 A mean field model for species abundanceThomas J. Pfaff Stochastic Processes and their Applications, 2003, vol. 104, issue 2, 325-347 Abstract: In this paper, we use the multitype mean field voter model as a model of species interaction, to obtain results about species abundance. Briefly, we start with the complete graph on n vertices, Cn, with each site occupied by a particle. Particles are represented by a value in (0,1), where distinct values represent different species. Particles then undergo mutation at rate [alpha], and are relabelled with a value chosen uniformly from (0,1). Particles also give birth at rate 1, and invade any of the other n sites randomly. This process has a unique stationary distribution denoted by [xi][infinity]n, which is given by the Ewens sampling formula. For each value in (0,1) that is present in [xi][infinity]n, we count the number of particles represented by the same value, and call that the patch size of the species. Let Kn[a,b] denote the number of species with patch size in [a,b]. We study the limiting distribution of Kn[a,b], for certain values of a and b, as the mutation rate [alpha] tends to 0, which will in turn force n-->[infinity]. Keywords: Species; abundance; distribution; Mean; field; voter; model; Moran; model; Linear; birth; process (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:104:y:2003:i:2:p:325-347 Ordering information: This journal article can be ordered from Access Statistics for this article Stochastic Processes and their Applications is currently edited by T. Mikosch More articles in Stochastic Processes and their Applications from Elsevier |
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