The variance spectra of phytoplankton, krill and water temperature in the Antarctic Ocean south of Africa

Deeo-SeaResearch.Vol. 33, No. 10. pp. 1327-1343,1986.

0198 ,q14t)/S6$3.(~)+ 0.(X) PergamonJournalsLtd.

Printed in Great Britain.

The variance spectra of p h y t o p l a n k t o n , krill and water temperature in the Antarctic O c e a n south of Africa LARRY H . WEBER,* SAYED Z . EL-SAYED* a n d ][AN HAMPTON'~

(Received 14 August 1985; in revised form 7 April 19861 accepted 13 May 1986)

Abstract--The scale dependence of the variability in phytoplankton and krill (Euphausia superba) abundance, and in the physical environment, are examined by applying the techniques of power spectral analysis to continuous horizontal records of surface seawater temperature, surface in vivo fluorescence and acoustically derived estimates of integrated krill density. Data were collected in the area between 60-70°S and 15-30°E. Similarity in the power spectra for temperature and in vivo fluorescence suggests that over the range of 4--20 kin, the variability in phytoplankton biomass is largely determined by physical processes. However, the steepness of the fluorescence variance spectrum relative to the temperature spectrum, together with consistent coherence between the phytoplankton and krill profiles, suggests that predator-prey interactions are also of importance in determining the distributional patterns of the phytoplankton. Krill distributions exhibit considerable small-scale patchiness, and over the 2-20 km length scales resolved in this study, the krill variance spectrum is similar to a white noise spectrum.

INTRODUCTION

OF THE numerous physical, chemical and biological factors which might limit the productivity of Antarctic marine phytoplankton, light, water column stability and grazing are generally concluded to be the most important (HOLM-HANSENet al., 1977; EL-SAVED, 1984; SAKSHAUGand HOLM-HANSEN, 1984). To date, much of the importance given to grazing has been by default. That is, the generally low phytoplankton biomass of Antarctic waters cannot be otherwise accounted for; therefore grazing pressure has been assumed to have an important limiting role. In examining the role of grazing in controlling Antarctic phytoplankton biomass and productivity, attention is logically focused on the Southern Ocean kriil,~ Euphausia superba, which constitutes perhaps 50% of the Antarctic zooplankton biomass (HOLDGATE,1967; BRINTONand ANTEZANA, 1984), is the dominant herbivorous species and serves as a key link between marine primary producers and top predators (EL-SAYED, 1984). The cruise of the S.A. Agulhas (Fig. l) in austral summer 1981 provided an excellent opportunity to study the phytoplankton-krili distributional relationship. Merging of the data on phytoplankton biomass, primary production, species composition and spatial * Department of Oceanography, Texas A&M University, College Station, TX 77843, U.S.A. t Sea Fisheries Research Institute, Private Bag X2, Rogge Bay 8012, South Africa. :[: In this study, Euphausia superba will be used synonymously with the term krill. Although E. superba is the dominant species, a number of other euphausiids are included under the term krill in its broadest sense. Also, other zooplankton (e.g. copepods and salps) can be important herbivores within the Antarctic ecosystem. However, in the present study, salps were negligible and copepod data were not collected. 1327

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L.H. WEBERet al.

Fig. 1. Cruise track of the S.A. Agulhas during February-March 1981.

distribution with the continuously recorded acoustic estimates of kriil abundance obtained during the cruise provided a unique dataset for examing the simultaneous interrelationships between phytoplankton, krill and the physico-chemical environment. These interrelationships are examined through two analytically different approaches-classical regression-type analysis and spectral analysis. Results of the regression-type (correlation, multiple regression and canonical correlation) analyses are reported elsewhere (WEBER, 1984; WEBER and EL-SAYED, 1985a). This paper presents the results of the spectral analysis. The scale dependence of the variability in phytoplankton and krill abundance, and in the physical environment, is examined by applying the techniques of power spectral analysis to continuous horizontal records of surface seawater temperature, surface in vivo fluorescence and acoustically derived estimates of integrated krill density. Although spectral analysis has now been applied to plankton patchiness research for more than a decade (PLAXX, 1972; DENMANand PLATr, 1975; FASHAMand PUGH, 1976; MACKAS, 1977; STEELEand HENDERSON, 1977, 1979; HORWOOD, 1978; LEKAN and WILSON, 1978; WILSON et al., 1979; WILSONand OKUBO, 1980), this statistical procedure has not been previously applied to Antarctic plankton data. Spectral analysis may be regarded as an analysis of variance in which the total variance in a data series (along a horizontal transect for instance) is partitioned among contributions having different characteristic length scales. The plot of partial variance against

