Spatial autocorrelation in marine birds DAVID C. SCHNEIDER Schneider, D . C. 1990: Spatial autocorrelation in marine birds. Polar Research 8, 89-97. All marine organisms exhibit some degree of spatial autocorrelation, which is the tendency for high (or low) densities to occur in proximity, rather than at random in the ocean. Autocorrelation occurs at scales ranging from the length of the organism to thousands of kilometres. Autocorrelation results from a wide variety of mechanisms, many of which act at characteristic scales. Consequently, some insight into causal mechanisms can be obtained from exploratory analysis of the scalc and intensity of autocorrelation of abundance or behaviour, and the scale and intensity (coherence) of cross-correlation with environmental variables such as water temperature or prey abundance. This paper uses seabird counts along extended transects t o illustrate standard measures of autocorrelation and cross-correlation. A brief discussion of exploratory and confirmatory analysis of autocorrelated data on marine birds follows. David C. Schneider, Ocean Science Centre, Memorial University of Newfoundland, St. John’s, Newfound- land, Canada, A I B 3x7; January 1989 (revised August 1989). Intuitive measures of autocorrelation Prior t o 1980, measurement of seabird abundance and behaviour occurred almost entirely at stations with fixed coordinates, separated by large distances. The unit of measurement was a count standardized by time, by length of a strip transect, or by area of a strip transect (Tasker et al. 1984). The method was well suited to large scale surveys (e.g. Shuntov 1974; Brown et al. 1975), which necessarily sacrificed information on smaller scale heterogeneity (Devillers 1978) in the interests of observer alertness. Through a fortunate cir- cumstance I was able to make spatially continuous counts along hundreds of kilometres of ocean in conjunction with PROBES, a multi-disciplinary investigation of circulation and biological pro- duction in the southeastern Bering Sea. The for- tunate circumstance was the sampling design of PROBES, which consisted of measurements at stations separated by 25 km along a 500 km tran- sect, running from the edge of the continental shelf northeastward toward the coast. By counting continuously between stations, I was able to obtain spatially (though not temporally) con- tinuous counts along the hundred or more kilo- metres that the ship traversed during the long daylight hours of mid-summer in the Bering Sea. Of course, I soon learned what many previous observers must have noticed, which is that one can expect to see many birds ahead if one sees many birds during the present count, and con- versely, few birds ahead if few birds are currently in sight. This meant that one had to exert extra effort when counts were low, the expectation of few birds ahead tending to re-inforce itself through relaxation of attention. After two traverses of the PROBES line in late May 1980, it also became clear that systematic increases and decreases in bird abundance occurred over distances of tens of kilometres, a pattern that had not been previously reported in marine birds. The pattern in the Bering Sea was repeatable from year to year. Fig. 1 shows the July 1982 distribution of birds along the same transect that was traversed in May 1980, Coarse- scale (1 t o 100 km) aggregations have now been reported in marine ecosystems as diverse as the California Current (Briggs et al. 1984), the Beng- uela Current (Schneider & Duffy 1985), the Lab- rador Current (Schneider & Piatt 1986), and the Agulhas Current (Abrams & Lutjeharms 1988). The Bering Sea transect could not be analysed by standard techniques for continuous data because of breaks in the series during nighttime transit between stations. The solution that I adopted, working from analogy with the structure of much smaller aggregations (Hoffman et al. 1981), was t o assume a characteristic structure for these aggregations - attenuation in density with increasing distance from some focal point. The analytic procedure was t o construct filters of vary- ing widths, each with the peaked shape of a hypo- thetical bird aggregation, slide each filter along the transect, and measure fit of the data to the 90 D. C . Schneider (slopel 1 Outer I I Middle I F F F 0 lo4 1- NORTHERN FULMAR 40 y 30 E r v) g 20 10 0 700 600 500 400 2 300 m 200 I00 x SHEAR WATERS IL f 1 , , I , I I I f I , , I I ) ( , I 2 4 6 8 10 12 14 16 18 20 22 Fig. 1. Abundance of fulmars Fulmarus glacialis and dark- bellied shearwaters, primarily Puffinus fenuirosrris, along a 534 km transect, running from