Summary: Pair statistics clarify percolation properties of
spatially explicit simulations
Jeffrey D. Achter , Colleen Webb
Department of Biology, Colorado State University, Fort Collins, CO 80523
Email addresses: firstname.lastname@example.org (Jeffrey D. Achter),
email@example.com (Colleen Webb).
URL: http://lamar.colostate.edu/jachter (Jeffrey D. Achter).
Preprint submitted to Elsevier Science 15 September 2005
Dispersal is a fundamental control on the spatial structure of a population. We inves-
tigate 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 thresh-
old this pair statistic, rather than other metrics proposed earlier, best explains
clustering, and we suggest more general circumstances under which this may hold.
Key words: dispersal, percolation, pair approximation, aggregation, spatial