Skip to main content Accessibility help
×
Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-22T12:07:47.959Z Has data issue: false hasContentIssue false

20 - Survival of species in patchy landscapes: percolation in space and time

Published online by Cambridge University Press:  05 August 2012

Beáta Oborny
Affiliation:
Loránd Eötvös University, Budapest
György Szabó
Affiliation:
Research Institute for Technical Physics and Materials Science, Budapest
Géza Meszéna
Affiliation:
Loránd Eötvös University, Budapest
David Storch
Affiliation:
Charles University, Prague
Pablo Marquet
Affiliation:
Pontificia Universidad Catolica de Chile
James Brown
Affiliation:
University of New Mexico
Get access

Summary

Introduction

This chapter is about some basic geometric considerations and scaling laws in the spatial structure of habitats and (meta)populations.

Conservation of a valuable species, or conversely, eradication of an invasive species can be significantly helped by mapping its potential habitats. It is not easy, however, to measure the value of a habitat patch for a population or subpopulation. Not only the quality, but also the size and shape of the patch can influence birth, death, migration or dispersal (Forman, 1995; Wiens, 1997; chapter 8 in Turner, Gardner & O'Neill, 2001). The wider context, patch-to-patch neighborhood is another matter of consideration, because it can directly influence the movement of individuals (cf. borderline penetrability; Wiens, 1997) or survival and reproduction (cf. edge effects, ecotone effects; chapter 3 in Forman, 1995; Milne et al., 1996; Harrison & Bruna, 1999). Spatial patterns on larger, regional scales are not negligible either. For example, habitat fragmentation is often a serious threat to survival (Fahrig, 2003). Many species require multiple patch types for completing the life cycle, or performing different activities (e.g. feeding and breeding). In this case, the proximity of different patch types in the patchwork also matters. Finally, the patches are rarely constant: they can shrink, expand, or shift; new patches can appear and old ones disappear. The changes can seriously challenge survival (Keymer et al., 2000; see also Wiens, 1997 about habitat tracking).

