Hierarchical patch dynamics and animal movement pattern ...

Oecologia (2006) 149:383–395 DOI 10.1007/s00442-006-0463-7

PO PU L AT I ON EC OL O G Y

Hierarchical patch dynamics and animal movement pattern Per Fauchald · Torkild Tveraa

Received: 3 November 2005 / Accepted: 3 May 2006 / Published online: 23 June 2006 © Springer-Verlag 2006

Abstract In hierarchical patch systems, small-scale patches of high density are nested within large-scale patches of low density. The organization of multiplescale hierarchical systems makes non-random strategies for dispersal and movement particularly important. Here, we apply a new method based on Wrst-passage time on the pathway of a foraging seabird, the Antarctic petrel (Thalassoica antarctica), to quantify its foraging pattern and the spatial dynamics of its foraging areas. Our results suggest that Antarctic petrels used a nested search strategy to track a highly dynamic hierarchical patch system where small-scale patches were congregated within patches at larger scales. The birds searched for large-scale patches by traveling fast and over long distances. Once within a large-scale patch, the birds concentrated their search to Wnd smaller scale patches. By comparing the pathway of diVerent birds we were able to quantify the spatial scale and turnover of their foraging areas. On the largest scale we found foraging areas with a characteristic scale of about 400 km. Nested within these areas we found foraging areas with a characteristic scale of about 100 km. The large-scale areas disappeared or moved within a time frame of weeks while the nested Communicated by Wolf Mooij Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at http://dx.doi.org/10.1007/s00442-006-0463-7. P. Fauchald (&) · T. Tveraa Norwegian Institute for Nature Research, Division for Arctic Ecology, The Polar Environmental Center, 9296 Tromsø, Norway e-mail: [email protected]

small-scale areas disappeared or moved within days. Antarctic krill (Euphausia superba) is the dominant food item of Antarctic petrels and we suggest that our Wndings reXect the spatial dynamics of krill in the area. Keywords Area-restricted search · First-passage time · Hierarchical foraging · Random walk · Satellite telemetry

Introduction The concept of patchiness is central to the description of patterns of spatial heterogeneity in ecology (Wiens 1976). However, heterogeneity occurs over several diVerent spatial and temporal scales, and an ecological pattern is therefore dependent on scale (Wiens 1989; Levin 1992, 2000; Fauchald et al. 2000). Hierarchical patch dynamics aims to link scale and heterogeneity (O’ Neill et al. 1986; Wu and Loucks 1995). The major element within this framework is the idea of patches nested within patches at larger scales forming nested patch mosaic hierarchies (Kotliar and Wiens 1990; Wu and Loucks 1995). For example, the spatial distribution of marine pelagic schooling Wsh and krill is typically organized in such nested patch hierarchies (Murphy et al. 1988; Fauchald et al. 2000; Fauchald and Erikstad 2002). At the smallest scale, individuals are congregated into schools and swarms. Schools and swarms are typically congregated into patches linked to mesoscale oceanographic features. Finally, these patches are typically congregated within large scale areas that reXect the habitat boundaries. When resources are distributed in patch hierarchies, the ability of an organism to move optimally within and

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among these hierarchies becomes particularly important (Senft et al. 1987; Fauchald 1999). Distance moved within such systems which is too great might be fatal since the organism might be put into a sub-optimal patch hierarchy. On the other hand, if the organism moves a distance which is too small it is unable to explore other, and perhaps more optimal, hierarchies. There should therefore be a strong selective pressure on traits that make the organisms able to orientate within such systems both in time and space. In models of prey taxis and area-restricted search in heterogeneous landscapes, it is assumed that animals modify their movement path in response to prey density such that the organism increases its turning rate in areas of high prey density and reduces its turning rate in areas of low prey density (Kareiva and Odell 1987; Grünbaum 1998; Farnsworth and Beecham 1999). Such behavioral responses have been termed “area restricted search” and will generate an aggregative response of predators towards a high density of prey. However, in a hierarchically structured system an organism should possess an arsenal of scale-dependent movement patterns that match the spatial structure of the environment (Fauchald 1999). The organism should choose movement pattern according to its position within the patch hierarchy such that it minimizes the probability of moving out of a proWtable large-scale patch while it at the same time maximizes the probability of Wnding proWtable patches at smaller scales. Due to the strong relationship between temporal and spatial scales in nested systems (Stommel 1963; Haury et al. 1978), the decision on movement pattern might be based on experience of, e.g., foraging success (Fauchald 1999). Accordingly, actions involving movement or dispersal on large scales should be based on average long-term experience while small-scale actions should be based on short-term experience (see Fauchald 1999). Nested hierarchical search strategies have been diYcult to demonstrate empirically. This might partly be due to the problems associated with analyzing the spatial pattern of nested systems (Fauchald et al. 2000). One major assumption in spatial statistics is the assumption of stationarity. That is, a spatial process has the same probability of occurring throughout space (Cressie 1993). However, non-stationarity is in fact a key property of nested patch hierarchies. In a nested system, patches at a given hierarchical level are found nested within patches at a larger scale. Thus, the probability of observing a patch at a given level is not equal throughout space. The results from global analyses of spatial structure (e.g., variograms, correlograms, spectral analyses, wavelet analyses and fractal analyses)

