Dynamic heterogeneous spatio-temporal pattern formation in host-parasitoid systems with synchronised generations

Peter G. Schofield, Mark A. J. Chaplain, Stephen F. Hubbard

    Research output: Contribution to journalArticle

    7 Citations (Scopus)

    Abstract

    In this paper we develop a general mathematical model describing the spatio-temporal dynamics of host-parasitoid systems with forced generational synchronisation, for example seasonally induced diapause. The model itself may be described as an individual-based stochastic model with the individual movement rules derived from an underlying continuum PDE model. This approach permits direct comparison between the discrete model and the continuum model. The model includes both within-generation and between-generation mechanisms for population regulation and focuses on the interactions between immobile juvenile hosts, adult hosts and adult parasitoids in a two-dimensional domain. These interactions are mediated, as they are in many such host-parasitoid systems, by the presence of a volatile semio-chemical (kairomone) emitted by the hosts or the hosts food plant. The model investigates the effects on population dynamics for different host versus parasitoid movement strategies as well as the transient dynamics leading to steady states. Despite some agreement between the individual and continuum models for certain motility parameter ranges, the model dynamics diverge when host and parasitoid motilities are unequal. The individual-based model maintains spatially heterogeneous oscillatory dynamics when the continuum model predicts a homogeneous steady state. We discuss the implications of these results for mechanistic models of phenotype evolution.
    Original languageEnglish
    Pages (from-to)559-583
    Number of pages25
    JournalJournal of Mathematical Biology
    Volume50
    Issue number5
    DOIs
    Publication statusPublished - 2005

    Fingerprint

    Edible Plants
    Spatio-temporal Patterns
    Pheromones
    Population Dynamics
    Pattern Formation
    Theoretical Models
    Phenotype
    Continuum Model
    Population
    Individual-based Model
    Motility
    Model
    Transient Dynamics
    Volatiles
    Discrete Model
    Diverge
    Unequal
    Interaction
    Stochastic Model
    Continuum

    Keywords

    • Host-parasitoid systems
    • Pattern formation
    • Spatio-temporal dynamics

    Cite this

    Schofield, Peter G. ; Chaplain, Mark A. J. ; Hubbard, Stephen F. / Dynamic heterogeneous spatio-temporal pattern formation in host-parasitoid systems with synchronised generations. In: Journal of Mathematical Biology. 2005 ; Vol. 50, No. 5. pp. 559-583.
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    Dynamic heterogeneous spatio-temporal pattern formation in host-parasitoid systems with synchronised generations. / Schofield, Peter G.; Chaplain, Mark A. J.; Hubbard, Stephen F.

    In: Journal of Mathematical Biology, Vol. 50, No. 5, 2005, p. 559-583.

    Research output: Contribution to journalArticle

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