Type
Chapter
Information
Scaling Biodiversity , pp. 409 - 440
Publisher: Cambridge University Press
Print publication year: 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Addicott, J. F., Aho, J. M., Antolin, M. F., Padilla, D. L., Richardson, J. S. & Soluk, D. A. (1987). Ecological neighborhoods: scaling environmental patterns. Oikos, 49(3), 340–346.CrossRefGoogle Scholar
Allee, W. C. (1931). Animal Aggregations: a Study in General Sociology. Chicago: University of Chicago Press.CrossRefGoogle Scholar
Anderson, R. M. & May, R. M. (1991). Infectious Diseases and Control. Oxford: Oxford University Press.Google Scholar
Andrén, H. (1994). Effect of habitat fragmentation on birds and mammals in landscapes with different proportion of suitable habitat: a review. Oikos, 71, 355–366.CrossRefGoogle Scholar
Barkham, J. P. & Hance, C. E. (1982). Population dynamics of the wild daffodil (Narcissus pseudonarcissus). Journal of Ecology, 70, 323–344.CrossRefGoogle Scholar
Bell, A. D. (1984). Dynamic morphology: a contribution to plant population ecology. In Perspectives on Plant Population Ecology, ed. Dirzo, R. & Sarukan, J.. Sunderland, MA: Sinauer Associates.Google Scholar
Broadabent, S. R. & Hammersley, J. M. (1957). Percolation processes. I. Crystals and mazes. Proceedings of the Cambridge Philosophical Society, 53, 629–645.CrossRefGoogle Scholar
Crawley, M. J. & May, R. M. (1987). Population dynamics and plant community structure: competition between annuals and perennials. Journal of Theoretical Biology, 125, 475–489.CrossRefGoogle Scholar
Crowley, P. H., Davis, H. M., Ensminger, A., Fuselier, L. C., Jackson, J. K. & McLetchie, D. N. (2005). A linear model of local competition for space. Ecology Letters, 8(2), 176–188.CrossRefGoogle Scholar
Deutscher, G., Zallen, R. & Adler, J. (1983). Percolation Structures and Processes.Bristol: Adam Hilger.Google Scholar
Dickman, R. & Moreira, A. G. (1998). Violation of scaling in the contact process with quenched disorder. Physical Reviews, E 57, 1263–1268.CrossRefGoogle Scholar
Dieckmann, U., Law, R. & Metz, J. A. J. (2000). The Geometry of Ecological Interactions. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Durrett, R. & Levin, S. A. (1994). Stochastic spatial models: a user's guide to ecological applications. Philosophical Transactions of the Royal Society of London, Series B, 343, 329–350.CrossRefGoogle Scholar
Fahrig, L. (2003). Effects of habitat fragmentation on biodiversity. Annual Reviews of Ecology, Evolution and Systematics, 34, 487–515.CrossRefGoogle Scholar
Forman, R. T. T. (1995). Land Mosaics: The Ecology of Landscapes and Regions. Cambridge: Cambridge University Press.Google Scholar
Franc, A. (2004). Metapopulation dynamics as a contact process on a graph. Ecological Complexity, 1, 49–63.CrossRefGoogle Scholar
Gardner, R. H., Milne, B. T., Turner, M. G. & O'Neill, R. V. (1987). Natural models for the analysis of broad-scale landscape pattern. Landscape Ecology, 1, 19–28.CrossRefGoogle Scholar
Gustafson, E. J. & Parker, G. R. (1992). Relationships between landcover proportions and indices of landscape spatial pattern. Landscape Ecology, 7, 101–110.CrossRefGoogle Scholar
Hanski, I. (1994). A practical model of metapopulation dynamics. Journal of Animal Ecology, 63, 151–162.CrossRefGoogle Scholar
Hanski, I. (1997). Metapopulation dynamics: from concepts and observations to predictive models. In Metapoplulation Biology: Ecology, Genetics and Evolution, ed. Hanski, I. & Gilpin, M. E., pp. 69–92. London: Academic Press.Google Scholar
Hanski, I. (1999). Metapopulation Ecology. Oxford: Oxford University Press.Google Scholar
Hanski, I. & Simberloff, D. (1997). The metapopulation approach, its history, conceptual domain, and application to conservation. In Metapopulation Biology: Ecology, Genetics and Evolution, ed. Hanski, I. & Gilpin, M. E., pp. 5–26. London: Academic Press.Google Scholar
Harris, T. E. (1974). Contact interactions on a lattice. Annals of Probability, 2, 969–988.CrossRefGoogle Scholar