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are, as a consequence, highly confounded in these systems (Fauchald et al. 2000). Accordingly, large-scale patterns will mask the nested small-scale patterns, and analyses should therefore be nested or stratiWed on the basis of the spatial structure at the subsequent larger scale. While such confounding large-scale structures might be relatively easily identiWed and controlled for in terrestrial systems, this is seldom done in marine pelagic ecosystems. This is probably partly a result of the diYculties in observing boundaries of patches and partly a result of the transient nature of these systems. In this study we use satellite transmitters to reveal the search strategy of a long ranging seabird, the Antarctic petrel (Thalassoica antarctica) and the spatiotemporal dynamics of its foraging areas. We apply a new methodology based on Wrst-passage time (FPT) (Fauchald and Tveraa 2003) to quantify the spatial scales and the nested search strategy of individual birds. Furthermore, by comparing the search eVort among birds, we quantify the spatial scales, spatial distribution and turnover of their foraging areas.

Materials and methods Study area and species In January 1997, thirty-six male Antarctic petrels were equipped with satellite transmitters at their nest at Svarthamaren (71°53⬘S, 5°10⬘E) and positions were collected via the Argos satellite system. Svarthamaren is a nunatac situated about 200 km inland in continental Antarctica. The colony comprises approximately 250,000 pairs of Antarctic petrels that breed in high densities on scree slopes. The male and female alternate between the duties at the nest and foraging trips at sea where they mainly prey on Antarctic krill (Euphausia superba) (Lorentsen et al. 1998). The birds were monitored from when the chicks were left alone for the Wrst time until the transmitters stopped sending signals or the males did not return to the colony, resulting in 58 complete trips between 18 January and 3 March. Of the 36 males originally equipped with a transmitter, one or more complete trips were recorded for 22 of them. Eight males did not return to the colony and six either lost their transmitter at an early stage or the transmitter failed to give signals. The median number of trips recorded for the remaining 22 males was 2 (range 1, 8). The satellite transmitters [platform terminal transmitters (PTTs), PTT100, 20 and 30 g; Microwave Telemetry, Columbia, Md.] were attached to the back of the males with a harness covered with TeXon padding during their last guarding spell. The weight of

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the device carried by each bird represented on average 3.2 and 4.7% (20 and 30 g PTTs, respectively) of their average body mass. Locations were provided on average every 1.5 h from the Argos system. Locations in the colony and when the birds were traveling over the permanent ice shelf were not included in the analyses. The Argos locations are given with an accuracy class. The mean location error for each accuracy class has recently been published in a similar study on yellownosed albatrosses (Thalassarche carteri) in the South Indian Ocean (Pinaud and Weimerskirch 2005). Using these estimates, the mean location error in the present dataset was estimated to 14.2 km. To remove outliers, locations giving a speed of more than 80 km/h were removed from the analyses (Weimerskirch et al. 1993). This limit is at the upper end of what can be considered as realistic Xying speeds for Antarctic petrels (cf. Alerstam et al. 1993), ensuring a relatively conservative strategy with respect to the removal of outliers. By this method 4,640 of 23,661 positions were removed. FPT analyses We used FPT to analyze the pathway of each trip (Fauchald and Tveraa 2003). Applied to an animal searching for food, the FPT is a scale-dependent measure of the animal’s search eVort at each point on its movement trajectory. Suppose that a pathway of an animal is described by a large number of points given by time and position and that all these points are the centers of circles with a given radius (r). The FPT for each point is found by measuring the time lag between the Wrst crossing of the circle back along the path and the Wrst crossing of the circle forward along the path. By increasing the radii of the circles, more loops of the pathway will be included within each circle and the mean FPT will increase. However, the FPT will increase more in the intensively searched areas compared to areas with less search eVort. The variance in log FPT will therefore increase for increasing r until r matches the scale of the intensively searched areas, and decreases thereafter (Fauchald and Tveraa 2003). Thus, the spatial scale at which the animal concentrates its search eVort is indicated by the value of r giving the maximum variance in log FPT. This scale has been termed the area-restricted search (ARS) scale (Pinaud and Weimerskirch 2005). The purpose of the FPT analysis is to capture the search eVort at each point along the entire movement path (sensu Fauchald and Tveraa 2003). Accordingly, each point along the path should have equal probability of being sampled. However, in most cases sampling of locations is done independently of the speed of the

