Scale-dependent correlations between the abundance of Brunnich's guillemots and their

saida, pelagic am phi pods Parathemisto spp. and euphausiids Thysanoessa showed low correlations with prey at low prey densities. Similarly, correlations between guillemots and prey were low at low bird densities. The data support the hypothesis that the birds associate with prey patches with densities above a certain threshold, and that 'regional' prey abundances affect local use of patches. 5. The nwnerical aggregative response curves between guillemot and prey density were classified as being neither hyperbolic (type II) or sigmoidal (type III) within the range of prey densities observed in this study. The aggregative response curves were sensitive to spatial scales, which suggest that studies of response curves should be conducted at a range of spatial scales.


Introduction
Spatial variability in the abundance of foraging animals and the spatial interactions between predators son et al. 1997). Investigations require the use of a multiscale approach if predator selection of foraging habitat is to be identified (Schneider & Duffy 1985;Schneider & Piatt 1986;Hunt, Harrison & Cooney 1990;Russell et al. 1992;Schneider 1993Schneider , 1994. The importance of selecting the appropriate spatial scales is illustrated by the observation that the sign of association between predators and prey may change from positive to negative when the scale of observation decreases (Fairweather, Underwood & Moran 1984;Smith 1978;Schmitt 1982Schmitt , 1985Fairweather 1988;Rose & Leggett 1990).
The spatial associations between predators and prey may be considered as a special case of habitat selection in which prey aggregations are patches wi thin a larger matrix. If the distribution and abundance of prey can be assessed by the predator, the spatial distribution of a predator would be expected to follow the dispersion of the prey at fine spatial scales as predicted by the ideal free distribution model (Fretwell & Lucas 1970;Morris 1987). Alternatively, if the prey cannot be assessed by the predator because of perceptual constraints, or if habitat selection is not related to resource exploitation, the distribution of predators may or may not be associated with that of their prey.
In predator-prey systems, the numerical response curve between predator aggregation and prey density is most often described as being nonlinear (Holling 1959(Holling , 1965Hassell & May 1974). This response curve may be hyperbolic (type II) or sigmoidal (type 111), the latter being the most common for higher vertebrates (Goss-Custard 1970, 1977Hassell & May 1974;Piatt & Methven 1992). Following Hassell & May (1974) the sigmoid al aggregative response curve may be interpreted as follows: In areas with low prey density, predators do not find it worthwhile to search for prey, and thus the densities of predators will be low. In areas with increased prey density, the predators can obtain their prey more easily, and successful predators may attract more predators and this reinforces their aggregation. However, at a certain level of prey density, satiation in predator density is reached, and the response cw·ve levels off.
Seabirds are predators which are patchily distributed while foraging al sea. The patchiness of marine birds and other predators at scales < 5 km has been partially explained by patchiness in the distri bution of their prey and by the birds' selection of foraging habi tats where prey could be most profitably acquired (Hunt & Harrison 1990;Hunt er al. 1990;Hunt, Heinemann & Everson 1992). At coarser scales, seabird distributions can to a large extent be explained by hydrographic structure, even though the underlying cause of their distributions most likely is determined by prey availability (Shuntov 1974;Pocklington 1979;Brown 1980;Hunt et al. 1981;Griffiths, Siegfried & Abrams 1982;Hunt & Schneider 1987;Veit 1988).
Recent improvements in acoustic techniques for measuring marine fish and plankton densities have allowed students to investigate the strength of associations between the abundance of foraging seabirds and their prey at multiple spatial scales. There is considerable variation in the strength of correlation between seabird and prey abundance reported by various authors (see review by Hunt 1990;Hunt et al. 1992). Typically, most investigations have reported weak correlations at fine scales ( < 5 km), and most studies have shown increasingly stronger correlations at larger scales. Previous studies of distri butions of marine avian predators with respect to their prey have employed techniques that integrated prey biomass over transect segments varying in length from O· l km to I 0 km. Mehl um et al. (1996) analysed the spatial correlation between Briinnich's guillemots Uria lomvia L. and thei r presumed prey at the scale of ~ I 0 km in the vicinity of two large high arctic breeding colonies in southern Spitsbergen. They differentiated two classes of signals in their hydroacoustic data -aggregated and dispersed. They interpreted aggregated targets to reflect schools of fish or dense aggregations of large zoopla11kters, whereas dispersed targets were reflected from scattered organisms. By classifying echo types, Mehl um et al. ( 1996) were able to show that whereas correlations between seabirds and all prey combined were similar to the values found in studies reviewed by Hunt et al. (1992), correlations between guillemots and aggregated prey were among the strongest recorded for any study of seabirds.
This study focuses on associations between Brunnich's guillemots and different classes of acoustically detected prey at a range of spatial scales from 150 m to 9 km. We reasoned that if guillemots were strongly associated with aggregated prey at relatively large spatial scales, similarly strong correlations should be found at smaller scales down to the scale at which the predators no longer differentiate between subsections of an aggregation (Kotliar & Wiens 1990). This minimum scale should be set by a combination of the density structme of au aggregation as well as by the spacing between schools within the aggregation. We also investigate the shape of the aggregative response curve for Brunnich's guillemots and their prey at multiple spatial scales.

