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Keywords:

  • blacktip reef sharks;
  • cognitive maps;
  • correlated random walks;
  • fractal analysis;
  • learning;
  • patch use;
  • thresher sharks;
  • tiger sharks

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

1. Animal search patterns reflect sensory perception ranges combined with memory and knowledge of the surrounding environment.

2. Random walks are used when the locations of resources are unknown, whereas directed walks should be optimal when the location of favourable habitats is known. However, directed walks have been quantified for very few species.

3. We re-analysed tracking data from three shark species to determine whether they were using directed walks, and if so, over which spatial scales. Fractal analysis was used to quantify how movement structure varied with spatial scale and determine whether the sharks were using patches.

4. Tiger sharks performed directed walks at large spatial scales (at least 6–8 km). Thresher sharks also showed directed movement (at scales of 400–1900 m), and adult threshers were able to orient at greater scales than juveniles, which may suggest that learning improves the ability to perform directed walks. Blacktip reef sharks had small home ranges, high site fidelity and showed no evidence of oriented movements at large scales.

5. There were inter- and intraspecific differences in path structure and patch size, although most individuals showed scale-dependent movements. Furthermore, some individuals of each species performed movements similar to a correlated random walk.

6. Sharks can perform directed walks over large spatial scales, with scales of movements reflecting site fidelity and home range size. Understanding when and where directed walks occur is crucial for developing more accurate population-level dispersal models.


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

To maximize lifetime fitness, animals should optimize search patterns for locating resource patches (defined as an area with an increased concentration of resources such as prey, safety from predators or potential mates). In new and unfamiliar locations or areas where patches are outside the sensory range of the animal, some form of random walk must be performed. Lévy flights (a random walk where move step length is drawn from a probability distribution with a power-law tail) are believed to be the most efficient strategy for locating resources when prey is sparse (e.g. Sims et al. 2008; Reynolds & Rhodes 2009; Humphries et al. 2010). In areas where prey is abundant, Brownian motion or various forms of correlated random walks (CRW, where movements are random but there is a correlation between movement steps) are thought to be more effective search strategies (Zollner & Lima 1999; Reynolds & Rhodes 2009; Humphries et al. 2010). However, many animals occupy well-defined home ranges where they may utilize cognitive maps to locate resources. In such circumstances, using a directed walk [where the animal moves towards a known goal (Nams 2006a)] to navigate between known locations should reduce search time and consequently conserve energy required to find key resources (Nams 2006a; Brooks & Harris 2008), yet few studies have quantified directed walks in animals (Girard, Benhamou & Dagorn 2004; Benhamou 2006; Brooks & Harris 2008). Determining when animals use directed walks, and over which spatial scales, will improve our understanding of population dispersal patterns (e.g. Armsworth & Roughgarden 2005; Benhamou 2006).

Although many animals use straight movement paths, (Klimley 1993; Zollner & Lima 1999; Brooks & Harris 2008) not all such paths result from a directed walk. Highly CRW lead to relatively straight movement paths over short time periods, and computer simulations suggest these straighter paths may be more effective than less straight random walks, for finding heterogeneously distributed patches (Zollner & Lima 1999). It is not sufficient to consider a straight path directed and a tortuous path random, as movement walks can be also be directed and tortuous (for example, an animal moving towards a known goal may have to move around various environmental features that are obstructing its desired passage, Nams 2006a). Determining whether an animal is moving using a directed walk is difficult, as we cannot know specifically what the animals goals or desired destinations were (with some exceptions, e.g. homing studies). However, true directed walks may be distinguished from un-oriented movements by the scale at which movement mechanisms operate. An animal moving using an un-oriented walk will only make movement decisions at small spatial scales. The individual may orient to features (e.g. prey) that are within its immediate sensory perception range, but at larger scales the movements become a CRW. True directed walks will utilize movement mechanisms that operate at large spatial scales. At these larger scales, directed walks will produce movement paths with greater displacement than a CRW (Nams 2006a). Based on these differences, a scaling test for orientation was developed by Nams (2006a). Some animals also perform biased correlated random walks (BCRW), where they move using a CRW but in a preferred direction (Benhamou 2006). However, if the BCRW is biased over a large scale (the animal consistently turns towards a certain direction), then these essentially become directed movements.

