Resolving discrepancies between deterministic population models and individual-based simulations.

Published

Journal Article

This work ties together two distinct modeling frameworks for population dynamics: an individual-based simulation and a set of coupled integrodifferential equations involving population densities. The simulation model represents an idealized predator-prey system formulated at the scale of discrete individuals, explicitly incorporating their mutual interactions, whereas the population-level framework is a generalized version of reaction-diffusion models that incorporate population densities coupled to one another by interaction rates. Here I use various combinations of long-range dispersal for both the offspring and adult stages of both prey and predator species, providing a broad range of spatial and temporal dynamics, to compare and contrast the two model frameworks. Taking the individual-based modeling results as given, two examinations of the reaction-dispersal model are made: linear stability analysis of the deterministic equations and direct numerical solution of the model equations. I also modify the numerical solution in two ways to account for the stochastic nature of individual-based processes, which include independent, local perturbations in population density and a minimum population density within integration cells, below which the population is set to zero. These modifications introduce new parameters into the population-level model, which I adjust to reproduce the individual-based model results. The individual-based model is then modified to minimize the effects of stochasticity, producing a match of the predictions from the numerical integration of the population-level model without stochasticity.

Full Text

Duke Authors

Cited Authors

  • Wilson, WG

Published Date

  • February 1998

Published In

Volume / Issue

  • 151 / 2

Start / End Page

  • 116 - 134

PubMed ID

  • 18811412

Pubmed Central ID

  • 18811412

Electronic International Standard Serial Number (EISSN)

  • 1537-5323

International Standard Serial Number (ISSN)

  • 0003-0147

Digital Object Identifier (DOI)

  • 10.1086/286106

Language

  • eng