the shelf break northeastward across the Bering Sea toward Cape Newenham. Transect begun 26 July 1982, completed 28 July 1982. Redrawn from Schneider, Hunt & Harrison (1986). A Stations filter at successive positions along the line. The analysis (Schneider 1982) showed good fit (r2 ranging from 77% to 95%) at two fronts, poor fit (r2 less than 77%) along the rest of the transect. This result meant that ten-minute counts (each approximately 3 km long) were autocorrelated at lags (separations) ranging from 1 (adjacent counts) t o 3 (half the observed chord length of an aggregation) near the two fronts. A simple Monte Carlo analysis, using random rearrangements of the observed ten-minute counts, showed that erroneous identification of structured aggre- gations (Type I error) by this filtering procedure was small (4%). Fig. 2 shows the location of 0.8 t A 0.7 - 0.6 - 0.5 Y 0.2 O 3 I I ------------d 2 4 6 8 10 12 14 16 18 20 22 24 STATIONS Fig. 2. Location of structured aggregations along same transect line as shown i n Fig. 1. Transect begun 31 May 1981, completed 3 June 19x1. Delta-t is a measure of change in thermal structure between adjacent stations. Redrawn from Schneider (1982). structured aggregations of seabirds along the tran- sect in June 1981. One extension of this analytic approach is to use a wider variety of filters, guided perhaps by a formal or informal model of patch shape. Abrams & Lutjeharms (1988) used bell-shaped (Gaussian) filters centred o n areas of high SST gradient to examine the relation between seabird abundance and fronts. Abrams used a routine from the BMDP package, a considerable savings in effort over the hand computations used in the analysis of the Bering Sea data. Still more sophisticated approaches can be found in the literature on digital filtering (e.g. Mendel 1987). A related approach, developed by Cliff & Ord (1973), is to test whether observed abundances fit a hypothetical pattern of association between counts, whether adjacent or not. This method requires specification of a join structure - some a priori pattern of relatedness in space against which to test the data. This technique has proved most useful in the analysis of discrete geographic units of unequal size (such as counties) and readily Spatial autocorrelation in marine birds 91 improvement in our analyses by using statistical control t o remove the effects of autocorrelation. Intuitively we might anticipate autocorrelation of marine bird counts at separations of tens of metres, because individuals of many species move toward other birds to form loose aggregations at this scale. The same observation leads us to anticipate less autocorrelation at separations beyond the limits of visual contact. These limits might vary from tens of meters for birds sitting on the water to several kilometres for large-bodied soaring species. This observation on seabird behaviour suggests that equation (1) might hold true for marine birds at separations ranging from tens to thousands of metres. An analysis of autocorrelation was carried out with data on the abundance of gliding species along a transect running westward across the Lab- rador Shelf, through a narrow pass with strong tidal currents (Gray Strait) and then out into Hudson Strait (Fig. 3). Turbulence in this passage reaches extraordinary levels. Turbulence in Gray Strait was evident in the motion of the research vessel (CSS ‘Hudson’ c. 7 0 m in length), which lurched laterally as it steamed at 11 knots relative to the water. Boils of water as large as the ship rose to the surface around and under the ship as it passed through the strait. Birds were observed hovering around these boils, which may have been bringing food to the surface. Marine bird concentrations have been reported in straits with turbulent flow in the Gulf of Maine (Braune & Gaskin 1982; Mercier & Gaskin 198.5), on the west coast of Scotland (Bourne & Harris 1979) and in the Bering Sea (Gould et al. 1982). Marine specified join structure (such as roads linking counties). The spatial scale of autocorrelation In marine ecosystems one rarely has any basis for specifying a join structure, but one often has enough data to measure the strength of auto- correlation between counts as a function of dis- tance between counts. In oceanography one needs to know the spatial scale of a phenomenon before one can proceed to estimating rates or investigate underlying processes. One way of determining scale is to ask whether the values of a variable are associated with previous values and over what distances. A correlation coefficient (e.g. the fam- iliar Pearson coefficient, r) can