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Nucleation and global time scales in ecological invasion under preemptive competition

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.