ST U DY AREA
Storfjorden is a shallow fjord with depths < 180 m located in the south-eastern part of Svalbard (Fig. la). The most prominent bathymetric feature of the fjord is a north-south orientated submarine ridge located in the western part of the fjord . The study area is usually completely ice-covered during winter. No sea ice was present during our study in this portion of Storfjorden.
Two large and several smaller breeding colonies of Briinnich's guillemots are located on the western coast . · .. The five east-west seabird transects and sampling stations included in the study, which were located to the south of the two ma in breeding colonies in Storfjorden. Each transect is separated in high (;;., the med ian) and low (<the med ian) guillemot density segments. The 100 m bathymetry contours are shown.
of Storfjorden (Mehl um et al. 1996). The populations of the two large colonies, Stellingfjellet (77°06' N, 17°20' E) and Kovalskifjellet (77°03' N, 17°17' E), have been recently estimated at about 450 000 and 90 000 individuals, respectively (Mehl um & Bakken 1994). Birds from these colonies forage in Storfjorden and in waters further south in Storfjordrenna. In Storfjorden, most guillemots forage in relatively deep waters in the western part, coincident with a weak subsurface front between warm Atlantic water and cold Arctic water (Mehlum er al. 1996).

SURVEY DESIGN
A ship-based transect study was conducted in an area where Brtinnich's guillemots from the two large breeding colonies of Stellingfjellet and Kovalskifjellet forage (Mehlum er al. 1996). The Brtinnich's guillemot was the only abundant avian consumer of larger zooplankton and fish in southern Storfjorden at the time of the study. To study relationships between gui llemot abundances and prey distribution, we selected five latitudinal transects (59-68 km in length) that ranged eastward from shallow waters near the eastern coast of Spitsbergen to 20° 00' E, at latitudes of 76° 35', 76° 40', 76° 45', 76° 50', and 77° 00' N ( Fig. lb). All transects were surveyed once during the period 21-24 July 1992. The ship travelled at a speed of 5·0-5· 5 knots and traversed ~ 150 m per minute. The transects were divided into segments, each 8-11 km in length, corresponding to the distance between oceanographic sampling stations (Fig. I b). For the analyses in this paper, data were not aggregated across oceanographic stations.

BIRDS
The abundance of Briinnich's guillemots observed sitting on the sea surface was recorded from the bridge of the research vessel Lance by standardized strip transect methods as described by Tasker et al. (1984). Bird observations were made continuously between stops at each station along transects. A 300 m transect width was used and all birds observed within the transect were entered dii-ectly into a field computer. The lowest spatial resolution of bird abundance along transects was set at I minute(or 150m).

