295,345 research outputs found
Coexistence in stochastic spatial models
In this paper I will review twenty years of work on the question: When is
there coexistence in stochastic spatial models? The answer, announced in
Durrett and Levin [Theor. Pop. Biol. 46 (1994) 363--394], and that we explain
in this paper is that this can be determined by examining the mean-field ODE.
There are a number of rigorous results in support of this picture, but we will
state nine challenging and important open problems, most of which date from the
1990's.Comment: Published in at http://dx.doi.org/10.1214/08-AAP590 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Spatial stochastic predator-prey models
We consider a broad class of stochastic lattice predator-prey models, whose
main features are overviewed. In particular, this article aims at drawing a
picture of the influence of spatial fluctuations, which are not accounted for
by the deterministic rate equations, on the properties of the stochastic
models. Here, we outline the robust scenario obeyed by most of the lattice
predator-prey models with an interaction "a' la Lotka-Volterra". We also show
how a drastically different behavior can emerge as the result of a subtle
interplay between long-range interactions and a nearest-neighbor exchange
process.Comment: 5 pages, 2 figures. Proceedings paper of the workshop "Stochastic
models in biological sciences" (May 29 - June 2, 2006 in Warsaw) for the
Banach Center Publication
Regulation mechanisms in spatial stochastic development models
The aim of this paper is to analyze different regulation mechanisms in
spatial continuous stochastic development models. We describe the density
behavior for models with global mortality and local establishment rates. We
prove that the local self-regulation via a competition mechanism (density
dependent mortality) may suppress a unbounded growth of the averaged density if
the competition kernel is superstable.Comment: 19 page
Stochastic models in population biology and their deterministic analogs
In this paper we introduce a class of stochastic population models based on
"patch dynamics". The size of the patch may be varied, and this allows one to
quantify the departures of these stochastic models from various mean field
theories, which are generally valid as the patch size becomes very large. These
models may be used to formulate a broad range of biological processes in both
spatial and non-spatial contexts. Here, we concentrate on two-species
competition. We present both a mathematical analysis of the patch model, in
which we derive the precise form of the competition mean field equations (and
their first order corrections in the non-spatial case), and simulation results.
These mean field equations differ, in some important ways, from those which are
normally written down on phenomenological grounds. Our general conclusion is
that mean field theory is more robust for spatial models than for a single
isolated patch. This is due to the dilution of stochastic effects in a spatial
setting resulting from repeated rescue events mediated by inter-patch
diffusion. However, discrete effects due to modest patch sizes lead to striking
deviations from mean field theory even in a spatial setting.Comment: 47 pages, 9 figure
Quasi-cycles in a spatial predator-prey model
We show that spatial models of simple predator-prey interactions predict that
predator and prey numbers oscillate in time and space. These oscillations are
not seen in the deterministic versions of the models, but are due to stochastic
fluctuations about the time-independent solutions of the deterministic
equations which are amplified due to the existence of a resonance. We calculate
the power spectra of the fluctuations analytically and show that they agree
well with results obtained from stochastic simulations. This work extends the
analysis of these quasi-cycles from that previously developed for well-mixed
systems to spatial systems, and shows that the ideas and methods used for
non-spatial models naturally generalize to the spatial case.Comment: 18 pages, 4 figure
Regional Tourism Competition in the Baltic States: a Spatial Stochastic Frontier Approach
This paper aimed at a statistical analysis of competition for tourists between regions within Baltic states (Estonia, Latvia, Lithuania) and estimation relative efficiency levels of regions. We apply a modern approach called Spatial Stochastic Frontier and corresponded to spatial modification of a stochastic frontier model. We specify two alternative spatial stochastic frontier models – distance and travel-time based to identify an influence of existing transport network on research results. Using the model we analyse region-specific factors (tourism infrastructure, employment, geographical position and natural attractors) having an effect on a number of visitors and estimate regions' efficiency values. We discover a significant level of inefficiency of Baltic states regions and propose some ways to improve the situation.spatial stochastic frontier, efficiency, competition, regional tourism, transport network
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