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animal. Such data sets include consequently a larger number of locations in the parts of the path where the animal has a low speed compared to parts where it has a high speed. This gives a sampling bias towards areas of high search eVort. To remove this sampling bias, the data should be made regular in space by spatial interpolation of locations (Fauchald and Tveraa 2003). We calculated the time and position for every second kilometer between successive locations assuming a linear path and a constant speed (e.g., Kareiva and Shigesada 1983). The FPT for a given r was calculated for each point in the resulting data set. ARS scales were identiWed for each individual trip by calculating the variance in log FPT as a function of spatial scale (r). The variance-scale function and consequently the observed ARS scale is related to individual foraging pattern and success as well as the spatial distribution of resources (Pinaud and Weimerskirch 2005). A small ARS scale might suggest that an individual encounters high resource densities relatively fast without much search eVort. However, a small ARS scale might also indicate that the resource is distributed within relatively small patches. The spatial dynamics of foraging areas can be studied by analyzing the spatial distribution of FPT among individuals (Fauchald and Tveraa 2003). To do this, it is necessary to select a scale on which the FPT is to be calculated. One might either use the individual ARS scale found for each path or one might use a common spatial scale for all the paths. In order to remove some of the noise due to stochastic and individual diVerences in ARS scales we chose to use a common spatial scale (SR). Because high foraging success in some of the trips will mask a large-scale search pattern, we chose a value of SR in the upper range of individual ARS scales. To investigate any nested search pattern, we used a nested approach starting with the pattern at the largest scale (Fauchald et al. 2000). We Wrst analyzed the large-scale, overall pattern. To investigate any search pattern within the most intensively searched areas, we selected the location with the longest FPT and the associated path within the circle for r = SR. The nested search pattern was explored by repeating the analyses on the selected part of each trip. Permutation test of the variance-scale functions To investigate whether the variance in log FPT as a function of spatial scale could be generated from randomized trips, we performed permutation tests on all trips from the sample. When a search pattern conforms to an area-restricted search, the spatial displacement between locations is short in areas of high search eVort

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and long in areas of low search eVort. This results in a non-random, autocorrelated sequence of displacements between locations which is depicted by the FPT analysis (Fauchald and Tveraa 2003). On the contrary, under the null hypothesis of random search, the sequence of displacements between locations is random. For each trip, we generated pathways under this null hypothesis by Wrst calculating the displacements between each ARGOS location and then calculating a new set of locations from a randomly shuZed sequence of the displacements. For each such randomized trip we calculated the variance-scale function as described above. A conWdence interval (CI) for the variancescale function under the null hypothesis was calculated from 2,000 permutations and compared to the observed variance-scale function for each trip. Individual foraging pattern Of the 22 males investigated, more than one trip was recorded for 15. It was therefore possible to study individual diVerences in foraging pattern. We expected individuals to return to the same areas where they had previously encountered food. Thus, we expected that the distance between the intensively searched areas should be closer between successive trips than between corresponding trips of diVerent individuals. To test this hypothesis we selected all successive trips of the same individuals and calculated the distance between the areas with the highest FPT for r = SR for each pair. To Wnd equivalent inter-individual pairs of trips, we substituted the second trip of each initial pair with the trip in the sample of other birds that was closest to the second trip in time. The distances between the intensively searched areas were calculated and compared to the intra-individual distances in an analysis of covariance (ANCOVA) with the time interval between trips as a covariate. Individual diVerences in foraging success might suggest that the ARS scale of a trip should be positively related to the ARS scale of the previous trip. Moreover, when the birds are feeding their chick, a short time lag between trips could indicate high foraging success and consequently small ARS scales. To test these hypotheses, we used the same pairs as above and analyzed how the ARS scale was related to the ARS scale of the previous trip in an ANCOVA with time interval between trips as a covariate. The spatial dynamics of foraging areas To investigate the spatio-temporal dynamics of the foraging areas utilized by the birds, we analyzed the spatio-temporal overlap in search eVort among diVerent

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trips by calculating cross-correlograms. We selected r = SR, calculated the FPT along the paths and aggregated these values on a geographical grid for each speciWc trip. Based on these grids, we calculated the correlation coeYcients between the FPT for all possible pairs of trips for varying time lags and spatial distance. From the resulting spatial and temporal cross-correlograms, we expected the correlation coeYcient to be large for small lags. This is because we expected the diVerent birds to increase their search eVort in the same area at the same time. Furthermore, we expected the coeYcient to decrease for increasing lags and approach zero at the characteristic spatial and/ or temporal scale of the common foraging area. CIs for the correlograms were calculated by a jackknife procedure (Efron and Tibshirani 1993). Assuming that the trips represent the observational units, we calculated the SE for each correlation coeYcient by removing one trip at a time from the analysis. The FPT analysis, permutation test, spatial statistics and the jacknife procedure were programmed in SIMULA (Kirkerud 1989).

