. Biol.

View full text Add to dashboard Cite

show abstract

How far to build it before they come? Analyzing the use of the Field of Dreams hypothesis in bull kelp restoration

Arroyo-Esquivel

Baskett

McPherson

et al. 2023

Ecological Applications

View full text Add to dashboard Cite

In restoration ecology, the Field of Dreams hypothesis posits that restoration efforts that create a suitable environment could lead to the eventual recovery of the remaining aspects of the ecosystem through natural processes. Natural processes following partial restoration has led to ecosystem recovery in both terrestrial and aquatic systems. However, understanding the efficacy of a "Field of Dreams" approach requires a com-

show abstract

Behavioral responses to resource heterogeneity can accelerate biological invasions

Lutscher

Musgrave

2017

Ecology

View full text Add to dashboard Cite

The abundance and spatial distribution of resources in a landscape and the behavioral response of individuals determines whether and how fast an invasive species spreads in an environment. Whether and how landscape manipulations can be used to slow invasive species is of great interest, in particular in forest ecosystems, where tree removal, thinning, and increasing tree diversity are discussed as management options. Classically, the focus is on availability and accessibility of resources; more recent considerations include individual-level behavioral movement responses to a spatially heterogeneous resource distribution. We derive a novel model for insect-host dynamics that includes three common behavioral aspects of foraging: higher movement rate in resource-poor areas, lower ovipositioning rate in resource-poor areas, and movement preference for resource-rich areas. We show that each of these basic mechanisms can increase the speed of invasion in a source-sink landscape above that in a homogeneous landscape with larger overall resource availability. We parameterize our model and illustrate our results with data for emerald ash borer, a recent highly destructive forest pest in North America. Our results highlight the importance of empirical work on movement behavior in different landscape types and near the interface between types.

show abstract

Dispersal and Pattern Formation in a Discrete-Time Predator-Prey Model

Cited by 270 publications

References 0 publications

Integrodifference equations in patchy landscapes

Integrodifference equations in patchy landscapes

How far to build it before they come? Analyzing the use of the Field of Dreams hypothesis in bull kelp restoration

Behavioral responses to resource heterogeneity can accelerate biological invasions

Contact Info

Product

Resources

About