title: The distribution of species range size: a stochastic process.
abstract: The major role played by environmental factors in determining the geographical range sizes of species raises the possibility of describing their long-term dynamics in relatively simple terms, a goal which has hitherto proved elusive. Here we develop a stochastic differential equation to describe the dynamics of the range size of an individual species based on the relationship between abundance and range size, derive a limiting stationary probability model to quantify the stochastic nature of the range size for that species at steady state, and then generalize this model to the species-range size distribution for an assemblage. The model fits well to several empirical datasets of the geographical range sizes of species in taxonomic assemblages, and provides the simplest explanation of species-range size distributions to date.
authors.affiliation: Biodiversity and Macroecology Group, Department of Animal and Plant Sciences, University of Sheffield, Sheffield S10 2TN, UK. k.j.gaston@sheffield.ac.uk
authors.forename: Kevin J
authors.initials: KJ
authors.lastname: Gaston
authors.forename: Fangliang
authors.initials: F
authors.lastname: He
mesh_terms: D000818:Animals; D001516:Bees / Q000502:physiology; D001824:Body Constitution / Q000502:physiology*; D017753:Ecosystem; D008322:Mammals / Q000502:physiology; D008954:Models, Biological; D015203:Reproducibility of Results; D013045:Species Specificity; D013269:Stochastic Processes