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

Peter G Schofield1, Mark A J Chaplain, Stephen F Hubbard

  • 1The SIMBIOS Centre, Division of Mathematicst:, The University of Dundee, Dundee, DD1 4HN, UK. p.schofield@dundee.ac.uk

Journal of Mathematical Biology
|November 19, 2004
PubMed
Summary

This study models host-parasitoid dynamics with synchronized generations. Unequal movement strategies cause individual-based models to show spatial oscillations, unlike continuum models predicting stable states.

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Host-parasitoid systems are crucial for ecological balance.
  • Generational synchronisation, like seasonal diapause, influences population dynamics.
  • Semiochemicals (kairomones) mediate interactions in many host-parasitoid systems.

Purpose of the Study:

  • To develop a mathematical model for spatio-temporal host-parasitoid dynamics with forced generational synchronisation.
  • To compare an individual-based stochastic model with an underlying continuum partial differential equation (PDE) model.
  • To investigate the impact of host and parasitoid movement strategies on population dynamics and stability.

Main Methods:

  • Developed an individual-based stochastic model with movement rules from a continuum PDE model.

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  • Incorporated within-generation and between-generation population regulation mechanisms.
  • Focused on interactions between juvenile hosts, adult hosts, and adult parasitoids in a 2D domain, mediated by kairomones.

    • Main Results:

    • The individual-based and continuum models show agreement for certain motility parameters.
    • Model dynamics diverge when host and parasitoid motilities are unequal.
    • The individual-based model predicts spatially heterogeneous oscillatory dynamics, contrasting with the continuum model's homogeneous steady state prediction.

    Conclusions:

    • Discrepancies between individual-based and continuum models highlight the importance of individual movement in host-parasitoid dynamics.
    • Unequal motility can lead to fundamentally different population dynamics (oscillations vs. steady states).
    • Results have implications for developing mechanistic models of phenotype evolution in ecological systems.