Animals often vary their movement structure at different spatial scales (e.g. Nams 2005; Papastamatiou et al. 2009). When an animal reaches a patch, it is predicted that it will decrease rates of movement and frequently change direction so that it remains within the patch (area restricted searching), whereas high-speed directed movements would be expected when moving between patches (Benhamou 1992). Therefore, movement path structure would be expected to vary when moving within vs. between patches. In fact, movements may be random or directed at the scale of patch use, but the opposite at larger spatial scales (e.g. Benhamou 1990; Nams 2005; Papastamatiou et al. 2009). An understanding of the size of patches used, and how movement structure varies within vs. between patches, is needed to explain overall patterns of movement and dispersal (e.g. Doerr & Doerr 2004).

Several species of shark have been shown to swim with straight movement paths, with some species migrating to specific locations many 100’s to 1000’s of kilometres away (e.g. Carey & Scharold 1990; Klimley 1993; Weng et al. 2007; Meyer, Papastamatiou, & Holland 2010). Shark species vary greatly in size and in the size of their home ranges, from reef-associated species with small home ranges (several square kilometres) to larger coastal/pelagic species that have home ranges that include island chains or ocean basins (e.g. Heupel et al. 2006; Weng et al. 2007; Papastamatiou et al. 2009; Meyer, Papastamatiou & Holland 2010). With impressive sensory abilities, it is likely that sharks are able to orient to features great distances away, but to date no studies have quantified directed walks or the scales of orientation. For example, do sharks reach favoured habitats by using some form of random walk, or do they orient to habitats and swim there using a directed walk? We utilized Nams (2006a) scale of orientation test to re-analyse active tracking data from three species of shark. Our goals were to determine whether (i) sharks were performing directed walks and the scales of orientation, (ii) individuals utilized directed walks at all spatial scales and (iii) an individual’s movements were at times confined to patches.

Materials and methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Study sites and animals

All data were obtained from previous active tracking of three shark species. Briefly, a high-frequency acoustic transmitter was attached to a shark, and the animal was tracked continuously for 7–72 h from a boat or kayak using a directional hydrophone. GPS location data were taken at time intervals of 3–15 min (although sampling intervals were consistent within studies). Data were for tiger sharks (Galeocerdo cuvier, n = 8) tracked off the south shore of Oahu, Hawaii (Holland et al. 1999), adult (n = 8) and juvenile (n = 7) common thresher sharks (Alopias vulpinus) tracked in the Southern California Bight (Cartamil et al. 2010a,b) and blacktip reef sharks (Carcharhinus melanopterus, n = 9) tracked in the lagoons of Palmyra Atoll, Central Pacific Ocean (Papastamatiou et al. 2009). Only tracks of animals that were followed continuously for at least 7 h were utilized. Acoustic transmitters used during thresher shark tracking also measured ambient water temperature, so we could quantify any relationships between water column temperature and tortuosity.

Correlated random walk (CRW) and orientation test

In its simplest form, an animal moving with a CRW will follow θi = θi−1 + ɛi, where θi is the direction of step i and ɛi is a random angle drawn from a normal distribution. Therefore, turning angles are independent of previous turning angles, although there will be some directional bias. To determine whether sharks were moving using a CRW, the CRWDiff statistic described by Nams (2006a) was utilized, where

  • image

where inline image represents the observed mean (net distance)2 for each number of n consecutive moves, E is the expected mean (net distance)2 according to the CRW model described by Kareiva & Shigesada (1983), l is the mean step length and k is the turning angle concentration. If CRWDiff > 0, then net displacement is greater than predicted by a CRW, while CRWDiff < 0 suggests that movements are more constrained than the CRW. CRWDiff compares observed net displacement against the predictions of the CRW model over a range of movement steps within a single path, providing a single overall estimate. We ran CRWDiff at both the species level (where each individual in a species group is a replicate and errors are based on among-path variation) and the individual level where error estimates are based on within-path measurements (of a single animal movement path).