Results Area-restricted search behavior For the sample of 58 trips (Fig. 1), the median trip duration was 7 days (range 2, 17) and the median maximum recorded distance from the colony was 1,159 km (range 233, 2.557) (see Appendix). For each trip we calculated the variance in log FPT with r ranging between 10 and 300 km. The CI for the variance function under the null hypothesis of random displacement between locations was calculated from 2,000 randomizations. A peak in variance, and consequently a distinct ARS scale, was detected in 55 of the 58 trips. Median ARS scale for these trips was 80 km (20, 220). In contrast, under the null hypothesis, the variance in FPT generally decreased for increasing scale. Thus, for a majority of trips with a detectable ARS scale (52 of 55 trips), the peak in variance was signiWcantly (P < 0.05) larger than the corresponding variance under the null hypothesis (Appendix). For the three remaining trips, the P-values ranged between 0.088 and 0.107. Visual inspection of the trips indicated that the majority of birds searched intensively within one single area before returning to the colony. Interestingly, for the three trips with no detectable ARS scale, the FPT variance decreased for increasing scale and was found within the 95% CI of the null hypothesis, suggesting random foraging with no distinct ARS behavior.

Oecologia (2006) 149:383–395 Fig. 1a–d Sample of 58 foraging trips of Antarctic petrels breeding at Svarthamaren, Antarctica, 1996–1997. The trips are sorted by the mean date of the positions. a Mean date between 22 January and 29 January. b Mean date between 29 January and 5 February. c Mean date between 5 February and 12 February. d Mean date later than 12 February

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The ARS scale was positively related to the maximum distance from the colony [
= 0.65 (95% CI 0.41, 0.88), R2 = 0.36, log-transformed data]. We therefore present the average variance functions for the 29 trips with the shortest maximum distance to the colony and the 29 trips with the longest maximum distance to the colony separately (Fig. 2a, c). The corresponding 95% CIs for the estimates under the null hypothesis are shown in the same Wgure and suggest highly signiWcant patterns. For trips close to the colony, the mean variance peaked at a scale of 50 km while for long-ranging trips the mean variance peaked at a scale of 140 km. Thus, the average scale at which the birds concentrated their search eVort was 50 km for birds foraging close to the colony and 140 km for birds foraging farther apart. We chose SR equal to 140 km and selected the part of each trip giving the longest FPT for r = SR. Within these parts, a distinct ARS scale was found in 45 of the 58 trips. Median ARS scale was 35 km (range 15, 85). Under the null hypothesis, the variance in log FPT generally decreased for increasing spatial scale. The majority of trips with a detectable ARS scale (37 of 45 trips), had a peak in variance that was signiWcantly (P < 0.05) larger than the corresponding variance under the null hypothesis (Appendix). For the remaining eight trips the P-values ranged between 0.056 and 0.175. Similar to the large-scale analyses, the variancescale function of the trips with no detectable ARS scale was found within the 95% CI of the randomized trips, suggesting random foraging. The ARS scale did not increase with maximum distance from the colony [
= 0.00 (95% CI ¡0.01, 0.01), log-transformed data] and the mean variance-scale

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Spatial scale r (km) Fig. 2a–d Observed mean variance (var) in log Wrst-passage time (solid line) and the corresponding 95% conWdence interval (CI) under the null hypothesis of random displacement between locations (hatched lines) as a function of spatial scale (r). a, c Variance calculated for whole trips. b, d Variance calculated for the selected part of each trip giving the longest Wrst-passage time (FPT) for r = 140 km. a, b The 29 trips with the longest maximum distance from the colony. c, d The 29 trips with the shortest maximum distance from the colony

function peaked at a scale of 35 km for both the longranging and the short-ranging trips (Fig. 2b, d). Birds foraging close to the colony did presumably Wnd

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The sample of 58 trips included 36 pairs of successive trips of the same individuals. The corresponding 36 inter-individual pairs were identiWed, and the positions giving the highest Wrst-passage time for r = 140 km was found for each trip in the sample. The distances between these intensively searched areas were calculated for each intra- and inter-individual pair. Distances were log transformed in the analyses. The intra-individual distances were not signiWcantly diVerent from the inter-individual distances [mean intra-individual distance (back-transformed from log-scale) was 502 km (95% CI 350, 720), mean inter-individual distance was 541 km (391, 750)]. Accordingly, previous individual foraging experience could not explain the spatial distribution in search eVort. However, there was a positive relationship between the time interval between pairs of trips and the distance between them [
= 0.255 (0.187, 0.322), R2 = 0.45, Fig. 3a]. This relationship was evident for both intra- and inter-individual pairs [test for diVerent slopes:
= 0.025 (¡0.111, 0.161)]. The relationship between time lag and distance suggest either a synchronous shift in foraging strategy among individual birds and/or high spatial dynamics in the distribution of prey. Because a distinct ARS scale could not be found for three of the trips, the number of pairs was reduced when comparing ARS scales (33 intra-individual and 34 inter-individual pairs). ARS scales were log transformed in the analyses. ARS scale was not signiWcantly related to the ARS scale of the previous trip in intra-individual pairs [
= 0.079 (¡0.526, 0.418), Fig. 3b] nor in inter-individual pairs [
= 0.133 (¡0.202, 0.468)]. Accordingly, there were no individual diVerences in ARS scales. However, ARS scale was positively related to the time since the previous trip [
= 0.112 (0.064, 0.160), R2 = 0.25], and this was evident for both intra- and inter-individual pairs [test for diVerent slopes
= 0.059 (¡0.038, 0.156)]. This result suggests synchronous changes in feeding behavior with periods of short trips associated with small ARS scales alternating with periods of long trips associated with large ARS scales. Plots of trip duration, maximum distance from colony and ARS scale (all log transformed) against

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small-scale patches of prey shortly after leaving the colony, while birds foraging farther apart Wrst had to Wnd a large-scale patch before starting to search for small-scale patches within.

