Scaling up population dynamics: integrating theory and data
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How to scale up from local-scale interactions to regional-scale dynamics is a critical issue in field ecology. We show how to implement a systematic approach to the problem of scaling up, using scale transition theory. Scale transition theory shows that dynamics on larger spatial scales differ from predictions based on the local dynamics alone because of an interaction between local-scale nonlinear dynamics and spatial variation in density or the environment. Based on this theory, a systematic approach to scaling up has four steps: (1) derive a model to translate the effects of local dynamics to the regional scale, and to identify key interactions between nonlinearity and spatial variation, (2) measure local-scale model parameters to determine nonlinearities at local scales, (3) measure spatial variation, and (4) combine nonlinearity and variation measures to obtain the scale transition. We illustrate the approach, with an example from benthic stream ecology of caddisflies living in riffles. By sampling from a simulated system, we show how collecting the appropriate data at local (riffle) scales to measure nonlinearities, combined with measures of spatial variation, leads to the correct inference for dynamics at the larger scale of the stream. The approach provides a way to investigate the mechanisms and consequences of changes in population dynamics with spatial scale using a relatively small amount of field data.
KeywordsHeterogeneity Nonlinear dynamics Scale Spatial ecology
We thank Kendi Davies, Göran Englund, Brian Inouye, and two anonymous reviewers for comments that improved the manuscript. B.A.M. was supported by an Australian Postgraduate Award and the National Science Foundation Biological Invasions IGERT program, NSF-DGE #0114432. P.C. was supported by NSF grant DEB-9981926. Computer code is available from B.A.M.
- Carroll RJ, Ruppert D, Stefanski LA (1995) Measurement Error in Nonlinear Models. Chapman & Hall, New YorkGoogle Scholar
- Chesson P (1996) Matters of scale in the dynamics of populations and communities. In: Floyd RB, Sheppard AW, De Barro PJ (eds) Frontiers of population ecology. CSIRO Publishing, Melbourne, pp 353–368Google Scholar
- Chesson P (1998a) Making sense of spatial models in ecology. In: Bascompte J, Solé RV (eds) Modeling spatiotemporal dynamics in ecology. Landes Bioscience, Austin, pp 151–166Google Scholar
- Chesson P (2001) Metapopulations. In: Levin SA (ed) Encyclopedia of biodiversity, Volume 4. Academic, San Diego, pp 161–176Google Scholar
- Chesson P, Donahue MJ, Melbourne BA, Sears AL (2005) Scale transition theory for understanding mechanisms in metacommunities. In: Holyoak M, Leibold MA, Holt RD (eds) Metacommunities: Spatial dynamics and ecological communities. University of Chicago Press, ChicagoGoogle Scholar
- Feller W (1971) An introduction to probability theory and its applications. Vol. 2, Second edn. Wiley, New YorkGoogle Scholar
- Hanski I, Simberloff D (1997) The metapopulation approach, its history, conceptual domain, and application to conservation. In: Hanski I, Gilpin ME (eds) Metapopulation biology: ecology, genetics, and evolution. Academic, San Diego, pp 5–26Google Scholar
- Hilborn R, Mangel M (1997) The ecological detective: confronting models with data. Princeton University Press, Princeton, New JerseyGoogle Scholar
- Melbourne BA, Sears AL, Donahue MJ, Chesson P (2005) Applying scale transition theory to metacommunities in the field. In: Holyoak M, Leibold MA, Holt RD (eds) Metacommunities: spatial dynamics and ecological communities. University of Chicago Press, ChicagoGoogle Scholar
- Pacala SW, Levin SA (1997) Biologically generated spatial pattern and the coexistence of competing species. In: Tilman D, Kareiva P (eds) Spatial ecology: the role of space in population dynamics and interspecific interactions. Princeton University Press, Princeton, New Jersey, pp 204–232Google Scholar
- Searle SR, Casella G, McCulloch CE (1992) Variance components. John Wiley and Sons, New YorkGoogle Scholar