To determine whether an individual was orienting while moving, we used Nams (2006a) scaling test of orientation. The test assumes that the movements of an animal orienting to a feature should have greater displacement at larger spatial scales than predicted by a CRW model; thus, CRWDiff should be positive at larger spatial scales. An animal showing un-oriented movements will only use mechanisms at small spatial scales; hence, CRWDiff should be less than or equal to 0 at all spatial scales (Nams 2006a; Brooks & Harris 2008). Rather than just measuring an overall CRWDiff value, we determined how the value changes with increasing spatial scale. We set the minimum step size based on the error estimates around the locations, while maximum step size was set above the size of the animal’s home range (in terms of net distance). We sampled each movement path at 200 spatial scales, the maximum allowed by the scaling test (Nams 2006a; Brooks & Harris 2008).

Fractal analysis

A fractal value (D) of a movement path is a measure of tortuosity and varies from 1 for a straight line to 2 for a path which is so tortuous that it completely covers a two-dimensional plane (Nams 1996; Doerr & Doerr 2004). The Fractal Mean value for each animal was calculated using the divider method, where a range of dividers of different size are run along the movement path, and total path length is measured. Movement path length decreases as divider size increases, and a log–log plot of divider size vs. path length is produced, with a line of slope 1−D. The line can be described by (G) = kG1−D, where L (G) is path length, k is a constant and G is divider size. A more tortuous path will have more turns and will produce a line with a steeper slope. Fractal Mean incorporates replication by measuring path length twice for each divider size, by running the dividers both forward and backward along the path, which reduces bias associated with previous Fractal D measures (Nams 2006b). This is particularly important when analysing animal movement paths, as bias associated with previous D estimates varies with path length, and tortuosity, which cannot be controlled for in tracking studies (Nams 2006b). For statistical comparisons, D was transformed to log (D−1). Based on the criticisms of Turchin (1996), we did not compare D values between species, only between individuals of the same species and study. The exception was for juvenile and adult thresher sharks, which were tracked using the same techniques, in the same locations, and the same range of divider sizes were used. The goal of the fractal analysis was to determine how movement path structure varied qualitatively between species and not to extrapolate movements to larger spatial scales.

Many animals show scale-dependent movement, implying that they may behave differently at different spatial scales. By examining how D changes with spatial scale (the location of such changes are known as domains), we can determine whether movements are scale dependent. To quantify the change in D with scale, we used the VFractal estimator, which is calculated from the turning angle of individual movement steps (Nams 1996). Similarly, we examined the variance in tortuosity at different spatial scales, as a decline in variance is also indicative of an animal using a domain (Nams 2005). The 95% confidence intervals (CIs) were calculated by using a bootstrapping procedure to randomly select turning angles from the path. For bootstrapping, the number of replications was varied from 10 at small spatial scales to 2000 at larger scales, with a mean of 1000 replications (Nams 1996). For all animals, the range of divider sizes varied based on the scale of movements for the species. For thresher sharks (juvenile and adult), scale varied from 10–50 000 m; for tiger sharks, spatial scale ranged from 100–50 000 m; and for blacktip reef sharks, these ranged from 10–1000 m. Tiger shark tracks were conducted when accuracy of GPS positions was reduced by the military; hence, errors in position estimates were larger (Holland et al. 1999).