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time (days from 22 January) conWrmed a synchronous change in foraging pattern (Fig. 4). A secondorder polynomial was Wtted to the data giving a signiWcant Wrst- and second-order term for all variables tested [trip duration,
1 = 7.52 (4.39, 10.64) (£10 ¡2),
2 = ¡0.27 (¡0.35, ¡0.18) (£10¡2), R2 = 0.51; maximum distance from colony,
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2 = ¡0.26 (¡0.36, ¡0.16) (£10 ¡2), R2 = 0.49; ARS scale,
1 = 7.03 (2.03, 12.02) (£10 ¡2),
2 = ¡0.23 (¡0.37, ¡0.10) (£10¡2), R2 = 0.23]. Accordingly, short trips with small ARS scales and of short duration were found early and late in the chick-rearing period, while long trips with large ARS scales and of long duration were found in the middle of this period. Spatial dynamics of foraging areas Using SR = 140 km, we calculated and aggregated the FPT for all trips (n = 58) on a 100 £ 100-km2 geographical grid. The grid size was selected so as to

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ing close to and to the east of the colony which progressed anti-clockwise, ending up close to the colony again after about 45 days. This pattern was conWrmed by Wtting the direction of the intensively searched areas to a sine function with the mean position of all trips as a center [y = a sin(2 x/b + c), where y is sine of direction, x is time and parameter estimates were a = 0.571 (95% CI 0.359, 0.783), b = 45.2 (30.3, 60.1), c = 6.28 (5.26, 7.30), R2 = 0.34, Fig. 6b]. To investigate the spatial dynamics of any smallscale foraging areas within the large-scale areas, we used the selected part of each trip (n = 58). We chose SR = 35 km and calculated the correlograms in FPT aggregated on a 25 £ 25-km2 geographical grid. The spatial correlation among trips was positively correlated for distances up to about 100 km (Fig. 5c); however, the spatial overlap in search pattern disappeared after a few days (Fig. 5d), indicating a relatively short duration of the nested small-scale foraging area.

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Fig. 4a–c Synchronous feeding behavior. DiVerent trip parameters plotted as a function of time. a Trip duration, b maximum distance from colony and c ARS scale. Lines are Wtted by linear regressions to second-order polynomials (see text). -Jan January, -Feb February, -Mar March

maximize the overlap between trips (large grid size) but within the scale of SR. Based on this grid dataset, we calculated the cross-correlogram between trips for diVerent distances and time lags (Fig. 5). The FPT was positively correlated between trips for distances up to about 400 km, indicating the spatial scale of the area that the birds were intensively searching (Fig. 5a). However, the spatial correlation was dependent on the time lag between observations (Fig. 5b). The correlation decreased and became non-signiWcant for time lags longer than 15 days, indicating the time-scale at which the intensively searched area either disappeared or changed position. To explore the dynamics of this large-scale pattern, we plotted the selected part of each trip with the longest FPT for r = 140 (Fig. 6a). The area was intensively searched with a circular movement start-

Discussion The results of this study suggest that Antarctic petrels use a nested search strategy to track a highly dynamic hierarchical patch system. At the largest scale, the birds concentrated their search eVort at a spatial scale of more than 100 km. Within these large-scale areas, the birds searched at a scale of tens of kilometers. Interestingly, these hierarchical scales resembles the ARS scales found in a similar study on yellow-nosed albatrosses breeding on Amsterdam Island in the Southern Indian Ocean (Pinaud and Weimerskirch 2005). However, the marine habitat diVers between the two species. The yellow-nosed albatrosses foraged in subtropical waters where they commuted to predictable areas associated with meso-scale cyclonic eddies associated with enhanced primary production. In contrast, the Antarctic petrels foraged in Antarctic waters, south of the polar front with a highly dynamic spatial distribution of foraging areas. The search pattern of individual birds probably leads to an underestimation of the spatial scale of their potential foraging area. This is because a predator does not necessarily search through the entire patch before entering a patch at a smaller scale. To investigate the spatio-temporal scales of prey distribution one therefore has to compare the simultaneous foraging pattern of many predators. As sus pected, the scales indicated by the spa tial