Variance spectra of phytoplankton, krill and water temperature

1329

scale is called a power spectrum, and the integrated area under this spectrum is equal to the total variance of the data series (DENMAN,1975; PLATT and DENMAN,1975). The scale-dependent interrelationship between two variables can be examined by crossspectral analysis, which yields estimates of squared coherency and phase. Squared coherency, which resembles the coefficient of determination (r 2) in regression analysis, provides a non-dimensional measure of the correlation between two series of data as a function of scale. A positive or negative correlation is indicated by a phase spectrum near 0 ° or near 180°, respectively. For a passive scalar under purely physical control, variance is usually great at large scales and has a systematic dependence on length scale representable by a simple power function of the type: C(k) = A k B,

(1)

where C(k) is the power density estimate at inverse wavelength k and A and B are fitted coefficients. When plotted on a log-log scale, the slope of a power spectrum is equal to the coefficient (B) of the exponential term in equation (1). Although the horizontal distribution of in vivo fluorescence values [herein used as an estimate of chlorophyll a concentration, and thus an index of phytoplankton abundance (LoRENZEN, 1966; PLATI"and DENMAN, 1980)] is controlled to varying degrees by the purely physical processes of advection and diffusion, phytoplankton abundance is by no means a conservative quantity. If temperature can be assumed to be a nearly conservative scalar, then differences between spectra of temperature and phytoplankton fluorescence variance may be used to infer biological influences on the spatial patterns in phytoplankton abundance (DENMANand PLATF, 1976). SAUNDERS(1972) found that the variance spectrum for temperature is a straight line with slope of about -2. The biological processes of reproduction and grazing alter the shape of the fluorescence variance spectrum (DENMANand PLATI', 1976; DENMANet al., 1977), so that at scales greater than about 1 kin, the spectra for fluorescence and temperature diverge (DENMANand PLAqT, 1976; FASHAMand PUGH, 1976; STEELEand HENDERSON, 1977, 1979; LEKANand W~LSON, 1978; WILSONand OKUBO, 1980). A flattening of the fluorescence variance spectrum above some characteristic length scale is usually attributed to phytoplankton growth processes (DENMANand PLATI', 1976; DENMANet al., 1977; WILSONet al., 1979). On the other hand, theoretical models (STEELE and HENDERSON, 1977) indicate that non-linear interactions (including grazing, as expressed by the simple Lotka-Volterra system of equations) cause proportionately more variance at larger scales, resulting in a steeper fluorescence variance spectrum over the length scales involved. We discuss here several of the problems involved in processing/interpreting the continuous data profiles and the conclusions suggested by the derived power spectra. The steepness of the fluorescence variance spectrum relative to the temperature spectrum, together with consistent coherence between the phytoplankton and krill profiles, suggests that predator-prey interactions are of importance in determining the distributional patterns of Antarctic marine phytoplankton. METHODS

Data collection

All profiles were collected while underway during the cruise of the M.V.S.A. Agulhas (10 February-20 March 1981) which surveyed the general area between 60-70°S and 15-

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L.H. WEBERet

al.

