Nucleation and Global Time Scales in Ecological Invasion under Preemptive Competition L. O’Malley a , A. Allstadt b , G. Korniss a , and T. Caraco b , a Department of Physics, Applied Physics, and Astronomy, Rensselaer Polytechnic Institute, 110 8 th Street, Troy, NY 12180–3590, USA; b Department of Biological Sciences, University at Albany, Albany, NY 12222, USA ABSTRACT The breakdown of biogeographic barriers allows some invasive species to reshape ecological communities and threaten local biodiversity. Most introductions of exotic species fail to generate an invasion. However, once introduction succeeds, invader density increases rapidly. We apply nucleation theory to describe spatio-temporal patterns of the invasion process under preemptive competition. The predictions of the theory are confirmed by Monte Carlo simulations of the underlying discrete spatial stochastic dynamics. In particular, for large enough spatial regions, invasion occurs through the nucleation and subsequent growth of many clusters of the invasive species, and the global densities are well approximated by Avrami’s law for homogeneous nucleation. For smaller systems or very small introduction rates, invasion typically occurs through a single cluster, whose appearance is inherently stochastic. Keywords: spatial competition, ecological invasion, nucleation theory 1. INTRODUCTION Human-caused environmental changes have eroded natural barriers to the long-distance dispersal of plants and animals. 1 Consequently, expanding geographic ranges of invasive species have begun to homogenize the biota of different regions. 2 Successful exotic invaders often replace native species, and produce additional economic, epidemiological or agricultural problems in their new environments. 3 Many exotics, including certain species purposefully introduced by humans, 4 combine a low probability of establishment at each introduction with rapid population growth once introduction succeeds. Modeling introduction as a rare stochastic process, the conditions for homogeneous mixing and the applicability of the corresponding mean-field equations immediately break down. In this case either continuum 5 or discrete 6 (individual-based) spatial models are needed to address the problem. In this paper we investigate a discrete spatial model for ecological invasion. Initially the spatial region is fully dominated by the “resident” species. The “invader” species is introduced stochastically where resources are locally available. The invader has an individual-level advantage over the residents, but the low probability of introduction, combined with a discrete spatial dynamics, can prevent the spread of the invader for extended times. Here we consider a model where the residents and the competitively superior invaders compete for a common limiting resource preemptively. 7–10 We demonstrate that under these conditions, invasion is governed by nucleation and growth 11–14 of clusters of the invasive species. A relatively old empirical study 15 on primary ecological succession in sand-dune communities, where persistent vegetation (oak-pine forest) replaces colonizing grassland during succession, motivates our hypothesis that nucleation theory can explain important properties of biological invasion. Further author information: Send correspondence to G.K., E-mail: korniss@rpi.edu Fluctuations and Noise in Biological, Biophysical, and Biomedical Systems III, edited by Nigel G. Stocks, Derek Abbott, Robert P. Morse, Proc. of SPIE Vol. 5841 (SPIE, Bellingham, WA, 2005) · 0277-786X/05/$15 · doi: 10.1117/12.609267 117