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Fig. 5a–d Cross-correlograms in log FPT between foraging trips (n = 58). Correlation coeYcient is Pearson’s r (§ 95% CI). CIs were calculated by a jackknife procedure using trip as the statistical unit. a, b Large-scale analyses. a Cross-correlogram for varying spatial distance between grid cells. Maximum time lag was set to 8 days. b Cross-correlogram for varying time lag between grid

cells. Maximum distance was set to 200 km. c, d Small-scale analyses within the most intensively searched large-scale areas. c Cross-correlogram for varying spatial distance between grid cells. Maximum time lag was set to 24 h. d Cross-correlogram for varying time lag between grid cells. Maximum distance was set to 50 km

correlations in search eVort among trips were larger than the scales indicated by the analyses of each individual trip. At the largest scale we found foraging areas with a characteristic scale of about 400 km. Nested within these areas the cross-correlograms revealed patches with a characteristic scale of about 100 km. Moreover, our analyses indicate a surprisingly large temporal dynamic in the spatial distribution of foraging areas at both levels; the large-scale foraging areas seemed to disappear or move within a time frame of weeks while the nested small-scale areas disappeared within days. Small-scale patchiness of krill (Miller and Hampton 1989a) and observational studies from ships (Veit 1999) suggest that these birds also concentrate their search eVort at even smaller scales. Dietary analyses from birds collected in the colony indicate that the Antarctic krill is the far most dominant food item during the chickrearing period (> 70%) (Lorentsen et al. 1998). We therefore suggest that the search pattern of Antarctic petrels in this study reveals the spatio-temporal distribution of krill in the area. The conclusions from the present study are based on average values from 58 foraging trips. However,

to investigate whether the observed pattern could be generated from randomized trips, we conducted permutation tests. In this test the displacements between locations were randomly shuZed and the FPT analysis was performed on the resulting random trips. The test demonstrated that the average movement pattern of the Antarctic petrels was non-random. While the variance in FPT of the true data peaked at intermediate scales, the randomized trips decreased monotonically for increasing scale, suggesting that these analyses are robust in detecting the ARS scales of search behavior. In fact, 52 of 58 trips had peaks in FPT variance that were signiWcantly diVerent from the random trips. Interestingly, for three trips the variance in FPT resembled that of the corresponding randomized trips, suggesting a random foraging strategy. It should be noted that the same individuals performed trips with ARS behavior both before and after the “random” trip (see Appendix). Although the nested, small-scale analyses on average revealed a highly signiWcant ARS behavior, fewer trips (37) showed a clear and signiWcant peak in variance compared to the largescale analyses. This is probably due to the fact that

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Fig. 6 a Distribution of the most intensively searched areas from each foraging trip with coloring indicating the date. When grid cells were covered by more than one trip, a randomly selected grid cell is shown. Grey line represents the ice edge for the maximum sea ice extension during the study [data from Comiso (1999)]. b Sine of the direction of the most intensively searched area for each trip as a function of date. Line is Wtted by least-square estimation to a sine function (see text). For abbreviations, see Fig. 4

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Weddell Sea 70˚

% [ Svarthamaren

Antarctica Date of maximum first-passage time 21 - 25 Jan. 25 - 29 Jan. 29 - 02 Feb. 02 - 06 Feb. 06 - 10 Feb.

0

500

1000

1500 Kilometers

10 - 14 Feb. 14 - 18 Feb. 18 - 22 Feb. 22 - 26 Feb. 26 - 02 Mar.

B 1

Sin(α)

0.5

0

-0 .5

-1

0

10 20 30 40 D ate ( day s from 18 Januar y)

location error and infrequent sampling of locations had a more pronounced eVect on the small-scale analyses. The estimated mean position error (before removal of outliers) was about 14 km and would probably aVect our ability to detect ARS behavior at the scale of tens of kilometers. In the present study, the foraging pattern of the petrels was constrained by the fact that they were feeding their chick at the nest. We would expect the individual birds to rely on previous experience and return to the same foraging areas on successive trips.

50

However, the median distance between foraging areas of successive trips was more than 500 km and, moreover, this distance was equivalent to the distance between comparable trips of diVerent individuals. Instead, trip duration, trip length and ARS scale were subject to a synchronous change across individual birds where short trips were associated with small ARS scales and short duration and long trips were associated with large ARS scales and long duration (cf. Fig. 4). Synchronous changes in foraging pattern across individuals and the fact that foraging