30°E (Fig. 1). A thermograph was used to continuously monitor surface seawater temperature. In vivo fluorescence of near-surface waters was monitored by using the flow-through mode of a Turner Designs Model 10 fluorometer. The intake for the scientific water supply was in the the ship's hull, approximately 3 m above the keel. Water was pumped by an Iwaki Magnet Pump and supplied to the lab through PVC piping. Bubbles and variations in the flow rate were minimized by diverting the water through an 8-1 cylindrical PVC chamber so that it entered the fluorometer by gravity flOW. ALLANSONet al. (1981) report that water from this supply is representative of seawater from a depth of about 5 m. Continuous profiles of in vivo fluorescence and surface seawater temperature were recorded on strip chart recorders and subsampled with a Numonics Model 1224 electronic digitizer at 1- and 2-kin intervals, respectively. Variable ship speed (averaged over 30-min intervals) was accounted for by changing the distance between points collected from the strip charts. In vivo fluorescence values were compared with ambient chlorophyll concentrations, as measured on triplicate 500-ml samples taken from the fluorometer's outflow every 6 h for in vitro analysis. These samples were filtered through glass fiber filters (Toyo GB100R) and acetone-extracted at 4°C in the dark for 24 h. Chlorophyll a concentrations were determined fluorometrically (EVANSand O'REmLY, 1982). Krill biomass in the upper 100 m of the water column was monitored by digital integration of the return signal from a Simrad EKS 120-kHz echo sounder with hullmounted transducer. Echo integrals were logged on magnetic tape and krill densities (g wet wt m-2) computed and averaged over each 300 transmissions (i.e. every 144 s) of the echo sounder. Using ship speeds averaged over 30-min intervals, the distance covered during each 300 transmissions was determined, and values of krill density were extracted at equal intervals of 1 km. For a discussion of calibration factors, computational equations, and the advantages and limitations of the acoustic estimation of krill density, particularly in relation to the Agulhas dataset, see HAMPTON(1983, 1985) and MILLER and HAMPTON(in press).

Analytical techniques The procedures followed are those outlined in DENMAN(1975), PLATYand DENMAN (1975), and MACKAS(1977), as well as those detailed in JENKINSand WATTS (1968). Trends in the original data series were removed by subtracting curves produced by least squares linear (temperature) and third degree polynomial (in vivo fluorescence) regressions (RAY, 1982). Power spectra, coherence squared and cross-phase spectra were generated using SPKTRA (BRooKs, 1977), which is a compilation of FESTSA (Fast and Easy Time Series Analysis; BROOKS, 1976) subroutines. In this procedure, sample and cross-spectra are calculated by taking the Fourier cosine transform of the auto and crosscovariance functions, respectively (the Blackman-Tukey method). As recommended in JENKINSand WATTS(1968), cross-spectrum analyses incorporated an alignment procedure such that the cross-covariance function was shifted to give maximum cross-covariance at zero lag. Smoothing was accomplished with a Hamming filter and the maximum number of lags was determined by the "window closing" approach of JENKINSand WATTS(1968). Replicate spectra were computed for each data series using three different values for the maximum number of lags. These values ranged from 5 to 30, depending on the length of the data series. In the majority of cases, a maximum lag of 10 appeared to give the best

Variance spectra of phytoplankton, krill and water temperature

1331

compromise between accuracy and resolution, and for consistency in presentation, all of the reported spectra were calculated using this value for the maximum lag. For the purpose of plotting power spectra on a log-log scale, the spectral estimates at zero inverse wavelength were arbitrarily assigned to an inverse wavelength of 0.01. Confidence limits at the 95% level were calculated after JENKINSand WATTS(1968) for the auto spectra. Significance levels (SL) on coherence squared estimates were calculated according to the algorithm: SL = (1 - 0 . 0 5 2 / ( D ° F - 2 ) ) ,

(2)

where DOF equals degrees of freedom. The SL is a conditional probability statement, such that if the true coherence squared is zero, no more than 5% of the coherence squared estimates will exceed the SL (BRooKs, 1977). A total of 12 daytime transects, each between 79 and 245 km in length and consisting of temperature, flourescence and krill profiles, were analyzed. For details on individual transects, see WEBER(1984). RESULTS Surface in vivo fluorescence vs water column chlorophyll a

At best, spatial variability in surface in vivo fluorescence will reflect variability in phytoplankton biomass only to the extent that this measurement correlates with extracted chlorophyll values from surface samples and to the extent that extracted surface chlorophyll values correlate with integrated water column chlorophyll (HAYWARD and VENmCK, 1982). Based on 58 calibration samples, 80% of the variance in in vivo fluorescence can be accounted for by changes in Chl a concentration. When in vivo fluorescence readings are grouped according to time of sampling and regressed against extracted Chl a, values of r 2 are 0.76, 0.98, 0.90, and 0.57 for samples taken at 2400, 0600, 1200, and 1800 h, respectively, For 34 stations which were sampled vertically for chlorophyll concentration, 48% of the variability in water column chlorophyll, integrated to the depth of 0.25% surface irradiance, can be related to the variance in surface samples. Excluding two stations which display strong deep chlorophyll maximum layers, the r 2 value between surface and integrated chlorophyll is 0.65 for the study a r e a "WEBER, 1984). Continuous profiles