To detect patch use, the correlation in tortuousity between adjacent path segments was calculated for a range of divider sizes. If the divider size is below the size of a patch used by the animal, then it is likely that consecutive path segments will be either inside or outside the patch; hence, the tortuousity correlation between adjacent path segments should be positive. As divider size approximates patch size, then it is likely that one path segment will include the entire patch (with high tortuousity) while the adjacent segment is outside the patch (with low tortuousity); hence, the correlation should be negative. Therefore, a positive correlation followed by a negative correlation is indicative of patch use and size (Nams 2005). If there is no patch use, then there should be no correlation between path segments and the correlation should be zero regardless of whether the animal is moving in a random or directed manner (Nams 2005). All CRW, fractal and correlation analyses were performed using fractal ver. 5 (V. Nams, Nova Scotia Agricultural College).

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Correlated random walks and directed movements

At the species level, none of the shark species utilized a CRW, with significant differences in net displacement when compared with a CRW in juvenile thresher (CRWDiff = 0·255, P = 0·025, d.f. = 6), adult thresher (CRWDiff = 0·387, P = 0·0017, d.f. = 7), tiger (CRWDiff = 0·303, P = 0·001, d.f. = 8) and blacktip reef sharks (CRWDiff = −0·064, P = 0·014, d.f. = 8). However, at the individual level, there were some animals that performed CRW, with between 13% and 67% of individuals within a species group moving with a CRW (Table 1). There were also species-specific differences in the scaling test for orientation (Fig. 1). Overall, juvenile thresher sharks showed orientation at scales of 330–1200 m, although the lower 95% CI is at 0 CRWDiff, indicating that some individuals showed un-oriented movements (Fig. 1a). Adult thresher sharks showed more oriented movements to scales of 1200–2000 m (Fig. 1b). Tiger sharks showed the most directed movements, with orientation to scales of at least 6000–8000 m (Fig. 1c). At spatial scales >6000 m, the 95% CI is too wide to infer conclusions of path structure. Finally, blacktip reef sharks were the only species that did not show oriented movements (Fig. 1d). At small spatial scales, blacktip reef sharks had negative CRWDiff values, indicating more constrained movements than those produced by a CRW, while CRWDiff approached zero at the largest scales.

Table 1.   Species-specific fractal and correlated random walk (CRW) analyses
SharkSize (cm)SexTrack duration (h)DCRWDiffPScale of patch use (m)
  1. D is Fractal Mean. CRWDiff is a measure of net displacement relative to the predictions of a CRW. An animal deviating significantly from a CRW will have P < 0·05 (bold). N means no patch use could be detected. Data are for juvenile thresher sharks (JT), adult thresher sharks (AT), tiger sharks (T) and blacktip reef sharks (BT). Data for BT1–13 are from Papastamatiou et al. 2009.

JT184F381·35430·16330·156619–30, 470–800
JT266M321·09210·55500·0004286–600
JT378F541·03050·65880·0000N
JT4108M671·23240·41860·0013100–600
JT5108M581·25070·22170·007325–50, 600–1400
JT673M461·11140·50850·002570–1000
JT7101M751·35790·35550·000350–200
AT1152F351·07750·42050·014670–120
AT2179F311·01310·84230·00N
AT3202F401·22870·25340·2243N
AT4200F431·11340·49380·0023N
AT5147F491·14650·46380·0018760–2000
AT6132M431·11170·40840·0024N
AT7203M261·04850·56490·0094420–2000
AT8122F221·04700·58630·0018170–570
T1200M301·11820·63430·007N
T2360F241·08670·67930·007490–2217
T3217M201·18680·73980·07230–500
T4305M191·23250·3370·043N
T5A304M301·06750·8950·037N
T5B319M311·11640·84190·035266–905
T6315M491·09820·46770·0013500–1100
T7342M71·03780·59050·009N
T8417F501·22660·47350·07200–600, 1400–3000
BT185241·3679−0·09980·256426–30, 76–88
BT275481·4901−0·04110·1951N
BT311091·2649−0·07220·6646N
BT4110481·3459−0·05770·0002105–190
BT59581·2967−0·50970·00N
BT610071·2425−0·04800·1487N
BT8120101·3406−0·10620·393735–80
BT9107M721·4806−0·04330·00103N
BT13125F481·4118−0·00650·904N
image