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pattern seemed to be independent of previous experience suggest a high turnover of foraging areas. A number of studies have shown that southern pelagic seabirds alternate between short and long foraging trips while feeding their chick (e.g., Weimerskirch et al. 1997, 2003; Weimerskirch 1998). During short foraging trips parents primarily feed their chick. This has a large parental cost through high energy expenditure and body mass decline. Long trips are, however, less energetic costly, the parents gain weight while the chick has to rely on its own body reserves. Our data suggest that this alternation could be initiated by large-scale changes in the availability of prey. When food is available close to the colony the cost of transportation is low and because the expected duration of this resource is limited, the parents should give priority to the delivery of food to the chick. When the resource close to the colony disappears, the cost of transportation increases and the parents should give priority to self-feeding. According to this hypothesis the alternation between short and long trips is initiated by environmental changes resulting in synchronous changes in foraging pattern among individual birds. A number of recent models have explored the success of search trajectories in habitats with diVerent spatial arrangements of patches on a single scale (e.g., Viswanathan et al. 1999; Zollner and Lima 1999). For example, it has been suggested that wandering albatrosses (Diomedea exulans) use a “longlooping” search strategy to Wnd randomly and sparsely distributed patches of prey (Weimerskirch et al. 1993, 1994, 2005; Fritz et al. 2003). In accordance with this hypothesis, Viswanathan et al. (1996) suggested that albatrosses randomly choose movement distances from a probability density distribution with a power tail. The resulting random walk has been termed Lévy Xight pattern and is supposed to maximize the encounter rate with randomly distributed patches of prey (Viswanathan et al. 1999). However, an animal using a hierarchical search strategy will indeed generate a highly skewed distribution in displacements with a large number of short movements within small-scale patches and a few long displacements between large-scale patches (Fauchald 1999). Contrary to the suggestions by Viswanathan et al. (1996), we show that most petrels in the present study did not choose displacement distances randomly but used a non-random nested search strategy. The adaptive signiWcance of a nested search strategy is large (Fauchald 1999). In the present study, it would for example, take a very long time for a petrel to reach a large-scale patch by

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using a small-scale search pattern. The birds would, on the other hand, have a high risk of leaving a proWtable small-scale patch when using a large-scale search pattern. Nested hierarchical spatial structures are probably ubiquitous in nature (Kotliar and Wiens 1990; Wu and Loucks 1995) and we therefore believe that variants of the search strategy documented in the present study are applicable to a wide array of species and ecosystems. It is generally accepted that the spatial heterogeneity in marine pelagic ecosystems is mainly driven by physical oceanography (see e.g., Haury et al. 1978; Hunt and Schneider 1987; Mann and Lazier 1991; Hofmann and Murphy 2004). Thus, although Antarctic krill is characterized by large intra- and inter-annual variation in abundance and distribution, it is assumed that the large-scale distribution of krill is determined by passive advection (Miller and Hampton 1989a; Murphy et al. 1998; Siegel 2000; Hofmann and Murphy 2004). However, the largescale foraging areas used by the petrels in the present study moved relatively fast and in a direction opposite to the main water circulation in the area, the Weddell Gyre (Orsi et al. 1993), possibly indicating the presence of an active and massive migration of prey. The foraging areas were found south of 60°S which is heavily covered with ice until spring. At the time when the study was conducted the sea ice had retreated to about 70°S (Fig. 3a), leaving this vast area open. Few studies on krill are available from this area; however, based on an acoustic survey of krill conducted in the period February–March 1981, covering 60–70°S and 0–30°E, Miller and Hampton (1989b) concluded that: “These observations suggest widespread randomness throughout the survey area, which is consistent with the absence of pronounced hydrographic or topographic concentrating mechanisms in the region.” Obviously, more studies are needed to form a Wrm conclusion on the nature of the spatio-temporal dynamics of krill in the area. We believe that one major task in marine spatial ecology will be to understand the origin of complex hierarchical patch systems. Our results indicate that in order to reach this goal it might be important to focus on behavioral and ecological interactions in addition to advection and physical oceanography. Acknowledgements This study was supported by the Norwegian Antarctic Research Expedition and the Norwegian Research Council. We thank H. Jensen for help with Weldwork. R. A. Ims, H. Jensen, B.-E. Sæther and N. G. Yoccoz gave helpful comments on earlier drafts. H. Weimerskirch and four anonymous reviewers gave valuable comments that improved the manuscript.

Oecologia (2006) 149:383–395

393

Appendix 1

Table 1 Statistics from 58 foraging trips of Antarctic petrels. ARS scale Area-restricted search scale [scale at which the observed variance in log Wrst-passage time (FPT) peaked], Observed var(FPT) observed variance at this scale, Mean var(FPT) under

H0 corresponding mean variance assuming random displacement between locations, P(H0) probability that the observed var(FPT) belongs to a random trip, NA not applicable, NS not signiWcant

Transmitter Trip Time Max distance Large-scale analysesa Small-scale analysesb no. no. used (days) to colony (km) ARS scale Observed Mean var P(H0) ARS scale Observed Mean var P(H0) (km) var(FPT) (FPT) under (km) var(FPT) (FPT) under H0 H0 11816 11816 11816 11820 11821 11822 11822 11822 11822 19002 19002 19002 19002 19002 19002 19002 19002 19004 19004 19004 19005 19005 19006 19006 19007 19007 19007 19008 19008 19008 19008 19008 19008 19010 19012 19012 19013 19013 19014 19016 19019 19019 19019 19019 19020 19020 19021 19021 19021 19021 19023

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51

3 11 9 13 9 7 9 8 5 7 9 10 3 3 3 2 3 5 9 17 7 12 5 17 5 8 5 13 7 6 3 4 3 13 10 15 5 7 12 7 6 8 6 10 8 17 4 7 9 6 17

