Species competition

Uncertainty on a double invariant loop

Robert A. Desharnais, Jeffrey Edmunds, Robert F Costantino, Shandelle M. Henson

Research output: Contribution to journalArticle

5 Citations (Scopus)

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.

Original languageEnglish (US)
Pages (from-to)311-325
Number of pages15
JournalJournal of Difference Equations and Applications
Volume11
Issue number4-5
DOIs
StatePublished - Apr 2005

Fingerprint

Uncertainty
Invariant
Poisson distribution
Stochastic Perturbation
Stable Manifold
Model
Binomial distribution
Bifurcation (mathematics)
Coupled Model
Ecology
Bifurcation Diagram
Coexistence
Prediction Model
Experiment
Attractor
Dynamic models
Aggregation
Discrete-time
Diagram
Agglomeration

Keywords

  • Invariant loop
  • Species competition
  • Stochasticity
  • Tribolium

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis
  • Applied Mathematics

Cite this

Species competition : Uncertainty on a double invariant loop. / Desharnais, Robert A.; Edmunds, Jeffrey; Costantino, Robert F; Henson, Shandelle M.

In: Journal of Difference Equations and Applications, Vol. 11, No. 4-5, 04.2005, p. 311-325.

Research output: Contribution to journalArticle

Desharnais, Robert A. ; Edmunds, Jeffrey ; Costantino, Robert F ; Henson, Shandelle M. / Species competition : Uncertainty on a double invariant loop. In: Journal of Difference Equations and Applications. 2005 ; Vol. 11, No. 4-5. pp. 311-325.
@article{39f394266a464194905c3a79eb1b7d0f,
title = "Species competition: Uncertainty on a double invariant loop",
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.",
keywords = "Invariant loop, Species competition, Stochasticity, Tribolium",
author = "Desharnais, {Robert A.} and Jeffrey Edmunds and Costantino, {Robert F} and Henson, {Shandelle M.}",
year = "2005",
month = "4",
doi = "10.1080/10236190412331335391",
language = "English (US)",
volume = "11",
pages = "311--325",
journal = "Journal of Difference Equations and Applications",
issn = "1023-6198",
publisher = "Taylor and Francis Ltd.",
number = "4-5",

}

TY - JOUR

T1 - Species competition

T2 - Uncertainty on a double invariant loop

AU - Desharnais, Robert A.

AU - Edmunds, Jeffrey

AU - Costantino, Robert F

AU - Henson, Shandelle M.

PY - 2005/4

Y1 - 2005/4

N2 - 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.

AB - 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.

KW - Invariant loop

KW - Species competition

KW - Stochasticity

KW - Tribolium

UR - http://www.scopus.com/inward/record.url?scp=22544467472&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=22544467472&partnerID=8YFLogxK

U2 - 10.1080/10236190412331335391

DO - 10.1080/10236190412331335391

M3 - Article

VL - 11

SP - 311

EP - 325

JO - Journal of Difference Equations and Applications

JF - Journal of Difference Equations and Applications

SN - 1023-6198

IS - 4-5

ER -