Figure 1.  Scaling test for oriented movements for three shark species. Data are for (a) juvenile thresher, (b) adult thresher, (c) tiger and (d) blacktip reef sharks. CRWDiff is a measure of how net displacement compares with that predicted for an animal moving using a correlated random walks (CRW). All species show some degree of oriented movements except for blacktip reef sharks. Dotted lines are 95% confidence intervals. Boxes and numbers show spatial scale at which movements become indistinguishable from a CRW. X-axis is on a log scale.

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Fractal analysis and patch use

Considerable individual variation in movement path structure was evident between species, although some general trends were also apparent (Fig. 2). Juvenile thresher sharks showed the highest degree of individual variation, with the widest range of Fractal D values (1·0305–1·3579, Table 1). There is some evidence that these differences were related to water temperature. Data for both adults and juveniles were combined, and multiple regression analysis showed that Fractal Mean was correlated with average water temperature measured during the tracks (T = 2·29, r2 = 0·25, P = 0·047, d.f. = 14) but not with shark size (T = 0·03, P = 0·979). When data were analysed only for juveniles, the correlation was stronger (temperature vs. D: T = 4·44, r2 = 0·72, P = 0·01; temperature vs. CRWDiff : T = −6·81, r2 = 0·88, P = 0·004). In other words, sharks tracked in warmer water had more tortuous movements. There was also a negative relationship between D and rate of movement (F = 29·3, r2 = 0·83, P = 0·003, d.f. = 6). When VFractal was calculated for all juveniles combined, the CI was too wide to make any inferences on movement structure (Fig. 2a). Generally, juvenile thresher shark movements could be divided into two groups: those with homogeneous movements at all spatial scales (e.g. JT 3, 4, 6, Table 1) and those with a domain at 400–700 m. The three sharks that showed homogeneous movements were tracked in the coolest waters. For those animals detected using patches, scale of patch use varied from 20–1400 m. Thresher shark no. 5 had homogeneous movements up until scales of 630 m, after which a domain occurred with constant D and variance at progressively larger scales (Fig. 3b,c). Patch use of 25–60 and 630–1400 m was detected, but movements were overall un-oriented (Fig. 3d,e).

image

Figure 2.  Changes in VFractal with spatial scale for (a) juvenile thresher (n = 7), (b) adult thresher (n = 8), (c) tiger (n = 9) and (d) blacktip reef sharks (n = 9). X-axis is on a log scale. Note use of different scales on x and y axes. The shaded rectangles give the location of domains in movement structure.

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image

Figure 3.  (a) Movement path (with Fractal D value), and changes in (b) Fractal D, (c) variance in tortuosity, (d) correlation in tortuosity between path segments and (e) the scaling test for orientation, with spatial scale for juvenile thresher shark no. 5. Boxed rectangle and numbers show locations of domains (b, c) or patch size (d). X-axis is on a log scale. Movements are un-oriented, but a domain occurs at 630 m, with more scale-invariant movements at larger scales.

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There was less variation amongst adult thresher sharks, with most individuals (n = 6, 75%) showing homogeneous movements up until a domain at 1100 m, after which movements were scale invariant at larger scales (Fig. 2b). Patch use was detected in a few individuals, with scale of patches ranging from 70–2000 m (Table 1). There was no relationship between D and ROM (F = 2·76, P = 0·148, d.f. = 7). Thresher sharks were the only species for which we could compare Fractal Mean between those individuals that performed oriented walks and those that had un-oriented movements. Thresher sharks using directed walks had straighter movement paths (D: 1·061 ± 0·002) than those performing un-oriented movements (1·262 ± 0·010, t = −2·586, P = 0·004, d.f. = 4). Thresher shark no. 1 showed a domain at approximately 1300 m, after which movements became straighter (D decreased, Fig. 4b,c). There was use of a small patch at a scale of 70–120 m (Fig. 4c), and the shark was able to orient to scales of at least 1200 m (Fig. 4d).

image

Figure 4.  (a) Movement path and changes in (b, c) movement structure, (d) patch use (e) and scaling test for orientation for adult thresher shark no. 1. Details are the same as those in Fig. 3. X-axis is on a log scale. Movements are oriented, with a domain at 1300 m and straighter movements at larger scales.

