Abstract
Understanding of large-scale spatial pattern formation is a key to successful management in ecology and epidemiology. Neighbourhood interactions between local units are known to contribute to large-scale patterns, but how much do they contribute and what is the role of regional interactions caused by long-distance processes? How much long-distance dispersal do we need to explain the patterns that we observe in nature? There seems to be no way to answer these questions empirically. Therefore, we present a modelling approach that is a combination of a grid-based model describing local interactions and an individual-based model describing dispersal. Applying our approach to the spread of rabies, we show that in addition to local rabies dynamics, one long-distance infection per 14000 km2 per year is sufficient to reproduce the wave-like spread of this disease. We conclude that even rare ecological events that couple local dynamics on a regional scale may have profound impacts on large-scale patterns and, in turn, dynamics. Furthermore, the following results emerge: (i) Both neighbourhood infection and long-distance infection are needed to generate the wave-like dispersal pattern of rabies; (ii) randomly walking rabid foxes are not sufficient to generate the wave pattern; and (iii) on a scale of less than 100 km x 100 km, temporal oscillations emerge that are independent from long-distance dispersal.
Full Text
The Full Text of this article is available as a PDF (1.0 MB).
Selected References
These references are in PubMed. This may not be the complete list of references from this article.
- Anderson R. M., Jackson H. C., May R. M., Smith A. M. Population dynamics of fox rabies in Europe. Nature. 1981 Feb 26;289(5800):765–771. doi: 10.1038/289765a0. [DOI] [PubMed] [Google Scholar]
- Källén A., Arcuri P., Murray J. D. A simple model for the spatial spread and control of rabies. J Theor Biol. 1985 Oct 7;116(3):377–393. doi: 10.1016/s0022-5193(85)80276-9. [DOI] [PubMed] [Google Scholar]
- Murray J. D., Stanley E. A., Brown D. L. On the spatial spread of rabies among foxes. Proc R Soc Lond B Biol Sci. 1986 Nov 22;229(1255):111–150. doi: 10.1098/rspb.1986.0078. [DOI] [PubMed] [Google Scholar]
- Okubo A., Maini P. K., Williamson M. H., Murray J. D. On the spatial spread of the grey squirrel in Britain. Proc R Soc Lond B Biol Sci. 1989 Nov 22;238(1291):113–125. doi: 10.1098/rspb.1989.0070. [DOI] [PubMed] [Google Scholar]
- SKELLAM J. G. Random dispersal in theoretical populations. Biometrika. 1951 Jun;38(1-2):196–218. [PubMed] [Google Scholar]
- Smith G. C., Harris S. Rabies in urban foxes (Vulpes vulpes) in Britain: the use of a spatial stochastic simulation model to examine the pattern of spread and evaluate the efficacy of different control régimes. Philos Trans R Soc Lond B Biol Sci. 1991 Dec 30;334(1271):459–479. doi: 10.1098/rstb.1991.0127. [DOI] [PubMed] [Google Scholar]
- Steck F., Wandeler A. The epidemiology of fox rabies in Europe. Epidemiol Rev. 1980;2:71–96. doi: 10.1093/oxfordjournals.epirev.a036227. [DOI] [PubMed] [Google Scholar]
- Toma B., Andral L. Epidemiology of fox rabies. Adv Virus Res. 1977;21:1–36. doi: 10.1016/s0065-3527(08)60760-5. [DOI] [PubMed] [Google Scholar]
- Wandeler A., Wachendörfer G., Förster U., Krekel H., Schale W., Müller J., Steck F. Rabies in wild carnivores in central Europe. I. Epidemiological studies. Zentralbl Veterinarmed B. 1974 Dec;21(10):735–756. [PubMed] [Google Scholar]