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Parameter estimation techniques for interaction and redistribution models: a predator-prey example.

H T Banks1, P M Kareiva2, K A Murphy3

  • 1Center for Control Sciences, Division of Applied Mathematics, Brown University, 02912, Providence, RI, USA.

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Summary
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New parameter estimation techniques for partial differential equations enable ecological modeling in complex environments. These methods accurately predict predator-prey dynamics, incorporating species movement and environmental heterogeneity.

Keywords:
Heterogeneous environmentsParameter estimationSpecies interactionredistribution

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Computational Science

Background:

  • Ecological models often simplify complex environments.
  • Parameter estimation for partial differential equations (PDEs) in ecology is challenging.
  • Previous methods could not account for spatial heterogeneity or organism movement.

Purpose of the Study:

  • To develop and demonstrate parameter estimation techniques for PDEs in ecological models.
  • To enable modeling of predator-prey interactions in heterogeneous environments.
  • To bridge the gap between experimental data and mathematical models.

Main Methods:

  • Applied parameter estimation techniques to a predator-prey model using partial differential equations.
  • Utilized field data from ladybird beetle (Coccinella septempunctata) and aphid (Uroleucon nigrotuberculatum) interactions.
  • Developed algorithms to identify best-fit models explaining observed population densities.

Main Results:

  • Parameter estimation algorithms explained over 80% of the observed variance in aphid and ladybird densities.
  • The developed techniques are broadly applicable to spatially complex ecological models.
  • Identified a need for a local taxis term in models of ladybird-aphid interactions.

Conclusions:

  • Parameter estimation for PDEs offers a powerful approach for ecological modeling.
  • The methods facilitate the integration of detailed experimental data into mathematical frameworks.
  • Ladybird beetle local taxis towards prey is a crucial factor in predator-prey dynamics within heterogeneous environments.