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At the group level (all sharks combined), tiger sharks had scale-invariant movements up until scales of 2000 m, after which CI’s became too large to draw conclusions (Fig. 2c). When analysed individually, tiger sharks either had movements that were scale invariant (T3, 5A, Table 1) or showed homogeneous movements until 215–2217 m, after which D started to decrease with spatial scale (i.e. movements became straighter). Scale of patches varied from 200 to 3000 m. Tiger shark no. 2 showed an increase in D and variance up until scales of 730–1400 m, after which both values started to decrease (Fig. 5b,c). Patch use of up to 430–2400 m was detected, and the animal was able to orient to scales of at least 1100 m (at larger scales, CI were too broad to make inferences, Fig. 5d,e).

image

Figure 5.  (a) Movement path and changes in (b, c) movement path structure, (d) patch use (e) and scaling test of orientation in tiger shark no. 2. Details are the same as those of Fig. 3. X-axis is on a log scale. Movements appear tortuous at small scales (up to 730 m) but become highly directed at larger scales.

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Blacktip reef sharks showed the least amount of intraspecific variation in movement structure. Movements were scale invariant up to scales of 30–60 m, before becoming more homogeneous (see Fig. 2d, Papastamatiou et al. 2009). Patch use varied from 26–200 m in scale (Table 1, Papastamatiou et al. 2009). These general patterns can be seen in data from blacktip reef shark no. 4, which shows patch use at scales of 100–200 m and overall un-oriented movements (Fig. 6).

image

Figure 6.  (a) Movement path and changes in (b, c) movement structure, (d) patch use (e) and scaling test of orientation in blacktip reef shark no. 4. Details are the same as those of Fig. 3. X-axis is on a log scale. Movements are un-oriented and fairly homogeneous although there is some patch use at small scales (100–200 m).

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Sharks show a variety of movement strategies both between and within species. Some species can orient and perform directed walks at impressive spatial scales, but inter- and intraspecific differences are likely related to a variety of factors including size, age, life history and energetic requirements. While the active tracking used in the present studies only record movements over short time periods (a few days), it is currently the main technique that provides high enough spatial resolution to quantify fine-scale horizontal movement structure in marine fish predators. However, up-and-coming technologies such as GPS tags (e.g. Sims et al. 2009) and Vemco VR2W Positioning System (VPS, Espinoza et al. in press) passive tracking will allow longer tracks with high spatial resolution, at least in certain environments.

Sharks were able to orient at large spatial scales, with at least some individuals (tiger sharks) performing directed walks at least 6–8 km away. By knowing the location of specific features, these individuals reduce search time and conserve energy, likely improving search efficiency (Brooks & Harris 2008). Some of these orientation distances are probably within range of the animal’s sensory systems, as sharks can use a variety of signals to navigate, including signals from water currents, temperature and geomagnetic fields (Klimley 1993; Montgomery & Walker 2001; Meyer, Holland & Papastamatiou 2005). It is also possible that sharks may be able to orient to olfactory signals over long distances, as seen in marine birds, although this has never been tested in the field (e.g. Nevitt, Losekoot & Weimerskirch 2008). Pelagic fish such as yellowfin tunas and dolphinfish are able to perform directed walks and orient to fish attracting devices (FADs, offshore buoys) up to 14 km away, although most directed walks were at scales of 100’s of metres to a few kilometres (Girard, Benhamou & Dagorn 2004; Girard et al. 2007). It was hypothesized that pelagic fish are orienting to sound produced by ocean currents passing over the mooring chains (Girard, Benhamou & Dagorn 2004).

