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An Interspecies Competition Model with Multiscale Interpretations

A method for simulating and analyzing the competition between similar species is presented here by first adapting a Gause type model that allows four fitting parameters [2]. From this deterministic model we derive conditions for the existence and stability of several equilibria, including multiple coexistence equilibria. An agent-based simulation is then created to model the biology of the species on the scale of individual interaction. Changes in the growth scale parameters for the deterministic model are then considered in order to try the replicate the behavior of the agent-based biology. This is done in an attempt to rationalize the growth scale parameters as a tool to capture all possible behaviors. In an effort to observe the dynamics on a different spatial scale, we implement a spatially structured stochastic simulation with parameters chosen to reflect the different outcomes of the agent-based model. This second simulation will track, on a larger scale, the interaction between groups or colonies of the species of interest. The multiscale method presented here allows for a broader interpretation of interspecies competition than is possible through interpretation of interspecies competition than is possible through deterministic analysis. For the purpose of an example, two species of ants will be considered (Solenopsis invicta and S. geminata).

  • Poster session award recipient at the 2006 AMS/MAA Joint Mathematics Meeting in San Antonio, TX
  • Poster session award recipient at the 2005 Los Alamos National Laboratory Undergraduate Research Symposium
  • Poster session award recipient at the 2006 MGE@MSA Conference in Tempe, AZ

Article Number:
MTBI-02-14M

Year:
2005

Authors:
José Almora, University of North Carolina at Chapel Hill
Nick Dowdall, Sonoma State University
Benjamin Morin, University of Maine
David Murillo, Arizona State University

an_interspecies_competition_model_with_multiscale_interpretations.pdf