Continuous profiles of integrated krill density, surface in vivo fluorescence, and surface seawater temperature (Fig. 2) suggest several problems which must be addressed prior to the application of spectral analysis techniques to the data. Night-time acoustic estimates of krill density are only about 30% of daytime values. Artifactual night-time minima result from an inability to detect krill acoustically when they migrate to the immediate surface (HAMPTON, 1985). The in vivo fluorescence profile also displays strong diel periodicity. Results are similar to those reported for the Central Equatorial Pacific (SETSER et al., 1982) and for the Southern Ocean region south of Australia (YAMAGUCHIand SHIBATA,1982). A plot of in vivo fluorescence, normalized against corresponding values of extracted chlorophyll (Fig. 3), suggests that the diel periodicity in fluorescence may have a physiological basis (KJEEER, 1973; LOFTUSand SELIGER, 1975). Maximum flourescence per unit chlorophyll

1332

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Variance spectra of phytoplankton, krill and water temperature

occurs at night, when minimal amounts of excitation light would be expected to be utilized by the phytoplankton's photosynthetic apparatus. The artifactual, low-frequency periodicity in the krill and phytoplankton profiles tends to overshadow shorter scales of variability that may be of ecological significance. The pattern of shading along the horizontal axis of Fig. 2 indicates that the ship traversed a different distance during each day-night cycle, a result of variable ship speed and length of time spent on station. Thus, any low-frequency period in the profiles cannot be assigned a precise temporal scale. Auto-correlation analysis of similar profiles of krill and in vivo fluorescence from the March 1980 S.A. Agulhas cruise showed weak positive correlation between points 300 and 400 km apart, a distance generally corresponding to that covered during one daynight period. More significantly, maximum correlation occurred between points separated by <100 km, with near-zero correlation at distances of 100-300 km (WEBERand ELSAVED, 1985b). These results suggest that individual daytime (between 0500 and 1900 h local ship time) transects from the 1981 Agulhas cruise are of sufficient length (79245 km) to adequately characterize the ecologically significant length scales of variability in krill and phytoplankton abundance within this region of the Southern Ocean. A representative set of horizontal profiles (taken on 6 March 1981; see Fig. 1) is shown in Fig. 4; both original (dashed line) and detrended (solid line) series are plotted.

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Variance spectra of phytoplankton, krill and water temperature

1335

Power spectra Composite plots of the spectral density functions of temperature, fluorescence, and krill from the 12 daytime transects are given in Fig. 5A-C, respectively. For these composite plots, the raw spectral estimates have been normalized by the variance of each respective series. At the lowest inverse wavelength, the normalized spectral density estimates for temperature are, in some cases, greater than one, a result of the extremely low variance of the temperature profiles and the fact that reported spectra have not been corrected for bias. Because of the coarser spatial resolution of the temperature data, temperature spectra stop at an inverse wavelength of 0.25 cycles km -z, while fluorescence and krill spectra include variance estimates up to an inverse wavelength of 0.50 cycles km -z. The power spectra of temperature and fluorescence appear very similar, while the spectra for krill are much flatter. This is seen clearly in the plot of mean spectral density estimates for the three parameters (Fig. 6) and in the calculated dependence on inverse wavelength for each of the derived spectra (Table 1). The spectral estimates at zero inverse wavelength have not been used in calculating slopes, both because they cannol be assigned a proper position on a log scale and because the temperature and fluorescence spectra appear to flatten out at the lowest inverse wavelengths (i.e. at the largest scales). The slopes of the temperature spectra, when plotted on a log-log plot (Fig. 5A), range between -0.74 and -2.48 with a mean of -1.66 (Table 1). Slopes of the fluorescence spectra range from -1.48 to -2.50 with a mean of-2.04. In contrast to the temperature and fluorescence spectra, the krill spectra have near-zero slopes (range of 0.11 to -0.70 and mean of-0.18, Table 1).

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Table 1.

