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Patterns of Patchy Spread in Deterministic and Stochastic Models of Biological Invasion and Biological Control

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Abstract

A few spatiotemporal models of population dynamics are considered in relation to biological invasion and biological control. The patterns of spread in one and two spatial dimensions are studied by means of extensive numerical simulations. We show that, in the case that population multiplication is damped by the strong Allee effect (when the population growth rate becomes negative for small population density), in a certain parameter range the spread can take place not via the intuitively expected circular expanding population front but via motion and interaction of separate patches. Alternatively, the patchy spread can take place in a system without Allee effect as a result of strong environmental noise. We then show that the phenomenon of deterministic patchy invasion takes place ‘at the edge of extinction’ so that a small change of controlling parameters either brings the species to extinction or restores the travelling population fronts. Moreover, we show that the regime of patchy invasion in two spatial dimensions actually takes place when the species go extinct in the corresponding 1-D system.

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Authors and Affiliations

  1. Shirshov Institute of Oceanology, Russian Academy of Science, Nakhimovsky Prosp. 36, Moscow, 117218, Russia

    Sergei V. Petrovskii

  2. Department of Mathematics and Computer Science, Institute for Environmental Systems Research, University of Osnabrück, 49069, Osnabrück,, Germany

    Horst Malchow & Frank M. Hilker

  3. Department of Mathematics, University of Torino, Via Carlo Alberto 10, Torino, 10123, Italy

    Ezio Venturino

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  1. Sergei V. Petrovskii
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  2. Horst Malchow
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  3. Frank M. Hilker
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  4. Ezio Venturino
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Correspondence to Sergei V. Petrovskii.

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Petrovskii, S., Malchow, H., Hilker, F. et al. Patterns of Patchy Spread in Deterministic and Stochastic Models of Biological Invasion and Biological Control. Biol Invasions 7, 771–793 (2005). https://doi.org/10.1007/s10530-005-5217-7

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  • DOI: https://doi.org/10.1007/s10530-005-5217-7

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