be calculated at increasingty large lags s to produce a vector of autocorrelations r(s). These numbers can be plot- ted against lag to obtain a correlogram. Sokal (1979) discusses the use and interpretation of correlograms in ecological contexts. One use of the correlogram is to determine how widely spaced counts need to be in order to be considered spatially independent. One should use separ- ations at which r(s) lies ‘near enough’ to zero. Correlograms of ecological data often show association at small lags, decaying to negligible association at larger lags. If such is the case, r(s) can be modeled using the exponential decay function: r(s) = e-ks where r(s) is the autocorrelation at lag s , e is the base of natural logarithms, and k is a constant decay rate to be estimated from the data. When s equals zero, r(s) equals one. An appropriate autocorrelation function can be used to filter out autocorrelation within a series (Box & Jenkins 1976), allowing accurate tests of treatment effects (e.g. ‘More birds here than there?’) with statistical control for autocorrelation of contiguous or closely spaced counts. This is a solution to the problem of ‘pseudo-replication’ (Hurlburt 1984), if one can estimate the auto- correlation function. How much autocorrelation can be expected in counts of marine birds along extended transects? If strong autocorrelation occurs in distributional data, then we need to worry about its effects on our analyses, and we can expect considerable 90’ 6 0 ° W 60°N 65’ 64-30’W Fig. 3. Location of 42.9 km transect through Gray Strait 92 D . C. Schneider 4 0 - 20 - Table 1 . Number o f birds observed along a transect through Gray Strait on 18 September 1985. Transect was 42.9 km long, starting at 1311 hrs. GMT, ending at 1440 hrs. GMT. F glacialis on water ~~ Species On water Flying F. glacial& 234 R . tridactyla 8 L a m s hyperboreus 0 321 2 113 bird abundance in areas of high turbulence, rela- tive to adjacent areas, has not been quantified. Counts through Gray Strait were made on one side of the ship out t o the limit of visibility, which was 100 m in foggy conditions. Table 1 shows the species and behaviour of all birds observed along the transect. Fig. 4 shows counts of the three most abundant groups - fulmars Fulmarus glacialis in R tridactyla flying 6o 1 F. glacialis flying Fig. 4 . Counts of flying birds (fulmars and kittiwakes) and birds on the water (fulmars) along Gray Strait transect. Counting interval of L = 0.3 km used to present data. the air, fulmars on the water and kittiwakes Rissa tridactyla in the air. Fig. 5 shows the auto- correiation of counts at lags from s = 0 to s = 100 (2 km). Flying fulmars were more strongly autocorrelated than fulmars on the water and flying kittiwakes. Fulmars in the air showed a pattern of autocorrelation at lags close to mul- tiples of 5 (100m). This is approximately the diameter of large boils of water upwelling to the surface in the strait, so one interpretation is that fulmars were aggregating in relation to these physical structures. None of the three analyses showed local auto- correlation decaying to negligible correlation at distances beyond the limit of visibility. Significant autocorrelation occurred at some lags, but no consistent pattern emerged in comparing one species across several transects, or in comparing several species along the same transect. Auto- correlation was weak (r(s) < 0.3) in the Gray Strait data. The spatial resolution was 20 m, so it will be interesting to see if weak autocorrelation proves generally true of marine bird counts taken at different spatial resolutions. Rather than looking at correlation as a function of increasing lag, one can divide continuous data into a sequence of counts in contiguous intervals, beginning at the interval of minimum spatial reso- lution and proceeding to larger intervals. If seabird counts are recorded directly on paper while underway, the minimum practical recording interval is 1 minute, corresponding to a spatial resolution of approximately 300 m at a ship speed of 10 knots (c. 5 m SKI). With a computer one can record sightings at temporal resolutions of a second or less t o obtain spatial resolutions of 10 m or less at ship speeds of ten knots. The traditional resolution used in seabird work has been 10 min- utes, or roughly 3 km at ship speeds of 10 knots. One consideration in choosing the minimum reso- lution interval is that more information can be extracted from high resolution than from lower resolution data. Another consideration is that one can always construct lower resolution data (e.g. a sequence of ten-minute counts) from