ACOUSTICS
Details of the methods used for bioacoustical recordings are described by Mehlum et al. (1996). We used a single beam/single frequency echo sounder (LAZ 4700 ELAC) operating at 30 kHz, and recorded echoes on a ping by ping basis. The transducer with a beam angle of 16° was mounted inside a V-fin body towed at a depth of2-3·5 m. Because we did not know the target strength of the organisms detected by the echo sounder, echo signals are represented as Volts 2 • Estimates of biomass are not essential in this study because we are interested in relative differences in acoustically detected biomass between different parts of transects. During most of the transects, the sea was calm (0-1 Beaufort scale), and unwanted noise and excess atten uation of acoustical signals from bubbles was low.
Post-processing of echo signals included filtering out the ship's echo sounder signals, echo type recognition, and integration of echo intensity at I-min ( 150m) intervals along the u·ansects. The sampli ng window for the quantitative analysis was in the interval from JO to 50 m depth. The acoustic signals were classified into two groups: dense concentrations of targets (echo type A -aggregated) and dispersed targets (echo type D -dispersed). A simple algorithm for discriminating between the two different type of echoes was developed based on the dimension and the strength of the echoes. The methods used for removing echoes from the ship's depth sounder are described by Mehlum eta!. (1996). The algorithm for discriminating between the two types of targets is presented in Appendix I. ANALYSES We analysed correlations between guillemot abundance and acoustic biomass along transects at scales ranging from 150 m to 9 km. When calculating correlations within each transect segment (8-1 I km), the largest spatial scale (bin size) used was 2·0 km. For analyses using a bin size of 2 km, the number of bins per transect segment varied between 3 and 5. For analyses using bin sizes smaller than 2 km, the number of bins per correlation statistic increased with decreasing bin size. When combining data from all segments, the sample sizes permitted analyses at scales up to 9 km (sample sizes ranged from 12 for 9 km segments to 1780 for 150 m segments).
Statistical analyses of guillemot and acoustical data were performed usi ng STATISTl.CA vs. 5·0 (Statsoft, Tnc. 1995), assuming 2nd order stationarity (i.e. expected value and variance constant for any subset of a time series) in guillemot and prey abundance within each 8-11 km transect segment. Because the Pearson correlation method is not robust to 'outliers' or asymmetry in data sets, we preferred to use nonparametric Spearman rank correlations. However, as most previous studies correlating seabird and prey abundances have used the Pearson method, we also present results using this method for comparative purposes in our initial analyses. If the two methods yielded similar results in the initial analyses, we selected the Pearson method for the subsequent analyses. We used autocorrelation analysis to investigate serial dependency in the abundance of guillemots within transect segments.
On transect segments with low bird densities we expected to obtain no or only weak positive correlations between the abundance of guillemots and their prey because there would be too few birds to provide proportional coverage of all prey patches available. We therefore selected transect segments with guillemot abundance ~ the median for further analyses of correlations between bird and prey abundance. To investigate the ability of the predator to track prey patches, we calculated cross-correlations between guillemot and the aggregated type prey at the smallest scale possible (150 m).
To characterize the horizontal dimension of prey patches, we used two different methods. In the first method, we determined the upper 25%, the median, and the lower 25% values of the distribution of acoustic return in all 150 m bins (n = 1780) surveyed during the five transects. These values were selected as thresholds for acoustic values above which we would classify the return as belonging to a prey patch. We then estimated the length of a patch (chord length) in a transect segment as the distance between contiguous bins with acoustic values above the threshold. Similarly, we estimated the interpatch distance as the distance between contiguous bins below the acoustic threshold.
The second method for characterizing prey patch dimensions was based on wavelet analysis (Bradshaw & Spies 1992). We also used wavelet analysis for tks1.:ribing pald1 dimensions uf foraging guilkmuls. This method is useful for analysing nonstationary or nonsinusoidal mu ltifrequency data (Bradshaw & Spies 1992;Bradshaw&Mclntosh 1994). Itcandetect aggregative patterns in lime series (or along transects) at different scales which may be overlooked by methods such as the Fourier spectral analysis.
We used the WaveLab 0·7 Toolbox (Stanford University freeware) under MATLAB (Math Works, Inc.) for calculating the wavelet transform at different spatial scales of aggregated prey and guillemot densities, respectively, in each transect segment. The selected analysing wavelet was 'Sombrero', which is similar to the 'Mexican Hat' wavelet described by Daubechies (1988). The wavelet variance was applied for detecting the spatial scales which dominated the spatial patterns in the data. This function is given for a specific scale as the average of the squares of the wavelet coefficients at every point along the transect at this scale (Bradshaw & Spies 1992). Large wavelet variance at a scale identifies this scale as important for describing the spatial pattern along the transect.