Harrison, S. & Bruna, E. (1999). Habitat fragmentation and large-scale conservation: what do we know for sure?Ecography, 22, 225–232.CrossRefGoogle Scholar
He, F. & Hubbell, S. P. (2003). Percolation theory for the distribution and abundance of species. Physical Review Letters, 91(19), 198103 /1–4.CrossRefGoogle ScholarPubMed
Henkel, M. & Hinrichsen, H. (2004). The non-equilibrium phase transition of the pair-contact process with diffusion. Journal of Physics A, 37, R117–R159.CrossRefGoogle Scholar
Herben, T. (1996). Founder and dominance control: neglected concepts in the community dynamics of clonal plants. In Clonality in Plant Communities, ed. Oborny, B. & Podani, J., pp. 3–11. Grangärde: Opulus Press.Google Scholar
Hinrichsen, H. (2000a). Non-equilibrium critical phenomena and phase transitions into absorbing states. Advances in Physics, 49, 815–958.CrossRefGoogle Scholar
Hinrichsen, H. (2000b). On possible experimental realizations of directed percolation. Brazilian Journal of Physics, 30(1), 69–82.CrossRefGoogle Scholar
Holmes, E. (1997). Basic epidemiological concepts in a spatial context. In Spatial Ecology: the Role of Space in Population Dynamics and Interspecific Interactions, ed. Tilman, D. & Kareiva, P., pp. 111–136. Monographs in Population Biology, 30. Princeton: Princeton University Press.Google Scholar
Holt, R. D. & Keitt, T. H. (2000). Alternative causes for range limits: a metapopulation perspective. Ecology Letters, 3, 41–47.CrossRefGoogle Scholar
Itoh, Y., Tainaka, K.-I., Sakata, T., Tao, T. & Nakagiri, N. (2004). Spatial enhancement of population uncertainty near the extinction threshold. Ecological Modeling, 174, 191–201.CrossRefGoogle Scholar
Janssen, H. K. (1997). On the nonequilibrium phase transition in reaction-diffusion systems with absorbing stationary state. Zeitschrift für Physik B, 42, 151–154.CrossRefGoogle Scholar
Juhász-Nagy, P. (1992). Scaling problems almost everywhere: an introduction. Abstracta Botanica, 16, 1–5.Google Scholar
Keymer, J. E., Marquet, P. A. & Johnson, A. R. (1998). Pattern formation in a patch occupancy metapopulation model: a cellular automata approach. Journal of Theoretical Biology, 194, 79–90.CrossRefGoogle Scholar
Keymer, J. E., Marquet, P. A., Velasco-Hernandez, J. X. & Levin, S. A. (2000). Extinction thresholds and metapopulation persistence in dynamic landscapes. American Naturalist, 156, 478–494.CrossRefGoogle ScholarPubMed
Lande, R., Engen, S. & Saether, B.-E. (1998). Extinction times in finite metapopulation models with stochastic local dynamics. Oikos, 83, 383–389.CrossRefGoogle Scholar
Levin, S. A. & Durrett, R. (1996). From individuals to epidemics. Philosophical Transactions of the Royal Society of London, Series B, 351(1347), 1615–1621.CrossRefGoogle ScholarPubMed
Levin, S. A. & Pacala, S. W. (1997). Theories of simplification and scaling in spatially distributed processes. In Spatial Ecology: the Role of Space in Population Dynamics and Interspecific Interactions, ed. Tilman, D. & Kareiva, P., pp. 271–295. Monographs in Population Biology, 30. Princeton: Princeton University Press.Google Scholar
Levins, R. (1969). Some demographic and genetic consequences of environmental heterogeneity for biological control. Bulletin of the Entomological Society of America, 15, 237–240.CrossRefGoogle Scholar
Li, B.-L. (2002). A theoretical framework of ecological phase transitions for characterizing tree-grassland dynamics. Acta Biotheoretica, 50, 141–154.CrossRefGoogle Scholar
MacArthur, R. H. & Wilson, E. O. (1967). The Theory of Island Biogeography. Princeton: Princeton University Press.Google Scholar
Mágori, K., Szabó, P., Mizera, F. & Meszéna, G. (2005). Adaptive dynamics on a lattice: role of spatiality in competition, co-existence and evolutionary branching. Evolutionary Ecology Research, 7, 1–21.Google Scholar
Marro, J. & Dickman, R. (1999). Nonequilibrium Phase Transitions in Lattice Models. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
Milne, B. T. (1998). Motivation and benefits of complex systems approaches in ecology. Ecosystems, 1, 449–456.CrossRefGoogle Scholar
