Species Competition: Uncertainty on a Double Invariant Loop
Invariant loop, Species competition, Stochasticity, Tribolium
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 of Difference Equations and Applications
Desharnais, Robert A.; Edmunds, Jeffrey; Costantino, R. F.; and Henson, Shandelle M., "Species Competition: Uncertainty on a Double Invariant Loop" (2005). Faculty Publications. 2087.