GUILLEMOTS
The average number of Briinnich's guillemots observed per minute in the 33 transect segments was 0·60 ± 0·76 (SD) (or 0· 18 ± 0·23 individuals per km 2 ), and median guillemot abundance was O· 31 birds per min (or 0· 11 birds per km 2 ). The locations where guillemot abundance was ~ the median ( = high) is shown in Fig. lb. Of the 18 transect segments in which guillemot densities were ~ the median, only two segments showed significant (P < 0·05) autocorrelation at a lag of 1 for the lowest bin size (I min or 150 m), but none of these autocorrelations was above 0·5. This indicated that the serial dependency of guillemot observations at a bin size of 150 m was negligible.

SCALE-DEPENDENT CORRELATION BETWEEN BIRD AND PREY ABUNDANC E
The strength of correlation between Bri.innich's guillemots and the acoustically determined biomass of presumed prey varied with bin size and whether prey were aggregated or dispersed. Using data from all 33 transect segments, we found that correlations between birds and acoustically detected biomass were weak at the smallest bin sizes, but increased, and then more or less stabilized, at bin sizes between 2 and 9 km (Fig. 2). Correlations between guillemots and acoustically detected biomass were consistently stronger for aggregated biomass than for diffuse biomass, regardless of bin size (Fig. 2). The Pearson conelation coefficient for guillemots and aggregated biomass stabilized at about r = 0·70 for bin sizes ~ 3 km. The differences in guillemul responses to biuma:;s aggregation were most striking when Pearson correlation's were used, especially for bin sizes of 3-9 km.

AMONG TRANSECT SEGMENTS
Correlations between guillemots and acoustically detected biomass were sensitive to the total density of prey (Fig. 3) and the average density of foraging guillemots within each transect segment (Fig. 4). For bin sizes between 0·3 and 2·0km, scatter in the distribution of Pearson correlation coefficients for individual transect segments in relation to summed (averaged) acoustic return increased markedly once echo return values fell below about 100 V 2 (Fig. 3). Above this value, correlation coefficients increased gradually with increasing acoustic biomass, and the correlations were consistently strong at relatively high acoustic biomass. Similarly, in transect segments where the average guillemot density was below about 0·2-0·3 birds km-2 , there was a wide scatter in Pearson correlation coefficients between guillemots and acoustic retum; the three data points above these values showed strong correlations (r > 0·80) over a range of bin sizes from 0·3 km to 2·0 km (Fig. 4).
We found differences between transect segments in the strength of the correlations between guillemot and echo returns. When calculating correlations between guillemots and aggregated biomass for each of the 33 F. Melzlum et al.     transect segments separately, we found that strong correlations (here defined as r ~ 0·6) were infrequent at bin sizes below 600 m, but were encountered in between 30% and 48% of correlations computed using larger bin sizes (Table I). When we used the 18 transect segments in which bird densities were ~ the median for all segments, strong correlations were obtained in 33-61 % of segments when bin sizes were ~ 600m.
[t is possible that our analyses underestimated the actual strength of the correlations reported above because of imperfect match between predator and prey aggregations. We performed cross-correlation analyses at a bin size of 150 m for transect segments with guillemot densities ~the median value. We found that the aggregations of guillemots were offset from prey aggregations in all 18 cases where significant cross-correlations were encountered at lags ~ I· 5 km (Fig. 5). Jn 12 segments, the strongest correlations were obtained between -3 and + 2 lags, equivalent to the prey being lagged 450 behind and 300 m in front of the birds along the transects, respectively. Examiuation of the spatial distribution of these lags with respect to the side of prey patches nearest the guillemot breeding colonies showed no tendency of the guillemots to use preferentially either side of prey patches (Mann-Whitney U-test, U = 126·0, P > 0·05).

