A multi-class extension of the mean field Bolker–Pacala population model

Published on Sep 1, 2018in Random Operators and Stochastic Equations
· DOI :10.1515/rose-2018-0013
Mariya Bessonov2
Estimated H-index: 2
Stanislav Molchanov28
Estimated H-index: 28
Joseph M. Whitmeyer13
Estimated H-index: 13
  • References (7)
  • Citations (1)
#1Dmitri Finkelshtein (NASU: National Academy of Sciences of Ukraine)H-Index: 13
#2Yuri Kondratiev (Bielefeld University)H-Index: 25
Last. Oleksandr Kutoviy (Bielefeld University)H-Index: 13
view all 4 authors...
A Markov evolution of a system of point particles in ℝ d is described at micro- and mesoscopic levels. The particles reproduce themselves at distant points (dispersal) and die, independently and under the effect of each other (competition). The microscopic description is based on an infinite chain of equations for correlation functions, similar to the BBGKY hierarchy used in the Hamiltonian dynamics of continuum particle systems. The mesoscopic description is based on a Vlasov-type kinetic equat...
9 CitationsSource
#1Nicolas FournierH-Index: 21
#2Sylvie Méléard (UPMC: Pierre-and-Marie-Curie University)H-Index: 20
We consider a discrete model describing a locally regulated spatial population with mortality selection. This model was studied in parallel by Bolker and Pacala, [2] and Dieckmann, Law and Murrell [9], [4], [10]. We first generalize this model by adding spatial dependence. Then we give a path-wise description in terms of Poisson point measures. We show that different re-normalizations may lead to different macroscopic approximations of this model. The first approximation is deterministic and giv...
190 CitationsSource
#1Benjamin M. Bolker (UF: University of Florida)H-Index: 46
#2Stephen W. Pacala (Princeton University)H-Index: 77
Last. Claudia NeuhauserH-Index: 23
view all 3 authors...
Abstract: A variety of models have shown that spatial dynamics and small‐scale endogenous heterogeneity (e.g., forest gaps or local resource depletion zones) can change the rate and outcome of competition in communities of plants or other sessile organisms. However, the theory appears complicated and hard to connect to real systems. We synthesize results from three different kinds of models: interacting particle systems, moment equations for spatial point processes, and metapopulation or patch m...
171 CitationsSource
#1Benjamin M. Bolker (Princeton University)H-Index: 46
#2Stephen W. Pacala (Princeton University)H-Index: 77
abstract: A plant lineage can compete for resources in a spatially variable environment by colonizing new areas, exploiting resources in those areas quickly before other plants arrive to compete with it, or tolerating competition once other plants do arrive. These specializations are ubiquitous in plant communities, but all three have never been derived from a spatial model of community dynamics—instead, the possibility of rapid exploitation has been either overlooked or confounded with coloniza...
433 CitationsSource
In [3] this author gave conditions under which a sequence of jump Markov processes X n ( t ) will converge to the solution X ( t ) of a system of first order ordinary differential equations, in the sense that for every δ > 0.
414 CitationsSource
In a great variety of fields, e.g., biology, epidemic theory, physics, and chemistry, ordinary differential equations are used to give continuous deterministic models for dynamic processes which are actually discrete and random in their development. Perhaps the simplest example is the differential equation used to describe a number of processes including radioactive decay and population growth.
655 CitationsSource
318 CitationsSource
Cited By1
#1Anastasiia Rytova (MSU: Moscow State University)H-Index: 2
#2Elena Yarovaya (MSU: Moscow State University)H-Index: 9