higher resolution data (e.g. a sequence of one minute counts) but not vice versa. A natural step at this point is to ask what happens if one changes the recording interval, either through better instrumental resolution, or as a way of looking at the data. The mean (per count) at any given recording interval can be calculated from the mean obtained at any other Spatial autocorrelation in marine birds 93 F. glacialis on water F. glocialis flying R. tridoctylo flying -01 0 01 0 2 03 -01 0 01 0 2 03 0 4 0 5 -01 0 01 0 2 .L L.LL-.A--.l- I. Fig. 5. Autocorrelation of flying birds (fulmars and kittiwakes) and birds on the water (fulmars) along Gray Strait transect. Dotted lines are 95% confidence intervals. recording interval. Let Ni[L] denote the observed count in the ith interval of length L, and let N[L] denote the mean of the Ni[L] counts. Explicitly, , m N[L] = Ni[L] m i z 1 where m is the number of intervals of length L in a transect of length T. If LO is the length of the minimum observable interval, then it can be shown that NIL,] = 1 "L] n (3) where n = L/Lo, the number of minimum reso- lution intervals within an interval of length L. Quantities L , L,, and T have the same units, such as kilometres. Equation (2) states that from any set of observations Ni[L], one can infer the mean count at intervals of any other length. What about the variance calculated at scale L, Nz[L]? This quantity, like N[L], is a function of L: -- Nz[L1 - Var(Ni) i = 1 to TL-' n (4) This quantity, unlike the mean N[L], cannot be rescaled to a constant. However, we do find that we have computed a familiar quantity, the mean squared variance among groups, MSamong: l m r n - l i = l Var(Ni) =-x (Ni[L] To see what happens when we change interval length L, we can begin with a transect of length T marked off into intervals of minimum resolu- tion, Lo, then calculate the variance at this scale, N2[Lo]. We can then group adjacent intervals into pairs to obtain intervals of length L = 2Lo. The variance at this scale, N2[2Lo] is: N2[2] = Var(Nkft + NFght) i = 1 to TL-' ( 6 ) where NPft symbolizes counts on the left side of pairs and NFght symbolizes counts on the right side of pairs. Consequently, N2[2L0] = Var(Npft) + Var(Nf'ght) + 2rl,Var(NYR) Var(NFght) (7) where rlr is the correlation between adjacent (left and right) subintervals. Dividing this equation by n, we obtain: M S a m o n g = M S w i t h i n + 2rl,n-'Var(N!,eft)Var(NFght) (8) 94 D. C. Schneider From this equation we see that if adjacent subintervals (left and right) are not correlated, then rlr will be zero and the variance at the scale of intervals (MSamong) will be the same as the variance at the scale of subintervals (MSwlthln). If adjacent subintervals are positively correlated, then variance at the scale of intervals (MSamong) will exceed variance at the scale of subintervals (MSwlthln), depending on the strength of corre- lation, rlr. If adjacent subintervals are negatively correlated, then the variance at the scale of inter- vals will be less than the variance at the scale of subintervals. This can be generalized to larger subintervals by grouping adjacent pairs to obtain intervals of L = 4L0, grouping these pairs to obtain intervals of L = 8Lo, etc. We obtain a similar result if we use the variance- to-mean ratio at successively larger intervals because: N*[L] I”L] = - “LI N*[L] “Lo1-I --. - n Scaling of the variance to the mean in this fashion produces a statistic that, in theory, will not vary with change in scale L as long as counts are independent (not autocorrelated), In practice, some systematic change in I’[L] with change in L can occur because of increase in bias (Reed 1983), as the number of intervals (m = TL-’) decreases (L increases). In working with seabird counts, my experience has been that this problem is serious enough to preclude attempts to estimate the true value of I’[L], but not serious enough to preclude plotting I‘[L] against L to look at scale-dependent structure in abundance of birds along transects. Not all measures of variability have the property of being theoretically independent of L if counts are independent (uncorrelated with themselves). The measure of variability advocated by Green (1979), for example, varies with L when random numbers are used. To obtain an idea of the spatial scale at which chord length of a patch. This is the contiguous quadrat method of Greig-Smith (1952), which was modified for line transect by Kershaw (1957). The contiguous grouping method has been used to examine the scale of variability of seabird counts (Schneider & Duffy 1985) and to show that cor- relation