However, some of the larger orientation distances are likely beyond the sensory ranges of the sharks and suggest that individuals utilize cognitive maps, requiring good spatial memory and awareness of features within their home range. To find these locations, these animals may use memory in combination with shorter directed walks to known landmarks within range of their sensory systems (Montgomery & Walker 2001; Brooks & Harris 2008). Within terrestrial environments, zebras are able to orient to forage grounds over 3 km away, most likely by using familiar features at smaller scales combined with good spatial awareness and memory (Brooks & Harris 2008). While previous studies have suggested that sharks may be capable of developing cognitive maps (e.g. Meyer, Papastamatiou & Holland 2010), they were not able to quantitatively determine whether individuals were moving using a directed walk at large scales or whether movements were highly CRW. Tiger sharks, in particular, are known to have large home ranges that vary in scale from 100’s to 1000’s of kilometres (Holland et al. 1999; Heithaus et al. 2007; Meyer, Papastamatiou & Holland 2010), and similarly, thresher shark home ranges span large areas including both pelagic and coastal habitats (Cartamil et al. 2010a,b). Efficient use of such large area may require cognitive maps of resource distribution or at least the location of probable resource ‘hotspots’. For example, the directed movements of tiger sharks in Hawaii took them across a deep channel, to a shallow and productive bank (Penguin Banks), in a fairly short period of time (see Holland et al. 1999). Computer simulations have suggested that highly CRW are more efficient at locating patches than less CRW, but the models did not include directed walks, which may be even more efficient (Zollner & Lima 1999; Nams 2006a).

The difference in orientation distance between adult and juvenile thresher sharks may also be indicative of learning abilities, suggesting older individuals may perform more efficient directed walks. Adult thresher sharks showed more oriented movements over greater spatial scales than juveniles. Such differences may arise from a combination of inexperience in juveniles and improved cognitive maps in adults through learning and possibly improved sensory capabilities (e.g. Mech & Zollner 2002; Sims et al. 2006; Guttridge et al. 2009). Similarly, a juvenile basking shark (Cetorhinus maximus) demonstrated prey encounter success rates (zooplankton patches) almost identical to those predicted by an animal moving using a random walk, while adults had encounter rates that were 90% more successful than predicted by a random walk (Sims et al. 2006). The authors attributed these differences to inexperience in juveniles and improved foraging abilities through learning in adults. An alternative explanation to the differences between thresher sharks is that there was variation in the distribution of prey and other resources between individual tracks. For example, if juveniles consume different prey types and utilize patches that are close together, then they may have less need to orient at large distances. However, the overall horizontal distances moved were similar between both size classes, and adult common thresher sharks consume many of the same small prey items as juveniles, even though their overall dietary breadth is greater (Preti, Smith & Ramon 1999; Cartamil et al. 2010a,b).

Blacktip reef sharks showed un-oriented movements and are also the only species to have small, well-defined home ranges, with high site fidelity (Papastamatiou et al. 2009). Fractal analysis shows that at the larger spatial scales, these sharks are probably moving randomly, although overall they are not moving using a simple CRW. A recent model suggested that a nonterritorial, randomly moving animal will maintain a home range if the animal uses a two-part memory system, where the location of patches is remembered (reference memory) as is the reduced quality of recently visited patches (working memory, Van Moorter et al. 2009). Furthermore, home range behaviour may lead to more efficient patch detection than more nomadic search patterns. Some blacktip reef sharks use well-defined patches, and the locations of these patches will likely vary spatially and temporally but will remain in certain habitat types and general locations. Hence, while these sharks move more randomly, they do show strong habitat selection for macrohabitat (different sand-flats) and microhabitat (ledges of sand-flats) (Papastamatiou et al. 2009). The scale-invariant movements at low spatial scales do suggest some oriented movements, which are most likely a function of orienting to prey patches within the sensory range of the animals, as they search the coral ledges within their home range (Papastamatiou et al. 2009). At certain times, blacktip reef sharks also show diel habitat shifts, so presumably must show some form of oriented walks (at small spatial scales) to move between habitat locations (Papastamatiou et al. 2009).

