ARTICLE IN PRESS ZOOLOGY Zoology 107 (2004) 3–11 www.elsevier-deutschland.de/zool Fractal analysis of narwhal space use patterns Kristin L. Laidrea,*, Mads P. Heide-J^rgensenb, Miles L. Logsdonc, Roderick C. Hobbsd, Rune Dietze, Glenn R. VanBlaricoma a Washington Cooperative Fish and Wildlife Research Unit, School of Aquatic and Fishery Sciences, University of Washington, Box 355020, Seattle, WA 98195, USA b Greenland Institute of Natural Resources, Box 570, DK-3900 Nuuk, Greenland c School of Oceanography, College of Ocean and Fishery Sciences, University of Washington, Box 355351, Seattle, WA 98195, USA d National Marine Mammal Laboratory, AFSC, 7600 Sand Point Way NE, Seattle, WA 98115, USA e Department of Arctic Environment, National Environmental Research Institute, Frederiksborgvej 399, Box 358, DK-4000 Roskilde, Denmark Received 25 April 2003; received in revised form 26 September 2003; accepted 29 September 2003 Abstract Quantifying animal movement in response to a spatially and temporally heterogeneous environment is critical to understanding the structural and functional landscape influences on population viability. Generalities of landscape structure can easily be extended to the marine environment, as marine predators inhabit a patchy, dynamic system, which influences animal choice and behavior. An innovative use of the fractal measure of complexity, indexing the linearity of movement paths over replicate temporal scales, was applied to satellite tracking data collected from narwhals (Monodon monoceros)(n ¼ 20) in West Greenland and the eastern Canadian high Arctic. Daily movements of individuals were obtained using polar orbiting satellites via the ARGOS data location and collection system. Geographic positions were filtered to obtain a daily good quality position for each whale. The length of total pathway was measured over seven different temporal length scales (step lengths), ranging from one day to one week, and a seasonal mean was calculated. Fractal dimension (D) was significantly different between seasons, highest during summer (D ¼ 1:61; SE 0.04) and winter (D ¼ 1:69; SE 0.06) when whales made convoluted movements in focal areas. Fractal dimension was lowest during fall (D ¼ 1:34; SE 0.03) when whales were migrating south ahead of the forming sea ice. There were no significant effects of size category or sex on fractal dimension by season. The greater linearity of movement during the migration period suggests individuals do not intensively forage on patchy resources until they arrive at summer or winter sites. The highly convoluted movements observed during summer and winter suggest foraging or searching efforts in localized areas. Significant differences between the fractal dimensions on two separate wintering grounds in Baffin Bay suggest differential movement patterns in response to the dynamics of sea ice. r 2004 Elsevier GmbH. All rights reserved. Keywords: Animal movement; Arctic; Fractal; Narwhal; Satellite tracking Introduction *Corresponding author. Present address: Alaska Fisheries Science In predictably changing habitats, animals often Center, National Marine Mammal Laboratory, 7600 Sand Point Way alternate space use patterns in a predictable way. For NE, Seattle, WA 98115, USA. E-mail address: [email protected] (K.L. Laidre). habitat changes on a seasonal scale, responses often 0944-2006/$ - see front matter r 2004 Elsevier GmbH. All rights reserved. doi:10.1016/j.zool.2003.09.001 ARTICLE IN PRESS 4 K.L. Laidre et al. / Zoology 107 (2004) 3–11 include switching between localized resource utilization path using a scale-independent measure of movement. and large-scale movements driven by migration. Beha- The index of fractal dimension ranges from D ¼ 1ifan vioral changes resulting in differential movement animal is moving along a perfectly linear path to D ¼ 2 patterns have been suggested as an effort to control if movement is extremely convoluted and essentially all environmental heterogeneity and create more stable life points in two-dimensional space are visited (analogous history responses to external perturbations (Ferguson to ‘‘Brownian-like’’ or random walk paths) (Wiens et al., et al., 1998a). 