AGGREGATIVE RESPONSE OF BRLJNNICH'S GUILLEMOT TO PREY DENSITY
The aggregative response of B1iinnich's guillemots showed no consistent pattern for low bin sizes ( < I km), but at larger bin sizes (1-4 km) we generally  obtained a positive response in bird density with increase in prey abundance (Fig. 6). There was a wide scatter in the data, but in general the data followed a concave curve and neither a hyperbolic (type JI) nor a sigmoidal (type III) curve. The number of high prey density data points was too low to let us draw a conclusion about the shape of the upper part of the curve.

PATCH SIZE CHARACTER ISTICS
The average sizes of prey patches depended on the a r bitrary threshold levels of echo return set to define ..

100
Bin size 3 km 1000 a patch. If we included only prey densities in the upper 25% of echo values from all 150 m bins, mean patch chord length was estimated to be 372 m and the mean interpatch distance was 992 m (Table 2). ln contrast, if the threshold for detection of a patch was set to include all echo return values above the bottom 25%, t hen the average length of a patch chord was 1107 m and the average distance between patches was 399 m.
T he wavelet analysis of acoustic biomass in the 33 transect segments showed the h ighest wavelet varian ce at small spatial scales (150-300 m), indicating that these scales dominated the spatial structure of our t ransect data. The curves representing wavelet vari-0 10 100 1000 Bin size 2 km ..  ance as a function of spatial scale for acoustic biomass showed qui te large individual variations but were of three major types (Fig. 7): 1. in seven cases (2 1 %),variance generally decreased with increasing scale; ., 2. 18 cases (55%) were similar to type 1 but with a second peak in variance at intermediate scales; and 3. eight cases (24%) were similar to type 1 at small and intermediate scales, but showed increasing va riance at larger scales. The high percentage of type 2 curves indicates that the acoustic biomass showed spatial structure at intermediate as well as small scales. The peak in variance at intermediate scale in the type 2 curves (mean ± SD = 1220 m ± 570 m, median = 1100 m, range = 600 m -2·7 km) was in the range of values obtained in our estimates of the distance between peaks of prey patches. This distance averaged 1363, 1129 and 1506m (calculated from Table2), when patches were defined by echo returns above the upper 25%, above the median, and above the lower 25% of all the 150 m bin echo values, respectively.
Wavelet analysis of guillemots in the 18 transect segments with guillemot abundances ~ the median value showed patterns similar to those found in the wavelet analysis of the acoustic biomass. For all segments, the highest wavelet variance was obtained at the lowest spatial scale (150-300 m). Four segments (22%) showed type I curves, l l segments (6 1 %), exhibited type 2 curves, and three segments (17%) type 3 ..  curves. The predominance of transect segments with type 2 curves of wavelet variance with peaks at scales 600 m to 2·3 km (mean ±SD= 1420 m ± 590 m, median = 1350 m, range = 600 m -2· 3 km) was interpreted as an indication of a spatial stmcture of the guillemot distribution. The scale of the intermediate peak in predator wavelet variance in type 2 curves was similar to the scale at which there was a corresponding peak in wavelet variance for acoustic biomass, as well as the distance between the centres of neighbouring prey patches (Table 2).

