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Both community ecology and conservation biology seek further understanding offactors governing the advance of an invasive species. We model biologicalinvasion as an individual-based, stochastic process on a two-dimensionallandscape. An ecologically superior invader and a resident species compete forspace preemptively. Our general model includes the basic contact process and avariant of the Eden model as special cases. We employ the concept of a"roughened" front to quantify effects of discreteness and stochasticity oninvasion; we emphasize the probability distribution of the front-runner'srelative position. That is, we analyze the location of the most advancedinvader as the extreme deviation about the front's mean position. We find thata class of models with different assumptions about neighborhood interactionsexhibit universal characteristics. That is, key features of the invasiondynamics span a class of models, independently of locally detailed demographicrules. Our results integrate theories of invasive spatial growth and generatenovel hypotheses linking habitat or landscape size (length of the invadingfront) to invasion velocity, and to the relative position of the most advancedinvader.

Ecological Invasion, Roughened Fronts, and a Competitor's Extreme Advance: Integrating Stochastic Spatial-Growth Models