Wavelength dependence o f power spectra. The value of r2 is given in parentheses

Date

Temp

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24 Feb.

-2.48 (0.89) -2.01 (0.98) -1.61 (0.96) - 1.96 (I).98) -1.35 (0.97) -0.98 (0.85) -1.90 (0.98) -1.57 ((I.87) -1.62 (0.88) -1.95 (0.88) -1.72 (0.89) -0.74 (0.96) -1.66 (0.99)

-1.48 (0.86) -2.511 (0.96) -2.03 (0.97) -1.62 (0.97) -1.74 (0.97) -2.20 ({).97) -2.12 (0.97) -2.21 (I).99) -2.28 (0.93) -2.13 (0.98) -1.83 (0.94) -2.28 ({).97) -2.04 (0.99)

25 Feb. 26 Feb. 27 Feb. 28 Feb. 04 Mar. 05 Mar. 06 Mar. 07 Mar. 08 Mar. 09 Mar. 10 Mar. Mean

Krill

Fluor:Temp* 1.06 (0.81) 0.36 (0.67) -0.58 (0.38) 0.59 (I).78) -I).45 (0.67) -0.8 l (0.79) -1). 14 ((I.08) -0.78 (11.59) -1.32 (0.64) -0.73 (1).41) -0.63 (0.29) -1.46 (0.98) -0.41 (I).6l)

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1337

Variance spectra of phytoplankton, krill and water temperature

Squared coherency and cross-phase spectra Composite plots of the 12 cross-phase and coherence squared spectra for fluorescencekrill are given in Fig. 7. The 95% significance levels on these coherence squared estimates range from 0.10 to 0.26 for the 12 individual transects, so that the larger of the peaks are all significantly different from zero. Mean values of the cross-phase and coherence squared estimates from the 12 daytime series are plotted in Fig. 8 for fluorescence-krill, temperature-fluorescence, and temperature-krill. On average, coherence squared is significantly (P < 0.05) greater than zero for all three crosses. Since the mean cross-phase estimates are all near 0 °, non-zero coherence squared estimates imply positive correlations between fluorescence and krill, between temperature and fluorescence, and between temperature and krill over all scales resolved.

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L . H . WEBER et al.

DISCUSSION

The waters surveyed during the 1981 Agulhas cruise were entirely within the Antarctic Zone except for the southernmost section near the continent which lay within the Continental Water Mass (M. ORREN, personal communication). Although there is evidence that the Weddell gyre extends to approximately 25°E, at its eastern extent it generally lies north of about 62°S (DEACON, 1979), SO that only a very small section in the northwest corner of the survey area may have been influenced by this feature. Thus, the discussion presented herein relates to an open-ocean region of the Antarctic where frontal mixing and bottom topography probably play a very limited role in determining phytoplankton and krill distributional patterns. Surface seawater temperature in the study area varied only between -2 and +2°C, and temperatures measured during each daytime period were all within _+0.2°C of the respective transect means. Extracted Chl a concentrations averaged only 0.12 mg m-3. However, 3-5 fold contrasts in in vivo fluorescence values within transects suggest fairly intense phytoplankton patchiness. Fluorescence values changed rather slowly with distance. In contrast, krill distributions exhibited intense patchiness over very short scales. The detected krill biomass was concentrated in 1304 aggregations having a mean diameter of only 13 m (HAMPTON, 1985). Krill densities (averaged over 144 s intervals) were commonly 3-7 times (and up to 34 times) greater than the mean area-wide density of 1.46 g wet wt m -2. The slopes of the temperature and fluorescence variance spectra from this study are similar to previously reported values, both from studies dealing with length scales of tens of meters to kilometers (PLATYand DENMAN, 1980) and from studies (MACKAS, 1977; STEELE and HENDERSON, 1977; LEKANand WtCSON, 1978) which analyzed profiles from transects of up to 240 km in length. Based on a divergence of the slopes of temperature and fluorescence spectra as a function of wavelength, LEKANand WlCSON(1978) hypothesized that the variance in phytoplankton in Long Island Sound was primarily a function of phytoplankton growth at scales <5 km, of physical processes (advection by tidal currents) at scales from 5 to 20 km, and of changing nutrient regimes at scales >20 km. General similarity between the mean temperature and fluorescence spectra (Fig. 6) suggests that for the area of the Antarctic surveyed during this study, the phytoplankton variance spectrum is determined to a large extent by physical processes at length scales of 4-20 km. However, the fact that the fluorescence spectrum has a steeper slope than the temperature spectrum (-2.04 vs -1.66; Table 1) implies an input of biological variance at the larger scales within this range. Following the approach of SVEELEand HENDERSON(1977, 1979), the ratio, variance in fluorescence:variance in temperature, was calculated and its dependence on inverse wavelength determined (Table 1). The spectral ratios (Fluor:Temp) are, in most cases, a negative function of inverse wavelength. Only 3 of the series (24, 25, and 27 February) yield spectral ratios with positive slopes. Of these, both the 25 and 27 February transects contain extensive regions in which no krill were detected. The transects from 7 and 10 March yield the most negative slopes of-1.32 and -1.45, respectively, and some of the largest krill aggregations detected during the cruise were encountered on these two transects. The mean slope of -0.41 from the 12 series is similar to the -0.5 predicted by the model of STEECEand HENDERSON(1977), which incorporated the Lotka-Volterra