335 1,550 1,715 1,276 1,266 950 1,280 1,154 318 989 1,770 1,256 442 441 233 380 320 1,013 1,556 1,587 1,262 1,508 653 2,557 950 1,250 1,025 1,219 1,368 307 361 259 350 1,242 1,330 1,838 405 538 629 1,123 1,292 561 1,164 1,239 1,390 2,017 1,059 1,289 1,272 410 1,505

30 160 30 150 110 50 50 50 100 70 NA 220 110 40 20 40 40 20 80 210 90 160 30 150 40 90 60 140 120 30 80 50 40 160 100 130 80 40 40 80 140 40 160 90 130 170 60 120 NA 60 120

0.108 0.183 0.081 0.108 0.104 0.116 0.108 0.086 0.129 0.139 NA 0.082 0.118 0.086 0.086 0.110 0.116 0.0634 0.151 0.077 0.156 0.160 0.094 0.122 0.083 0.153 0.112 0.186 0.207 0.163 0.127 0.218 0.101 0.134 0.177 0.140 0.212 0.153 0.121 0.127 0.153 0.151 0.134 0.120 0.109 0.118 0.071 0.162 NA 0.216 0.102

0.091 0.052 0.070 0.050 0.066 0.062 0.078 0.062 0.041 0.068 NA 0.042 0.063 0.067 0.067 0.080 0.075 0.0575 0.058 0.047 0.060 0.067 0.072 0.052 0.057 0.055 0.066 0.060 0.052 0.110 0.045 0.082 0.053 0.054 0.062 0.051 0.146 0.126 0.083 0.069 0.043 0.075 0.048 0.066 0.047 0.058 0.052 0.063 NA 0.119 0.053

0.094 0.000 0.025 0.004 0.006 0.000 0.007 0.014 0.001 0.000 NS 0.027 0.036 0.046 0.012 0.042 0.002 0.107 0.000 0.034 0.000 0.001 0.022 0.001 0.002 0.000 0.006 0.000 0.000 0.002 0.000 0.000 0.005 0.001 0.000 0.000 0.042 0.033 0.000 0.002 0.000 0.000 0.002 0.000 0.002 0.002 0.088 0.001 NS 0.000 0.003

30 40 55 20 45 35 NA NA 20 80 NA 30 NA 35 NA 40 40 20 25 85 NA 20 NA 65 30 60 35 25 NA 30 80 15 40 NA NA NA 15 25 35 30 60 50 30 35 25 NA 20 40 20 30 85

0.108 0.089 0.068 0.102 0.120 0.101 NA NA 0.131 0.110 NA 0.076 NA 0.084 NA 0.128 0.111 0.079 0.219 0.156 NA 0.147 NA 0.241 0.079 0.155 0.090 0.179 NA 0.138 0.122 0.136 0.098 NA NA NA 0.183 0.108 0.127 0.139 0.137 0.161 0.183 0.146 0.164 NA 0.167 0.130 0.241 0.124 0.103

0.089 0.071 0.051 0.086 0.075 0.062 NA NA 0.100 0.038 NA 0.054 NA 0.066 NA 0.093 0.074 0.065 0.148 0.057 NA 0.125 NA 0.096 0.061 0.065 0.049 0.128 NA 0.092 0.042 0.102 0.053 NA NA NA 0.157 0.074 0.087 0.112 0.067 0.120 0.104 0.096 0.127 NA 0.114 0.075 0.123 0.072 0.054

0.067 0.105 0.175 0.026 0.021 0.028 NS NS 0.001 0.001 NS 0.017 NS 0.048 NS 0.062 0.009 0.076 0.006 0.002 NS 0.029 NS 0.001 0.066 0.001 0.011 0.003 NS 0.010 0.001 0.033 0.011 NS NS NS 0.008 0.007 0.002 0.056 0.011 0.089 0.001 0.024 0.022 NS 0.047 0.010 0.012 0.004 0.025

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Table 1 continued Small-scale analysesb Transmitter Trip Time Max distance Large-scale analysesa no. no. used (days) to colony (km) ARS scale Observed Mean var P(H0) ARS scale Observed Mean var P(H0) (km) var(FPT) (FPT) under (km) var(FPT) (FPT) under H0 H0 19024 19024 19024 19024 19026 19028 19028 a b

52 53 54 55 56 57 58

10 6 4 8 12 11 7

1,332 1,228 793 970 1,331 790 804

210 220 60 NA 70 30 60

0.173 0.162 0.107 NA 0.168 0.072 0.133

0.040 0.037 0.047 NA 0.087 0.063 0.085

0.001 0.000 0.000 NS 0.000 0.035 0.001

50 25 45 25 20 NA 45

0.136 0.198 0.132 0.086 0.205 NA 0.182

0.071 0.144 0.045 0.066 0.163 NA 0.108

0.004 0.006 0.002 0.024 0.007 NS 0.007

Analyses of whole trips Nested analyses within the part of each trip giving the highest FPT for scale equal to 140 km

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