Discussion
Diet analyses of Brilnnich's guillemots collected during the study period showed that crustaceans and fish were the main prey items (Mehlum et al. 1996). The crustaceans consisted mainly of two species of pelagic amphipods, Parathemisto abyssorum and P. fib ellula , and the euphausiid Thysanoessa inermis. Of fishes, polar cod Boreogadus saida occurred most frequently, whereas capelin Ma/lotus villas us was encountered less frequently. These prey species are the most abundant pelagic fish and large zooplankton species in the northern Barents Sea region (Sakshaug et al. 1994).
Although we had no information on the composition of the biomass from which we obtained echoes, we interpreted the class of aggregated targets as being from schools of fish or dense aggregations of large zooplankters such as Para1hemisto spp. and Thysanoessa inermis.
Our results show that spatial correlations between aggregated determined biomass and Briinnich's guillemot densities along ship transects were weak at small bin sizes and increased strongly at bin sizes between 150 m and I km, reaching a plateau at a bin size of 2-3 km. Thus, the transition region between low and high spatial association of guillemots and their prey occurred at scales where the spatial variance in prey biomass was high (Fig. 7). Our wavelet analysis showed that the spatial varia11ce of both guillemot distribution and presumed prey biomass showed a peak at these scales. Similarly, Logerwell et al. ( 1998) found peaks in spatial variance around 3 km and greater for Brilnnich's guillemots and at 2 km and greater for prey in a study in the Bering Sea using spectral analysis. They found little spatial varia11ce at smaller scales.
The increase i11 correlation strength with increasing bin size is in agreement with those of most other workers (see review by Hunt eta!. 1992), and may be the result of reduction of the variance from aggregating data. However, the finding that correlation values reached a plateau at a bin size of2-3 km is new, and suggests that at least a portion of the change in correlation strength with bin size reflects the scale at which guillemots in this study were related to prey distributions. Our transects were too short to docu-ment the strength of association between guillemots and their prey at scales larger than 9 km.
Our correlation analyses showed that there was a low spatial association between guillemots and their prey at the smallest scales ( < I km), and our crosscorrelation analysis showed that the guillemots did not perfectly track the patches of prey at the smallest scales. We interpret these results as indicating that the guillemots were indifferent (Kotliar & Wiens 1990) to patches at these scales. Thus, in the terminology of Kotliar & Wiens (1990) we argue that the first-order patchiness, or gra in, of prey patches as perceived by the guillemots occurred at scales close to l km. Alternatively, the lack of association between foraging seabirds and their prey at small spatial scales might be explained by the patches being too ephemeral for the birds to track (Hunt & Schneider 1987), or that there was a spatial shift or drift that resulted in a displacement of the predators subsequent to foraging on their prey (Veit, Silverman & Everson 1993).
In this study, we split the echo signals into aggregated and dispersed biomass, respectively. Correlations between guillemots and aggregated prey biomass were much stronger than with diffuse biomass. Also, the correlations between guillemots and aggregated prey were stronger compared to most previous studies, where no differentiation between aggregated and diffuse biomass had been made (Hunt et al. 1992). This result agrees with previous studies which have indicated that correlations between aggregated prey, such as schooling fish (capelin) or surface swarming zooplankton (McClatchie, Hutchinson & Nordin 1969), and birds are stronger, and often at smaller bin sizes (Schneider & Piatt 1986;Erikstad, Mourn & Vader 1990) than correlations with prey that form diffuse patches (Hunt et al. I 990, 1992). In a recent study of association between guillemot Uria spp. density and acoustic biomass of capelin schools, Skarsfjord (1995) reported stronger correlation coefficients at scales of 15-41 km than those reported for BrUnnich's guillemots and aggregated prey in the present study (scales 2-9 km). As stated by Mehlum et al. ( 1996), om· results suggest that in future studies it will be important to separate diffuse biomass from aggregated biomass. This will require a ping by ping recording of data for post processing of the acoustic returns, something that has also been lacking in most previous studies which have integrated primary echo returns over hundreds to thousands of meters.
