The VFractal: a new estimator for fractal dimension of animal movement paths (original) (raw)
Abstract
Fractal measurements of animal movement paths have been used to analyze how animals view habitats at different spatial scales. One problem has been the absence of error estimates for fractal d estimators. To address this weakness, I present and test 4 new estimators for measuring fractal dimension at different spatial scales, along with estimates of their variation. The estimators are based on dividing the movement path into pairs of steps, forming V's, and then estimating various statistics from each V.
I measured the performance of these estimators by comparing them to the traditional divider d method, using data generated by two different animal movement models. The estimator based on the net distance between the two steps and the cos turning angle was most accurate, giving estimates similar to those of the traditionally-used divider d method. Precision increased with longer and straighter paths.
Strengths of this new estimator are that it can estimate fractal d at different spatial scales, give an estimate of variation, and combine data from many separate path segments which have been gathered at various spatial scales.
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References
- Benhamou, S. 1990. An analysis of movements of the wood mouse_Apodemus sylvaticus_ in its home range. Behavioural Processes 22: 235–250.
Google Scholar - Boonstra, R. and Craine, I.T.M. 1986. Natal nest location and small mammal tracking with a spool and line technique. Canadian Journal of Zoology 64: 1034–1036.
Google Scholar - Crist, T.O., Guertin, D.S., Wiens, J.A. and Milne, B.T. 1992. Animal movement in heterogeneous landscapes: an experiment with_Eleodes_ beetles in shortgrass prairie. Functional Ecology 6: 536–544.
Google Scholar - Dicke, M. and Burrough, P.A. 1988. Using fractal dimensions for characterizing the tortuosity of animal trails. Physiological Entomology 13: 393–398.
Google Scholar - Efron, B. and Tibshirani, R. 1991. Statistical data analysis in the computer age. Science 253: 390–395.
Google Scholar - Goodyear, N.C. 1989. Studying fine-scale habitat use in small mammals. Journal of Wildlife Management 53: 941–946.
Google Scholar - Kotliar, N.B. and Wiens, J.A. 1990. Multiple scales of patchiness and patch structure: a hierarchical framework for the study of heterogeneity. Oikos 59: 253–260.
Google Scholar - Krummer, J.R., Gardner, R.H., Sugihara, G., O'Neill, R.V. and Coleman, P.R. 1987. Landscape patterns in a disturbed environment. Oikos 48: 321–324.
Google Scholar - Lemen, C.A. and Freeman, P.W. 1985. Tracking mammals with fluorescent pigments: a new technique. Journal of Mammalogy 66: 134–136.
Google Scholar - Mandelbrot, B. 1967. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156: 636–638.
Google Scholar - Milne, B.T. 1991. Lessons from applying fractal models to landscape patterns.In Quantitative Methods in Landscape Ecology, pp. 199–235. Edited by M.G. Turner and R.H. Gardner. Springer, New York.
Google Scholar - Sherry, T.W. and Holmes, R.T. 1988. Habitat selection by breeding American Redstarts in response to a dominant competitor, the Least Flycatcher. The Auk 105: 350–364.
Google Scholar - Sugihara, G. and May, R.M. 1990. Applications of fractals in ecology. Trends in Ecology and Evolution 5: 79–86.
Google Scholar - Wiens, J.A., Crist, T.O. and Milne, B.T. 1993. On quantifying insect movements. Environmental Entomology 22: 709–715.
Google Scholar - With, K.A. 1994a. Ontogenetic shifts in how grasshoppers interact with landscape structure: an analysis of movement patterns. Functional Ecology 8: 477–485.
Google Scholar - With, K.A. 1994b. Using fractal analysis to assess how species perceive landscape structure. Landscape Ecology 9: 25–36.
Google Scholar - Zhang, Z. and Sanderson, J.P. 1993. Spatial scale of aggregation in three acarine predator species with different degrees of polyphagy. Oecologie (Berl.) 96: 24–31.
Google Scholar
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Authors and Affiliations
- Department of Biology, NSAC, Box 550, B2N 5E3, Truro, Nova Scotia, Canada
Vilis O. Nams
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Nams, V.O. The VFractal: a new estimator for fractal dimension of animal movement paths.Landscape Ecol 11, 289–297 (1996). https://doi.org/10.1007/BF02059856
- Issue date: October 1996
- DOI: https://doi.org/10.1007/BF02059856