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equations and horizontal diffusion. Overall, the steepness of the fluorescence spectrum suggests that, in addition to physical mixing processes, grazing plays an important role in determining the phytoplankton variance spectrum. The interrelation between horizontal distribution of phytoplankton and krill biomass is also suggested by the coherence squared spectra for fluorescence-krill (Figs 7 and 8). Peaks in the coherence squared estimates for individual transects (Fig. 7) occur consistently at inverse wavelengths corresponding to length scales of 2-5 km. Peaks in variance are seen in the temperature, fluorescence and krill spectra over similar scales. Although such peaks may be artifacts of the short transect lengths and non-Gaussian nature of the data, the fact that they occur consistently at inverse wavelengths of 0.2-0.4 cycles km -~ suggests that length scales of 2-5 km may be of particular significance. Peaks in the variance spectra of the several parameters at these scales may result from the aliasing of variance having frequencies higher than that resolvable by the data. If phytoplankton growth has caused a flattening of, or peak in, the variance spectrum for fluorescence at scales of 2-5 kin, a characteristic length scale less than this is implied. Based on models of scale-dependent diffusion (OKuBO, 1978), the characteristic length scale would be 1-2 km for phytoplankton with a growth rate of one division per day and 16-5[) km for cells doubling every 10 days. Reported growth rates for Antarctic phytoplankton range from 0.1 to about 1.0 doubling day -1 (JACQUES, 1983). Finer scale resolution of the phytoplankton biomass variance, coupled with growth rate measurements, is needed to resolve this question. The mean power spectral density function for krill (Fig. 6) resembles a white noise spectrum. That is, the spectrum is nearly horizontal and has no significant peaks. This implies that any estimates of krill biomass will display equal variability, regardless of the distance separating the estimates. The available sampling resolution (2-20 km) may only yield the plateau region of the krill variance spectrum. As with the phytoplankton, the need for finer sampling resolution is implied. With a mean diameter of only 13 m for the detected krill aggregations, the spectral peaks at 2-5 km length scales obviously do not indicate characteristic patch sizes. Rather, they may reflect a characteristic distance between patches, at least to the extent that very small patches can be represented by biomass data averaged over 1-kin intervals. As discussed by MACKASand BOYD(1979) and MACKAS(1977), models that are used to explain phytoplankton patchiness are not applicable for explaining zooplankton heterogeneity at the observed scales of 2-20 km. Because the growth rate of zooplankton (and in this context, particularly of krill) is low, the minimal patch size predicted on the basis of a balance between physical dissipation and intrinsic growth rate would be very large. Thus, a behavioral mechanism must be invoked, and the question arises as to what the underlying cause of such small-scale krill aggregations might be. The postive coherence observed in the present study between phytoplankton and krill agrees with reports of positive correlation between phytoplankton and zooplankton in the Mediterranean and over Georges Bank (MACKAS, 1977) and in the North Pacific (STAR and MULLIN, 1981), but is in contrast to the inverse correlation found between phytoplankton and zooplankton in the North Sea (MACKAS, 1977; MACKASand BOYD, 1979), Additionally, the positive correlation between phytoplankton and krill biomass observed here at scales of 2-20 km is in contrast to the negative correlations reported between these two entities on the basis of random, discrete samples usually separated by

