Bulletin of Mathematical Biology

, Volume 71, Issue 5, pp 1160–1188 | Cite as

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

  • Lauren O’Malley
  • G. Korniss
  • Thomas CaracoEmail author
Original Article


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 exhibits 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.


Ecological invasion Front-runner distribution Extreme-value statistics Preemptive competition Spatial model Stochastic roughening 


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Copyright information

© Society for Mathematical Biology 2009

Authors and Affiliations

  1. 1.Department of Physics, Applied Physics, and AstronomyRensselaer Polytechnic InstituteTroyUSA
  2. 2.Department of Biological SciencesUniversity at AlbanyAlbanyUSA

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