between alcid abundance and capelin prey changes with spatial scale (Schneider & Piatt 1986). Fig. 6 shows the results of contiguous grouping of the kittiwake data from the Gray Strait transect. More birds were observed in the strait than on either side; this shows as an increase in variability at grouping intervals of more than half an hour, equivalent to interval lengths of 8 km or more. We began by thinking about change in varia- bility with increase in the length of the counting interval. We then plotted a measure of variability, the variance-to-mean ratio, among contiguous intervals. The abscissa is the bin size, or frame size: 1 minute count, 5 minute count, 10 minute count, 20 minute count, etc. (Fig. 6). We can think about the abscissa of this plot in another way. It is a measure of the frequency of counts along a transect of fixed length. For a 16km transect we have 1/16, 2/16, 4/16, etc. What we have done is to have plotted variability against frequency, with high frequencies on the left, low frequencies on the right. The jargon term for this operation is ‘working in the frequency domain’. The contiguous grouping method (where stat- istics are calculated in the frequency domain) is related to spatial autocorrelation (which is cal- culated as a function of separation) through the 8 0 0 8 I I m m L . o variability is concentrated, one can plot the vari- ance among groups against the length of the 0.02 0.08 0.32 1.28 5.12 20.48 counting interval, L. One expects variability to correlated). One expects variability to increase until one reaches the interval roughly equal to the BIN SIZE (Km) be unchanged if counts are independent (not auto- Fig. 6. Variability, as measured by the variance-to-mean ratio I’[L], of kittiwakes on Gray Strait transect. L is grouping inter- val. Spatial autocorrelation in marine birds 95 periodogram I(w), which uses periodic functions to describe variability as a function of the fre- quency of grouping (w) within the set of data. The contiguous grouping method of Greig-Smith results in a periodogram constructed from square waves (Ripley 1978). The correlogram r(s) and the periodogram I(w) are related via the Fourier transform (cf. Ripley 1981). After obtaining a plot of variability as a function of scale, one naturally asks whether the plot can be reduced to some simple functional expression, in much the same way that one approached the correlogram. The statistical literature warns us, however, that the periodogram I(w) is a poor estimator of the underlying continuous function, which is called the spectral density. Better results can be obtained (given certain conditions on the data) by using a filter to compute a smoothed estimate of the spectral density. One can also estimate the cross-spectra between two series to obtain the coherence h(w), which is a measure of association between the two series at frequency w. Much of the art in performing this sort of analysis comes in choosing the filter. The result, a spectral analysis, is a sophisticated version of the contiguous grouping method of Greig-Smith (Ripley 1978). In a comparison of several dif- ferent methods of analysing transect data, Ripley (1978) found that spectral analysis seems to be the most reliable method for detecting a pattern. Platt & Denman (1975) discuss the use of spectral analysis in ecology. An extensive catalogue of other spatial methods can be found in Upton & Fingleton (1985). A mathematical review of spatial methods can be found in Ripley (1981). Diggle (1983) covers tests of randomness in spatial data and the construction of stochastic models. Exploratory and confirmatory analysis In the abstract, spectral analysis and lagged auto- correlation analysis are closely related. In practice, spectral analysis can usually tell us more about the data at hand than analysis on the auto- correlation side (Tukey 1970). To illustrate this point, we can compare autocorrelation analyses of the Gray Strait data to spectral analyses of the same data. Fig. 7 shows the spectral density of counts of fulmars on the water, fulmars in the air and kittiwakes in the air. In the plot of the data (Fig. 4) we see large scale variability in abundance associated with passage into and out of Gray Strait. We can see that substantial variability exists at smaller scales, but we cannot compare species with respect to this variability at these scales. Autocorrelation analysis (Fig. 5) shows that fulmars and kittiwakes differ in patterns of smaller scale variability and that fulmars in the water differ from flying birds with respect to smaller scale variability. The plot of auto- correlations (Fig. 5) gives no sense of the larger scale variability in abundance, or how this com- pares with the smaller scale variability. We could plot the autocorrelations at lags up to half the length of the series, but such a plot, with over 1,000 correlation coefficients, is not an informa- tive way of summarizing the data for examination. In Fig. 7 we see that all three groups - flying kittiwakes, flying fulmars, and sitting fulmars - exhibit more variability at spatial scales greater than 1 km than at smaller scales. We also see a second concentration of variability at scales on the order of 100m in flying kittiwakes and fulmars, but not in fulmars on the water. At the smallest scale, less than 5 0 m , we see a con- centration of variability in fulmars, both on the water and in the air. These patterns are not evi- dent in the autocorrelation analyses, which are less effective at summarizing the variability in data through a range of scales. An interpretation of the Gray Strait transect can now be offered along the following lines: Two surface feeding species, kittiwakes and fulmars, were found at higher concentrations in turbulent waters of the strait than in adjacent, less turbulent DISTANCE (m) 800 200 100 80 60 40 / Nf 0 010 020 030 040 0 50 FREQUENCY Fig. 7. Spectral analysis of flying birds (fulmars and kittiwakes) and birds on the water (fulmars) observed along Gray Strait transect. The smoothing window (bandwidth = 0.2) was tri- angular. 96 D. C . Schneider water. In addition, flying kittiwakes and fulmars showed spatial variability at the scale of large boils of water rising to the surface. Fulmars were abundant on the water, which suggests that birds were feeding and that the boils were bringing food to the surface. Fulmars on the water did not retain the same spatial structure as birds in the air, possibly due to passive transport of birds toward convergences at the edge of boils. This inter- pretation focuses on interactions between pre- dators and prey in relation to the physical struc- ture of the environment rather than on inter- actions between groups of birds. Cross-spectral analysis showed a positive association between each of the three groups at spatial scales greater than 1 km, no association (positive or negative) between any of the three groups at smaller spatial scales. Interactions between species do not appear to be an important source of variation in the abundance of kittiwakes and fulmars along this transect. This analysis illustrates two related ideas. The first is that we need to distinguish between an exploratory approach and a confirmatory approach to data. Exploratory analysis, such as the Gray Strait study, is a matter of discovering what the data have t o tell us. Confirmatory analy- sis, such as the identification of structured aggre- gations along the PROBES lines, is a matter of circumscribing what we can say with certainty. In this latter analysis the data were not used to construct the model, which was developed from prior surveys of the transect. In the Gray Strait analysis we could have used confirmatory pro- cedures to test the a priori expectation of more birds in the strait than in adjacent waters. However, analysis of the smaller scale variability was entirely exploratory, with concepts being developed from investigation of the data at hand. Related to this distinction between exploratory and confirmatory analysis is the second idea, which is that some techniques work better in exploratory than in confirmatory settings. Spec- tral analyses and factor analyses are good examples of techniques that work well in explora- tory situations. We also have a large arsenal of confirmatory techniques, such as model fitting, that functions much better as confirmatory than as exploratory techniques. The idea of exploratory analysis, the attitude that this is a legitimate part of data analysis and the idea that some methods are better than others for exploring data have been elaborated by Tukey (1986). Acknowledgements. -Field work aboard the CSS ‘Hudson’ was supported by funds from the Newfoundland Institute for Cold Ocean Science (Memorial University of Newfoundland) and the Bedford Institute of Oceanography, Dartmouth, NS, Canada. Field work in the Bering Sea was supported by grants DPP7910386 and DPP8206036 from the National Science Foun- dation, Washington, D.C. Free computing time was provided by the Zoology Department at the University of Rhode Island (Kingston, RI. USA) and by Computing Services at Memorial University of Newfoundland (St. John’s, Canada). Travel to Norway was provided by grants from the Nordic Council and the Troms0 Museum. I thank C . Bajdik for comments o n the manuscript. This is Ocean Science Centre contribution 34. References Abrams, R. W. & Lutjeharms, .I. R. E . 