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much larger distances (HARDYand GUNTHER, 1935; HART, 1942; WITEK, 1979; WITEKet al., 1982; RAKUSA-SuszczEwsKI, 1982; URIBE, 1982; WEBER, 1984; WEBERand EL-SAYED, 1985a). The estimates of coherence squared between temperature and fluorescence and between temperature and krill are less stable than those for fluorescence-krill. The larger sampling interval of 2 km for temperature reduces the number of degrees of freedom for these cross-spectral analyses by half, resulting in greater variance. For temperaturefluorescence, consistent peaks in squared coherency are not evident at any inverse wavelength, but appear randomly over the range of length scales resolved. For temperature-krill, most estimates of coherence squared greater than the 95% significance level occur at low inverse wavelengths, suggesting that small-scale fluctuations of temperature are of little consequence in terms of krill aggregations. However, reported transects were all taken in an open-ocean region where absolute variance in temperature is minimal. Relationships in more neritic waters or in a region of fronts may be entirely different. The present study identifies several problems in the study of phytoplankton-krill relationships that need further elucidation. In terms of interpreting the results, the most serious problem in the dataset stems from the fact that in vivo fluorescence values yield estimates of surface phytoplankton concentrations, while acoustic estimates of krill density give water column values integrated from near-surface to a depth of 100 m. During the day, krill were generally concentrated near the top of the thermocline at a depth of 40-60 m; whereas, at night they were found near the surface and could not be detected acoustically (HAMPTON, 1985). Although there is fair correlation between surface and integrated water column values of chlorophyll, the different sampling strategies for krill and in vivo fluorescence result in an implicit time lag between these two parameters. Moreover, the lag period varies as a function of the time of sampling. Thus, the use of daytime transects confounds temporal and spatial variability. Side-scan sonar (which was not available on the Agulhas cruise) could adequately sample the upper 20 m of the water column and thus provide reliable night-time acoustic estimates of krill. These night-time estimates, together with simultaneous records of surface in vivo fluorescence, could then be analyzed by cross-spectral analysis without having to contend with the problems of implicit temporal variability. Additional advantages of using nighttime transects would be the relatively larger signal-to-noise ratio for the in vivo fluorescence, as well as a decrease in the amount of data manipulation necessary to detrend these profiles. If daytime transects are to be analyzed, the photosynthetic inhibitor DCMU (3-(3,4-dichlorophenyl)-l, 1-dimethylurea) might be used to reduce variability in fluorescence yi01d (SLOVACEKand HANNAN,1977; PREZELINand LEY, 1980; PARKER and TRANTER, 1981) or continuous irradiance data might enable a significant portion of the small-scale variability in daytime fluorescence profiles to be accounted for. CONCLUSION The present study has used the techniques of spectral analysis to examine the scale dependence of variability in Antarctic phytoplankton and to explore how the observed phytoplankton patchiness may be related to the distributional patterns of krill and to the physical environment. It is recognized that any representation of biological relationships by a mathematical formulation must not be over-interpreted. As an example, an underlying assumption in cross-spectral analysis is that the relationship between the two variables is linear. If this is not the case (as is most likely for predator-prey interaction),

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estimates of squared coherency will be depressed and the coherency spectrum must be interpreted with caution (STAR and CULLEN, 1981). Additionally, ARMI and FLAMENT (1985) have recently cautioned against interpreting causality from power spectra, as most of the unique information from a data series appears to be in the phase spectrum. Despite the caveats, further application of power spectral analysis to profiles of in vivo fluorescence and acoustically estimated krill density should prove valuable in addressing questions related to the interactions between these very important components of the Antarctic marine ecosystem. Insights gained on phytoplankton-krill interrelationships are of importance, not only in the context of the Antarctic, but the principles learned will further the understanding of predator-prey relationships in general. Acknowledgements--We are indebted to the Captain and crew of the M.V.S.A. Agulhas, together with the scientific party aboard during this South African FIBEX (First International BIOMASS Experiment) cruise. E. E. Hofmann and K. L. Denman are gratefully acknowledged for their helpful discussions and critical review of the manuscript.

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