Milne, B. T., Keitt, T. H., Hatfield, C. A., David, J. & Hraber, P. T. (1996). Detection of critical densities associated with pinion-juniper woodland ecotones. Ecology, 77, 805–821.CrossRefGoogle Scholar
Nee, S. & May, R. M. (1992). Dynamics of metapopulations – habitat destruction and competitive coexistence. Journal of Animal Ecology, 61, 37–40.CrossRefGoogle Scholar
Newman, M. E. J. & Watts, D. J. (1999). Scaling and percolation in a small-world network model. Physical Reviews E, 60, 7332–7342.CrossRefGoogle Scholar
Noest, A. J. (1986). New universality for spatially disordered cellular automata and directed percolation. Physical Review Letters, 57, 90–93.CrossRefGoogle ScholarPubMed
Oborny, B., Meszéna, G. & Szabó, G. (2005). Dynamics of populations on the verge of extinction. Oikos, 109, 291–296.Google Scholar
Ovaskainen, O., Kazunori, S., Bascompte, J. & Hanski, I. (2002). Metapopulation models for extinction thresholds in spatially correlated landscapes. Journal of Theoretical Biology, 215, 95–108.CrossRefGoogle Scholar
Plotnick, R. & Gardner, R. (1993). Lattices and landscapes. Lectures on Mathematics in the Life Sciences, 23, 129–156.Google Scholar
Potter, M. A. (1990). Movement of North Island brown kiwi (Apteryx australis Manelli) between forest remnants. New Zealand Journal of Ecology, 14, 17–24.Google Scholar
Primack, R. B. (1998). Essentials of Conservation Biology. Sunderland, MA: Sinauer Associates.Google Scholar
Salzman, A. G. (1985). Habitat selection in a clonal plant. Science, 228, 603–604.CrossRefGoogle Scholar
Snyder, R. E. & Nisbet, R. M. (2000). Spatial structure and fluctuations in the contact process and related models. Bulletin of Mathematical Biology, 62, 959–975.CrossRefGoogle ScholarPubMed
Stanley, H. E. (1971). Introduction to Phase Transitions and Critical Phenomena. Oxford: Clarendon Press.Google Scholar
Stanley, H. E., Amaral, L. A. N., Gopikrishnan, P., Ivanov, P. C., Keitt, T. H. & Plerou, V. (2000). Scale invariance and universality: organizing principles in complex systems. Physica A, 281, 60–68.CrossRefGoogle Scholar
Stauffer, D. (1979). Scaling theory of percolation clusters. Physical Reports, 54, 1–74.CrossRefGoogle Scholar
Stauffer, D. & Aharony, A. (1992). Introduction to Percolation Theory. London: Taylor & Francis.Google Scholar
Stephens, P. A. & Sutherland, W. J. (1999). Consequences of the Allee effect for behavior, ecology, and conservation. Trends in Ecology and Evolution, 14(10), 401–404.CrossRefGoogle ScholarPubMed
Szabó, G., Gergely, H. & Oborny, B. (2002). Generalized contact process on random environments. Physical Reviews E, 65, 066111.CrossRefGoogle ScholarPubMed
Tilman, D. (1994). Competition and biodiversity in spatially structured habitats. Ecology, 75(1), 2–16.CrossRefGoogle Scholar
Tilman, D. & Kareiva, P. (eds.) (1997). Spatial Ecology: the Role of Space in Population Dynamics and Interspecific Interactions. Princeton: Princeton University Press.Google Scholar
Tilman, D., May, R. M., Lehman, C. L. & Nowak, M. A. (1994). Habitat destruction and the extinction debt. Nature, 371, 65–66.CrossRefGoogle Scholar
Turner, M., Gardner, R. H. & O'Neill, R. V. (2001). Landscape Ecology in Theory and Practice: Pattern and Process. New York: Springer-Verlag.Google Scholar
Wiens, J. A. (1989). Spatial scaling in ecology. Functional Ecology, 3, 385–397.CrossRefGoogle Scholar
Wiens, J. A. (1997). Metapopulation dynamics and landscape ecology. In Metapopulation Biology: Ecology, Genetics and Evolution, ed. Hanski, I. & Gilpin, M. E., pp. 3–68. London: Academic Press.Google Scholar
With, K. A., Gardner, R. H. & Turner, M. G. (1997). Landscape connectivity and population distribution in heterogeneous environments. Oikos, 78, 151–169.CrossRefGoogle Scholar
Yu, D. W. & Wilson, H. B. (2001). The competition-colonization trade-off is dead; long live the competition-colonization trade-off. American Naturalist, 158(1), 49–63.Google ScholarPubMed
Zobel, M., Palmer, M. W., Kull, K. & Herben, T. (eds.) (1994). Vegetation Structure and Species Coexistence. Uppsala: Opulus Press.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×