1988: Relationships between seabirds and meso-scale hydrographic features in the Agulhas Current retroflection region. Proc. XIXlnternat. ornithol. Congr., 991-996. Bourne, W . R. P. & Harris, M. P. 1979: Birds of the Hebrides: seabirds. Proc. Roy. SOC. Edinb. 7 7 8 , 445475. Box, G . E. P. & Jenkins, G. M. J . 1976: Time Series Anulysis: Forecasfing and Control. Holdcn-Day. San Francisco. 575 pp. Braune, B. M. & Gaskin, D. E. 1982: Feeding ecology of non-breeding populations of larids off Deer Island, New Brunswick. Auk 99, 67-76. Briggs, K . T., Dettman, K. F.. Lewis, D. B. & Tyler. W. B. 1984: Phalarope feeding in rclation to autumnal upwelling off California. Pp. 51-62 in Nettleship, D. N., Sanger. G. A . & Springer, P. F. (eds.): Marine Birds: Their Feeding Ecology and Commercial Fisheries Relationships. Canadian Wildlife Service, Ottawa. Brown, R. G. B.. Nettleship, D. N., Germain, P.. Tull. C. E. & Davis, T. 1975: Atlas of Eastern Canadian Seubirdr. Canadian Wildlife Service. Ottawa. 220 pp. Cliff, A . D. & Ord. J . K . 1973: Spatial Autocorrelation. Pion. London. Devillers, P. 1978: Patchiness of scabird distribution and the shortcomings of sampling methods. Ibis 120. 125. Diggle, P. J . 1983: Sfatistical Analysis of Spatial Point Patterns. Academic Press, London. 148 pp. Gould, P. J . , Forsell, D . & Lensink. C. 1982: M a g i c Distri- bution and Abundance of Seabirds in the Gulf of Alaska and Eastern Bering Sea. US Fish and Wildlife Service. Washing ton, D.C. 294 pp. Green, R. H . 1979: Sampling Design and Statistical Methods for Enuironmental Biologists. Wiley, New York. Greig-Smith, P. 1952: The use of random and contiguous quad- rats in the study of the strueturc of plant communities. Annals of Botany 16, 293-316. Hoffman, W., Heinemann, D . & Wiens, J . 1981: The ecology of seabird feeding flocks in Alaska. Auk 98. 437-456. Hurlburt, S. H . 1984: Pseudoreplication and the design of ecological field experiments. Ecol. Monogr. 54, 187-211. Kershaw, K. A. 1957: The use of cover and frequency in the detection of pattern in plant communities. Ecology 38, 291- 299. Mendel, J. M. 1987: Lessons in Digital Estimation Theory. Prentice-Hall, Englewood Cliffs, NJ. Mercier, F. M . & Gaskin, D . E. 1985: Feeding ecology of migrating Red-necked Phalaropes (Phalaropus lobatus) in Spatial autocorrelation in marine birds 97 the Quoddy region, New Brunswick, Canada. Can. J . Zool. Platt, T. & Denman, K. L. 1975: Spectral analysis in ecology. Ann. Rev. Ecol. Syst. 6, 189-210. Reed, W. 3. 1983: Confidence estimation of ecological aggre- gation indices based on counts - a robust procedure. Bio- metrics 39, 987-998. Ripley, B . D . 1978: Spectral analysis and the analysis of pattern in plant communities. Journal of Ecol. 66, 965-981. Ripley, B . D . 1981: Spatial Statistics. Academic Press, New York. 252 pp. Schneider, D. C. 1982: Fronts and seabird aggregations in the southeastern Bering Sea. Mar. Ecol. -Progr. Ser. 10.101-103. Schneider, D. C. & Duffy, D. C. 1985: Scale-dependent varia- bility in seabird abundance. Mar. Ecol.-Progr. Ser. 2 5 , 211- 218. Schneider. D. C. & Piatt, J . F. 1986: Scale-dependent cor- relation of seabirds with schooling fish in a coastal ecosystem. Mar. Eco1.-Progr. Ser. 32, 237-246. Schneider, D. C., Hunt, G. L., Jr. & Harrison, N . M. 1986: Mass and energy transfer to pelagic birds in the southeastern Bering Sea. Cont. Shelf Res. 5 , 241-257. 63, 1062-1067. Shuntov, V. P. 1974: Seabirds and the Biological Structure of the Ocean. National Technical Information Service, Springfield, VA, USA. Sokal, R . R . 1979: Ecological parameters inferred from spatial correlograms. Pp. 167-196 in Patil, G. P. & Rosenzweig, M. L. (eds.): Contemporary quantitative ecology and related ecometrics. Statistical Ecology Series 12. International Co- operative Publishing House, Fairland, Md., USA. Tasker, M. L., Hope-Jones, P., Dixon, T. & Blake, B. F. 1984: Counting seabirds at sea from ships: A review of methods employed and a suggestion for a standardized approach. Auk 101, 567-577. Tukey, J . W. 1970: Some further inputs. Pp. 16?-174 in Merriam, D . F. (ed.): Geostatics: A colloquium. Plenum Press, New York. Tukey, J. W. 1986: The Collected Works of John W . Tukey. Volumes 3 and 4. Wadsworth & Brooks/Cole Advanced Books and Software, Monterey, California, USA. Upton, G. J . G. & Fingleton, B . 1985: Spateal Data Analysis by Example. Vol. I . Point Pattern and Quantitative Data. John Wiley, Chichester.