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Pair-edge approximation for heterogeneous lattice population models.

Nikkala A Thomson1, Stephen P Ellner

  • 1Department of Statistics, North Carolina State University, Raleigh, NC 27695, USA. nikkala@worldnet.att.net

Theoretical Population Biology
|October 3, 2003
PubMed
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The pair-edge approximation accurately predicts population persistence on heterogeneous lattices. However, it underestimates invasion speed reduction caused by habitat fragmentation, especially with clustered dead sites.

Area of Science:

  • Ecology
  • Mathematical Biology
  • Computational Biology

Background:

  • Lattice stochastic spatial population models are crucial for understanding ecological dynamics.
  • Analytical tractability is often limited, necessitating approximations.
  • The pair-edge approximation is a moment-closure method effective on homogeneous lattices.

Purpose of the Study:

  • To evaluate the pair-edge approximation's effectiveness on spatially heterogeneous lattices with unoccupiable sites.
  • To compare its accuracy against the ordinary pair approximation for persistence and invasion speed.
  • To identify limitations of the pair-edge approximation in heterogeneous environments.

Main Methods:

  • Developing and analyzing a lattice stochastic spatial population model with habitat heterogeneity (unoccupiable sites).

Related Experiment Videos

  • Applying the pair-edge approximation and the ordinary pair approximation to this heterogeneous model.
  • Comparing approximation predictions with simulation results for persistence criteria and invasion speeds.

    • Main Results:

    • The pair-edge approximation significantly improves accuracy over the ordinary pair approximation for predicting persistence conditions.
    • Habitat heterogeneity reduces invasion speed more than predicted by the pair-edge approximation.
    • Discrepancies increase with greater clustering of unoccupiable sites.

    Conclusions:

    • The pair-edge approximation provides valuable qualitative insights into population spread dynamics on heterogeneous lattices.
    • Habitat heterogeneity poses limitations to the pair-edge approximation's accuracy, particularly concerning invasion speed.
    • Understanding these limitations is crucial for refining spatial population models.