METHODS Vilis O. Nams Using animal movement paths to measure response to spatial scale Received: 6 May 2004 / Accepted: 8 December 2004 / Published online: 19 January 2005 Ó Springer-Verlag 2005 Abstract Animals live in an environment that is patchy and hierarchical. I present a method of detecting the scales at which animals perceive their world. The hierarchical nature of habitat causes movement path structure to vary with spatial scale, and the patchy nature of habitat causes movement path structure to vary throughout space. These responses can be mea- sured by a combination of path tortuousity (measured with fractal dimension) versus spatial scale, the vari- ation in tortuousity of small path segments along the movement path, and the correlation between tortu- ousities of adjacent path segments. These statistics were tested using simulated animal movements. When movement paths contained no spatial heterogeneity, then fractal D and variance continuously increased with scale, and correlation was zero at all scales. When movement paths contained spatial heterogene- ity, then fractal D sometimes showed a discontinuity at transitions between domains of scale, variation showed peaks at transitions, and correlations showed a statistically significant positive value at scales smaller than patch size, decreasing to below zero at scales greater than patch size. I illustrated these techniques with movement paths from deer mice and red-backed voles. These new analyses should help understand how animals perceive and react to their landscape structure at various spatial scales, and to answer questions about how habitat structure affects animal movement patterns. Keywords Fractal Æ Domain Æ Heterogeneity Æ Hierarchy Æ Tortuousity Introduction Animals live in an environment that is patchy and hierarchical—that is, there are patches within patches. Animals perceive and react to this structure at many different spatial scales, and each aspect of their biol- ogy (e.g. foraging behaviour (Fritz et al. 2003), dispersal patterns (Blums et al. 2003), animal orien- tation (Benhamou 1989), and population dynamics (Lewis and Murray 1993) relates to specific sections of this scale. Wiens (1989) called such sections ‘‘domains’’ and called the boundaries between them ‘‘transitions’’. There can be heterogeneity both along spatial scale and through space—domains refer to heterogeneity along spatial scale. For example, an animal may travel towards a certain place and forage for food on the way. There would be two domains: at the large scale the animal travels, and on the small scale the animal forages. In the large domain the movement pattern is homoge- neous, as the animal travels in a directed walk; in the small domain the movement pattern is heterogeneous, as the animal enters and leaves patches of food. Scale and pattern intertwine. In order to understand how animals perceive and react to their landscape structure, we need to detect the boundaries of these domains of scale (i.e. locations of transitions), and then study how the animals react to their landscape within each domain. Thus we need to address both spatial scale and spatial heterogeneity. Most current techniques of analysis of animal movement paths do not successfully incorporate both spatial scale and heterogeneity. For example, fractal analysis of movement paths (With 1994; Ma˚rell et al. 2002) has been used to study how animals respond to their environment at different spatial scales, but does not deal with the issue of spatial heterogeneity. On the other hand, modelling animal movements with state space models (Blackwell 1997; Jonsen et al. 2003) has repre- sented animals’ switching from one type of movement to V. O. Nams Department of Environmental Sciences, Nova Scotia Agricultural College, Box 550, Truro, Nova Scotia, B2N 5E3, Canada E-mail: vnams@nsac.ns.ca Fax: +1-902-8931404 Oecologia (2005) 143: 179–188 DOI 10.1007/s00442-004-1804-z