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How does stochasticity in colonization accelerate the speed of invasion in a cellular automaton model?

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  • Theoretical ecology
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Ecological Research

Abstract

We investigate the speed of invasion waves for a single species generated by stochastic short- and/or long-distance colonizations in a time-continuous cellular automaton (CA) model on a two-dimensional homogenous landscape. By simulating the CA models, we demonstrate that stochasticity can dramatically increase the speed of invasion compared to the corresponding deterministic CA model or the corresponding one-dimensional stochastic CA model. To explain this phenomenon, we first develop a mathematical model for the invasion involving only short-distance colonization (i.e., colonization only occurs from the eight adjacent cells), and present several approximation methods for solving the model. Our analyses show that the increased wave speed in the stochastic model is due to irregularity in the shape of the wavefront. Further extension of this model to include long-distance colonization demonstrates that stochasticity influences speeds to even greater extents in this case. Using dimension analysis, we deduced a semi-empirical formula for the speed as a function of three parameters intrinsic to short- and long-distance colonization, which agrees well with simulation results. Based on these results, we discuss how important stochasticity in colonization and spatial dimensionality are in the acceleration of invasion speed.

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Acknowledgments

We thank N. Osawa, K. Uehara, T. Takayanagi, C. Mukaino, and S. Baba for their contribution at the initial stage of this study. We also appreciate Dr S. Takahashi for valuable comments. Part of this study was supported by the Grant-in-Aid for Scientific Research Fund from the Japan Ministry of Education, Science, Culture and Sports (no. 13640627 and no. 09NP1501). HC acknowledges support from NSF Grant DEB-0235692.

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Authors and Affiliations

  1. Faculty of Culture and Information Science, Doshisha University, Kyotanabe, 610-0321, Japan

    Kohkichi Kawasaki & Nanako Shigesada

  2. Department of Information and Computer Sciences, Nara Women’s University, Kita-Uoya Nishimachi, Nara, 630-8506, Japan

    Fugo Takasu

  3. Biology Department MS34, Woods Hole Oceanographic Institution, Woods Hole, MA, 02543, USA

    Hal Caswell

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  1. Kohkichi Kawasaki
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  2. Fugo Takasu
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  3. Hal Caswell
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  4. Nanako Shigesada
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Correspondence to Nanako Shigesada.

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Kawasaki, K., Takasu, F., Caswell, H. et al. How does stochasticity in colonization accelerate the speed of invasion in a cellular automaton model?. Ecol Res 21, 334–345 (2006). https://doi.org/10.1007/s11284-006-0166-x

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  • DOI: https://doi.org/10.1007/s11284-006-0166-x

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