There were some general, species-specific differences in movement path structure and in the response of path structure to spatial scale. Fractal analysis suggests that during the tracks, tiger sharks tended to use more tortuous, possibly random movements at the scale of patches, but highly directed and straight movements at larger spatial scales. Thresher sharks also showed more tortuous movements at the scale of patch use, but more scale-invariant movements at larger spatial scales. Blacktip reef sharks had straighter directed movements at the scale of patch use, but more random un-oriented movements at larger scales. However, certain individuals within each species showed movements similar to a CRW. Recent research is showing that individual specialization in movement patterns exists in animal populations, including marine predators (e.g. Austin, Bowen & McMillan 2004; Bailey & Thompson 2006; Roshier, Doerr & Doerr 2008). These differences may arise through different learning experiences, unique cognitive maps, variation in body mass and the energetic state of the individual. It is also possible that in some cases the individual differences in the use of CRW may be an artifact of heterogeneous movements, as the CRWDiff test may mistake movement paths with strong patch use as a CRW (Nams 2005). These were also intraspecific differences in path structure, patch size and tortuousity which were particularly pronounced in thresher sharks. In thresher sharks, some of this variability was associated with water temperature, with more tortuous movements occurring in warmer waters. The factors behind these changes in behaviour are unknown but may be related to increased ocean productivity and larger forage base. Blacktip reef sharks showed more consistent movement path structure, and patch sizes only differed in scale by a maximum of 100 m, although there are also individual differences in movement patterns (e.g. diel habitat shifts, Papastamatiou et al. 2009). Owing to the short nature of active tracking, it is unknown whether individual sharks were being tracked while within an established home range or whether they were exploring new environments (at least for tiger and adult thresher sharks).

Our movement analysis only examined horizontal movements, but search behaviour in the marine environment also has a vertical component. Several marine predators (including sharks) have shown shifts in vertical diving behaviour, performing lévy walks when in heterogeneous habitats and shifting to Brownian motion when in more homogeneous environments (Humphries et al. 2010). In the present study, all individuals (for which diving data existed) performed continuous vertical oscillations, and some showed diel shifts in vertical habitat use (Holland et al. 1999; Cartamil et al. 2010a,b; Y. P. Papastamatiou, unpublished data). When vertical movements are incorporated with horizontal movements (e.g. using 3D fractal analysis Uttieri et al. 2005), the location and size of patches may appear different. Furthermore, the vertical movements will change the overall displacement performed by the animal, which could potentially bias the results of the CRW tests (which are based on displacement). While this may influence both observed and expected displacement (i.e. net difference in displacement, and hence the CRW test remains the same), it is unclear as to how this will affect statistical tests that have been designed for a 2D environment. It is important that future studies try to combine high-resolution vertical and horizontal information on marine predator movements to more fully characterize movement patterns.

Clearly, animals alternate their movement patterns between periods of directed movements to specific features within their home range, and random walks when they encounter new environments, and must choose an optimal random search pattern (e.g. Sims et al. 2008; Humphries et al. 2010). However, it is important to understand when and under which circumstances movement path structures switch, and the spatial scales over which these patterns will be displayed. Ultimately, movement decisions by individuals collectively influence dispersal at the population level (e.g. Benhamou 2006), and movement studies of marine predators should include the analysis of path structure and search patterns, in addition to common measures such as home range size, movement rates and habitat selection.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

We thank V. Nams and three reviewers for advice and helpful comments.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Materials and methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References