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

Abstract

Both community ecology and conservation biology seek further understanding of factors governing the advance of an invasive species. We model biological invasion as an individual-based, stochastic process on a two-dimensional landscape. An ecologically superior invader and a resident species compete for space preemptively. Our general model includes the basic contact process and a variant of the Eden model as special cases. We employ the concept of a "roughened" front to quantify effects of discreteness and stochasticity on invasion; we emphasize the probability distribution of the front-runner's relative position. That is, we analyze the location of the most advanced invader as the extreme deviation about the front's mean position. We find that a class of models with different assumptions about neighborhood interactions exhibit universal characteristics. That is, key features of the invasion dynamics span a class of models, independently of locally detailed demographic rules. Our results integrate theories of invasive spatial growth and generate novel hypotheses linking habitat or landscape size (length of the invading front) to invasion velocity, and to the relative position of the most advanced invader.

The original publication is available at www.springerlink.com/content/8528v8563r7u2742/

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Cited by in corpus (10)

• Extreme value statistics from the Real Space Renormalization Group: Brownian Motion, Bessel Processes and Continuous Time Random Walks
• Distribution of the time at which N vicious walkers reach their maximal height
• Interference competition and invasion: spatial structure, novel weapons and resistance zones
• Extreme Fluctuations in Stochastic Network Coordination with Time Delays
• Extreme-Value Distributions and the Freezing Transition of Structural Glasses
• Spatial competition and the dynamics of rarity in a temporally varying environment
• Infection fronts in randomly varying transmission-rate media
• Influence of invasion on natural selection in dispersal-structured populations
• Restoration Ecology: Two-Sex Dynamics and Cost Minimization
• Dispersal limitation and roughening of the ecological interface