Control of invasive hosts by generalist parasitoids

Christelle Magal, George Cosner, Shigui Ruan, J. Casas

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

This article was motivated by the invasion of leaf-mining microlepidopteron attacking horse chestnut trees in Europe and the need for a biological control. Following Owen & Lewis (2001, Bull. Math. Biol., 63, 655-684), we consider predation of leafminers by a generalist parasitoid with a Holling Type II functional response. We first identified six equilibrium points and discussed their stabilities in the non-spatial model. The model always predicts persistence of the parasitoid. Depending on the parameter values, the model may predict that the host persists and goes extinct or there is something like an Allee effect where the outcome depends on the initial host density. Special cases were also studied for small carrying capacities leading to complex dynamical behaviours. Then, numerical simulations of the spatial reaction-diffusion model enabled us to identify the conditions for which the leafminer's advance can be stopped and reversed by parasitoids. Compared to the ordinary differential equation model, the incorporation of space, combined with the polyphagy of the parasitoid, leads to a decrease of the parameter domain of coexistence. This is in stark to several other models in which space promotes coexistence by enabling hosts to escape.

Original languageEnglish (US)
Article numberdqm011
Pages (from-to)1-20
Number of pages20
JournalMathematical Medicine and Biology
Volume25
Issue number1
DOIs
StatePublished - Apr 28 2008

Fingerprint

Aesculus
Space Simulation
Conservation of Natural Resources
generalist
parasitoid
leafminer
Coexistence
coexistence
Biological Control
Allee Effect
Predict
Model
Carrying Capacity
Functional Response
Reaction-diffusion Model
Invasion
Spatial Model
Allee effect
Dynamical Behavior
Equilibrium Point

Keywords

  • Apparent competition
  • Biological control
  • Generalist parasitoid
  • Host-parasitoid system
  • Invasion process
  • ODE
  • PDE

ASJC Scopus subject areas

  • Pharmacology
  • Neuroscience(all)
  • Immunology and Microbiology(all)
  • Environmental Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Modeling and Simulation
  • Applied Mathematics
  • Medicine(all)

Cite this

Control of invasive hosts by generalist parasitoids. / Magal, Christelle; Cosner, George; Ruan, Shigui; Casas, J.

In: Mathematical Medicine and Biology, Vol. 25, No. 1, dqm011, 28.04.2008, p. 1-20.

Research output: Contribution to journalArticle

@article{552b0de94b604539846b6f7c9fb6e6b1,
title = "Control of invasive hosts by generalist parasitoids",
abstract = "This article was motivated by the invasion of leaf-mining microlepidopteron attacking horse chestnut trees in Europe and the need for a biological control. Following Owen & Lewis (2001, Bull. Math. Biol., 63, 655-684), we consider predation of leafminers by a generalist parasitoid with a Holling Type II functional response. We first identified six equilibrium points and discussed their stabilities in the non-spatial model. The model always predicts persistence of the parasitoid. Depending on the parameter values, the model may predict that the host persists and goes extinct or there is something like an Allee effect where the outcome depends on the initial host density. Special cases were also studied for small carrying capacities leading to complex dynamical behaviours. Then, numerical simulations of the spatial reaction-diffusion model enabled us to identify the conditions for which the leafminer's advance can be stopped and reversed by parasitoids. Compared to the ordinary differential equation model, the incorporation of space, combined with the polyphagy of the parasitoid, leads to a decrease of the parameter domain of coexistence. This is in stark to several other models in which space promotes coexistence by enabling hosts to escape.",
keywords = "Apparent competition, Biological control, Generalist parasitoid, Host-parasitoid system, Invasion process, ODE, PDE",
author = "Christelle Magal and George Cosner and Shigui Ruan and J. Casas",
year = "2008",
month = "4",
day = "28",
doi = "10.1093/imammb/dqm011",
language = "English (US)",
volume = "25",
pages = "1--20",
journal = "Mathematical Medicine and Biology",
issn = "1477-8599",
publisher = "Oxford University Press",
number = "1",

}

TY - JOUR

T1 - Control of invasive hosts by generalist parasitoids

AU - Magal, Christelle

AU - Cosner, George

AU - Ruan, Shigui

AU - Casas, J.

PY - 2008/4/28

Y1 - 2008/4/28

N2 - This article was motivated by the invasion of leaf-mining microlepidopteron attacking horse chestnut trees in Europe and the need for a biological control. Following Owen & Lewis (2001, Bull. Math. Biol., 63, 655-684), we consider predation of leafminers by a generalist parasitoid with a Holling Type II functional response. We first identified six equilibrium points and discussed their stabilities in the non-spatial model. The model always predicts persistence of the parasitoid. Depending on the parameter values, the model may predict that the host persists and goes extinct or there is something like an Allee effect where the outcome depends on the initial host density. Special cases were also studied for small carrying capacities leading to complex dynamical behaviours. Then, numerical simulations of the spatial reaction-diffusion model enabled us to identify the conditions for which the leafminer's advance can be stopped and reversed by parasitoids. Compared to the ordinary differential equation model, the incorporation of space, combined with the polyphagy of the parasitoid, leads to a decrease of the parameter domain of coexistence. This is in stark to several other models in which space promotes coexistence by enabling hosts to escape.

AB - This article was motivated by the invasion of leaf-mining microlepidopteron attacking horse chestnut trees in Europe and the need for a biological control. Following Owen & Lewis (2001, Bull. Math. Biol., 63, 655-684), we consider predation of leafminers by a generalist parasitoid with a Holling Type II functional response. We first identified six equilibrium points and discussed their stabilities in the non-spatial model. The model always predicts persistence of the parasitoid. Depending on the parameter values, the model may predict that the host persists and goes extinct or there is something like an Allee effect where the outcome depends on the initial host density. Special cases were also studied for small carrying capacities leading to complex dynamical behaviours. Then, numerical simulations of the spatial reaction-diffusion model enabled us to identify the conditions for which the leafminer's advance can be stopped and reversed by parasitoids. Compared to the ordinary differential equation model, the incorporation of space, combined with the polyphagy of the parasitoid, leads to a decrease of the parameter domain of coexistence. This is in stark to several other models in which space promotes coexistence by enabling hosts to escape.

KW - Apparent competition

KW - Biological control

KW - Generalist parasitoid

KW - Host-parasitoid system

KW - Invasion process

KW - ODE

KW - PDE

UR - http://www.scopus.com/inward/record.url?scp=46249100476&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=46249100476&partnerID=8YFLogxK

U2 - 10.1093/imammb/dqm011

DO - 10.1093/imammb/dqm011

M3 - Article

C2 - 18445582

AN - SCOPUS:46249100476

VL - 25

SP - 1

EP - 20

JO - Mathematical Medicine and Biology

JF - Mathematical Medicine and Biology

SN - 1477-8599

IS - 1

M1 - dqm011

ER -