1995). Fractal dimensions lie somewhere between these The narwhal (Monodon monoceros) is a high Arctic two extremes, with values for insects generally o1.5 and cetacean species whose annual movement patterns are values for large mammals generally >1.5 (Ferguson strongly influenced by predictable seasonal changes in et al., 1998b). their environment. Narwhals have high site fidelity to Recent advances in satellite tracking technology and summering and wintering grounds, yet their movements the miniaturization of transmitters have enabled the are also influenced by the spatial pattern of sea ice acting collection of large amounts of movement data from as a structuring agent. Narwhals spend the summer in species inhabiting remote or inaccessible environments. the sheltered bays and fjords of the Canadian Arctic In the case of marine predators such as the narwhal, archipelago and West Greenland. They migrate south in extending landscape-based pattern metrics to the marine the fall before sea ice forms and spend the winter in environment can identify important foraging zones, Baffin Bay and North Davis Strait in restricted areas potentially even elucidating areas with unique or covered by dense offshore pack ice. In spring they return important oceanography. This study applied concepts to summering grounds following the receding sea ice of fractal geometry to quantify space–time related edge. The annual round trip distance of the migration is differences in the linearity of seasonal movement up to three thousand kilometers (Heide-J^rgensen et al., patterns of narwhals. Differences in sub-population 2002a). Detailed seasonal movement patterns of nar- specific movements were investigated across seasons and whals have been described for three separate sub- discussed in the context of causal factors or potential populations thought to be isolated based on satellite environmental heterogeneity encountered in the high tracking and genetic studies (Dietz and Heide- Arctic. J^rgensen, 1995; Dietz et al., 2001; Heide-J^rgensen et al., 2002a). These sub-populations occupy two different wintering grounds in the Baffin Bay/Davis Strait area (Heide-J^rgensen et al., 2002a, 2003), where Materials and methods they show population-specific dive behavior and fora- ging preference (Laidre et al., 2003). There is a high Location data degree of spatial and temporal variability in Arctic marine habitats. Changes in climate, coupled with Satellite location data were collected from three extreme seasonality in sea ice, influence primary and narwhal sub-populations in the eastern Canadian high secondary production processes and ultimately the Arctic and West Greenland. Studies were conducted in distribution and abundance of top predators (Ferguson Melville Bay, West Greenland in August 1993–1994 and Messier, 1996; Parkinson, 2000a, b; Mauritzen et al., (Dietz and Heide-J^rgensen, 1995; Heide-J^rgensen and 2001; Root et al., 2003). In the case of Arctic cetaceans, Dietz, 1995), in Tremblay Sound, Baffin Island, Canada the long-term effects of this variation are unknown both in August 1997–1999 (Dietz et al., 2001; Heide- on local and global scales (Tynan and DeMaster, 1997). J^rgensen et al., 2002a), and in Creswell Bay, Somerset A first step in understanding this link lies in quantita- Island, Canada in August 2000 (Heide-J^rgensen et al., tively describing cetacean behavioral patterns and 2003)(Fig. 1). Narwhals were captured using nets set relating them to environmental heterogeneity in the perpendicular to the shoreline (details on capturing and context of seasonal changes. handling described in Dietz et al., 2001; Dietz and A relatively new approach for assessing animal Heide-J^rgensen, 1995; Heide-J^rgensen et al., 2002a). movement involves calculating the fractal dimension of Two types of tags were used: Telonics (Mesa, AZ) and paths, which describes variation in animal movement at Seimac (Canada) satellite-linked time depth recorders a range of spatial scales across time (Mandelbrot, 1983; with approximately 0.5 W power output, programmed Milne, 1991; Turchin, 1998). Fractals have been linked and cast in epoxy by Wildlife Computers (Redmond, to animal movement and terrestrial landscape structure WA). Transmitters were attached to female whales on for a wide range of species, from invertebrates (Crist the dorsal ridge with two or three 5–8 mm polyethylene et al., 1992; With, 1994; Wiens et al., 1995) to large pins. Transmitters were attached to the tusk of males mammals (Bascompte and Vila," 1997; Ferguson et al., using two stainless-steel bands (Seimac SSC3 or the 1998a, b, Mouillot and Viale, 2001). The fractal dimen- Telonics ST-6 transmitter unit programmed and cast by sion (D) indexes the overall complexity of a movement Wildlife Computers). Whale movements were obtained ARTICLE IN PRESS K.L. Laidre et al. / Zoology 107 (2004) 3–11 5 Fig. 1. Movement paths of 20 narwhals obtained from satellite tracking studies at three summering localities (Creswell Bay, Tremblay Sound, and Melville Bay) in the eastern Canadian high Arctic and West Greenland. using the ARGOS Data Location and Collection System The time series of data for each whale were divided (Harris et al., 1990). Tags transmitted ultra-high into three seasons: summer period (tagging date to frequency messages, which were received by National September 15), migration