Our results show that the strength of the spatial association between the guillemots and the presumed prey biomass is sensitive both to prey abundance, as did Veit el al. (1993), and predator abundance. Strong correlations between guillemots and prey were only found when mean guillemot densities within transect segments were above a threshold of 0·2-0·3 birds km· 2 • At lower bird densities there may have been too few birds to provide a match between the abundances of birds and their prey.
When prey is scarce, a high quality, but isolated, patch has a lower probability of being used by a predator than an intermediate quality patch in close proximity to a high quality patch (Milne, Johnston & Forman 1989). Thus, whether a prey patch is used depends on the overall quality of the 'region' within which Lhe prey patch is embedded. Guillemots, apparently did not select relatively dense prey patches in transect segments where average prey densities were below a biomass corresponding to the top third of maximum prey biomass recorded during this study. This pattern was evident for bin sizes of 0·3-2·0 km, but was most pronounced at the largest bin sizes. We interpret this result to indicate that unless a region had a relatively high biomass of prey, the guillemots made little effort to prospect it for patches of high density (see also Veit et al. 1993). This may be similar to the foraging by 'expectation' shown by Gibb ( 1962), or it may represent threshold foraging, where the threshold is set for a region rather than for an individual patch. Threshold foraging behaviour at different prey densities has been suggested forcapelin predators such as common guillemots Uria aalge and Atlantic puffins Fratercula arctica (Piatt 1990) and guillemots Uria spp. (Erikstad et al. 1990), and for baleen whales (Piatt & Methven 1992).
The numerical aggregative response curves (Fig. 6) between guillemot and prey density were sensitive to spatial scale. Consistent responses were not obtained at small spatial scales ( < I km), but strong positive responses were evident at larger scales. The response curves could not be classified as being hyperbolic (type II) or sigmoidal (type III) within the range of prey densities observed in this study. As pointed out by Hassell & May (1974), it is difficult to resolve the shape of the upper part of the response curve without an adequate number of data points representing high prey density. It is likely that Briinnich's guillemots in the study area sometimes encounter higher prey densities than those observed by us. Under such circumstances the aggregative response curve might level off and approach the sigmoidal type, which is most common for higher vertebrates (Goss-Custard 1970, 1977Hassell & May 1974;Piatt & Methven 1992). Our results are similar to those obtained in a study of several shorebird species (Bryant 1979), in which strong correlations were obtained between invertebrate prey density and the density of foraging birds. Bryant (1979) also observed no levelling off of the aggregative response curves at high prey densities.
Our results illustrate that the aggregative response of predators to different prey densities should be studied at a range of spatial scales (Horne & Schneider 1994). Only a single spatial scale was considered in the original descriptions of the aggregative response curve between predator and prey density (Holling 1959(Holling , 1965Hassell & May 1974). Piatt (1990) choose a single spatial scale of 2·5 km in his study of spatial association between two capelin predators, common guillemot and Atlantic puffin, and their prey. He found a sigmoidal aggregative response in about onethird of his transects and suggested that the response was best resolved at spatial scales similar to the scale of aggregations ( ~ 2-4 km). Our data showed a similar strong aggregative response within this range of spatial scales.
Ecologists have long recognized that predators are sensitive to the disttibution and availability of prey. By using a continuous record of predator and prey numbers over long transect lengths, we have been able to demonstrate the range of distance scales over which predators show sensitivity to variation in prey density. Using these techniques we have also been able to demonstrate that 'regional' prey abundances affect local use of patches. Detection of these effects would have been problematic using survey methods with discontinuous sampling. Our results are important because they nol only confirm that there is a lower limit to the grain size that predators will discriminate, but also that predators respond to the major variations in their resource landscape, which correspond to the size and spacing of the major aggregations of prey.