title: Pair statistics clarify percolation properties of spatially explicit simulations.
abstract: Dispersal is a fundamental control on the spatial structure of a population. We investigate the precise mechanism by which a mixed strategy of short- and long-distance dispersal affects spatial patterning. Using techniques from pair approximation and percolation theory, we demonstrate that dispersal controls the extent to which a population is completely connected by modulating the proportion of neighboring sites which are simultaneously occupied. We show that near the percolation threshold this pair statistic, rather than other metrics proposed earlier, best explains clustering, and we suggest more general circumstances under which this may hold.
authors.affiliation: Department of Mathematics, Colorado State University, Fort Collins, 80523, USA. j.achter@colostate.edu
authors.forename: Jeffrey D
authors.initials: JD
authors.lastname: Achter
authors.forename: Colleen T
authors.initials: CT
authors.lastname: Webb
mesh_terms: D016000:Cluster Analysis; D003710:Demography; D004463:Ecology; D005828:Genetics, Population / Q000706:statistics & numerical data*; D006801:Humans; D008957:Models, Genetic