Species Competition: Uncertainty on a Double Invariant Loop

Document Type

Article

Publication Date

4-1-2005

Keywords

Invariant loop, Species competition, Stochasticity, Tribolium

Abstract

The Tribolium (flour beetle) competition experiments conducted by Park have been highly influential in ecology. We have previously shown that the dynamics of single-species Tribolium populations can be well-described by the discrete-time, 3-dimensional larva-pupa-adult (LPA) model. Motivated by Park's experiments, we explore the dynamics of a 6-dimensional "competition LPA model" consisting of two LPA models coupled through cannibalism. The model predicts a double-loop coexistence attractor, as well as an unstable exclusion equilibrium with a 5-dimensional stable manifold that plays an important role in causing one of the species to go extinct in the presence of stochastic perturbations. We also present a stochastic version of the model, using binomial and Poisson distributions to describe the aggregation of demographic events within life stages. A novel "stochastic outcome diagram," the stochastic counterpart to a bifurcation diagram, summarizes the model-predicted dynamics of uncertainty on the double-loop. We hypothesize that the model predictions provide an explanation for Park's data. This "stochastic double-loop hypothesis" is accessible to experimental verification. © 2005 Taylor & Francis Group Ltd.

Journal Title

Journal of Difference Equations and Applications

Volume

11

Issue

4-5

First Page

311

Last Page

325

DOI

10.1080/10236190412331335391

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