OIKOS 91: 233–244. Copenhagen 2000

Eelgrass, Zostera marina, growth along depth gradients: upperboundaries of the variation as a powerful predictive tool

Dorte Krause-Jensen, Anne Lise Middelboe, Kaj Sand-Jensen and Peter Bondo Christensen

Krause-Jensen, D., Middelboe, A. L., Sand-Jensen, K. and Christensen, P. B. 2000.Eelgrass, Zostera marina, growth along depth gradients: upper boundaries of thevariation as a powerful predictive tool. – Oikos 91: 233–244.

1200 measurements of eelgrass (Zostera marina) biomass, shoot density and coveralong 19 depth gradients in Øresund, located between Denmark and Sweden, wereanalysed to characterise growth of eelgrass in relation to depth. The large data setallowed analyses of boundaries of distribution as well as of average trends. Naturalvariability is large in shallow water where populations are disturbed by wave actionand other physical parameters. Models based on average values, therefore, did notadequately describe growth regulation by resources, and only explained a minor part(up to 30%) of the overall variation in data. In contrast, boundary functions, whichdescribe the upper bounds of distributions, focus on the variation produced by theultimately growth-regulating resource, and therefore provide models with high pre-dictive power. An exponential model explained up to 90% of the variation in upperbounds of eelgrass shoot density as a function of depth and indicated that shootdensity was ultimately regulated by light availability. The boundary functions demon-strated that eelgrass shoot density, biomass and cover followed markedly differentpatterns as functions of depth and were affected differently by the factors governingtheir distribution. In addition, boundary functions revealed informative spatialstructures in data and illustrated whether a given general trend was caused bychanges in maximum values, minimum values or both. For example, upper and lowerboundaries of biomass-shoot density relations changed markedly with depth, demon-strating depth-related changes in intraspecific succession and competition patterns.Boundary functions are therefore suggested as a promising tool for analysingultimate regulating factors of distribution and growth of organisms when large datasets are available.

D. Krause-Jensen, A. L. Middelboe, and P. B. Christensen, Dept of Lake and EstuarineEcology, National En6ironmental Research Inst., Vejlsø6ej 25, DK-8600 Silkeborg,Denmark (dkj@dmu.dk). – K. Sand-Jensen (and present address of ALM), FreshwaterBiological Laboratory, Uni6. of Copenhagen, Helsingørsgade 51, DK-3400 Hillerød,Denmark.

Seagrasses are important structural components andprimary producers of shallow, soft-bottom coastal wa-ters throughout the world (Den Hartog 1970, Mann1982). The lower depth limit of seagrass meadowsdelimits the coastal area potentially covered by sea-grasses, and several studies have documented that vari-ations in seagrass depth limits among species and sitesare mainly regulated by light attenuation in the watercolumn (e.g. Ostenfeld 1908, Backman and Barilotti1976, Duarte 1991, Sand-Jensen et al. 1994). In contrast

to seagrass depth limits, seagrass abundance alongdepth gradients has not been intensively analysed. Pre-vious studies indicate that seagrasses display either abell-shaped distribution along depth gradients, withmaximum abundance at intermediate depths and lowerabundance in shallow and deep water (Bay 1984, Sand-Jensen et al. 1997), or a general decline in seagrassabundance with increasing depth (Buesa 1975, Hulings1979, West 1990). Exposure, desiccation and ice-scourmay reduce seagrass abundance in shallow water

Accepted 10 May 2000

Copyright © OIKOS 2000ISSN 0030-1299Printed in Ireland – all rights reserved

OIKOS 91:2 (2000) 233

(Robertson and Mann 1984, Thom 1990, Sand-Jensenet al. 1997), while reductions in seagrass abundancetowards the lower depth limit correlate with light atten-uation along the depth gradient (Backman and Barilotti1976, Duarte 1991, Sand-Jensen et al. 1997). The result-ing bell-shaped patterns of depth distribution have alsobeen identified for macrophytes in lakes (Spence 1975,Rørslett 1987, Chambers and Kalff 1985, Duarte andKalff 1990). Altogether, the studies demonstrate a largenatural variability in macrophyte abundance withdepth, influenced by several regulating factors, whichrenders mean values of macrophyte abundance at givendepths highly unpredictable.

Patterns of variations, such as variations in seagrassabundance with depth, have typically been describedusing average values in univariate correlation and re-gression analyses. Such procedures are useful for de-scribing central tendencies in data. Given a large dataset, the identified relationships are often highly signifi-cant, although they typically only account for a smallpart of the variation, since no single hypothesis orvariable is able to predict the outcome of regulationprecisely. A satisfactory model may be obtainedthrough multivariate statistics, such as path analyses,but these techniques require measurements of severalpotentially regulating factors (Thomson et al. 1996),and may still fail to elucidate the functional interdepen-dency among the processes producing the complex pat-tern of variation.

When large data sets are available, we can identifymajor limiting processes in complex systems using acompletely different approach. Recent findings in otherbiological fields demonstrate that the effects of funda-mental processes may often be revealed as constraintson the observed patterns of statistical variation (Brownand Maurer 1989, Blackburn et al. 1992, Brown 1995,Thomson et al. 1996, Guo et al. 1998, Scharf et al.1998). For example, the survivorship of annual desertplants shows much variation as a function of density,but the upper bound of the survivorship-density rela-tionship in the large data set closely follows the self-thinning law that ultimately governs the survival ofplants in competitive situations (Guo et al. 1998). Mod-els describing bounds generally have high predictivepower because they focus on the variation caused bythe ultimate regulating factor, while ignoring the re-maining variation. When using boundary functions weapply the principle of Leibig’s ‘‘law of the minimum’’,which states that organisms are controlled by theweakest link in the ecological chain of requirements(e.g. Odum 1975).

The Danish and Swedish Authorities’ Control- andMonitoring Programme for the Fixed Link acrossØresund has provided a large data set of shoot density,biomass, and cover of eelgrass (Zostera marina L.)along depth gradients in Øresund. The data set hasthree advantages compared with earlier data on sea-

grass depth distribution. Firstly, the large amount ofdata allows us to characterise the growth of eelgrass inrelation to depth by using boundary functions andtraditional average values, permitting an evaluation oftheir mutual potentials. Secondly, the data set makes itpossible to evaluate the course of the different eelgrassparameters, shoot density, biomass, and cover withdepth. Thirdly, the data set contains information on therelation between eelgrass biomass and shoot density indifferent depth intervals, which is important for theregulation of eelgrass shoot biomass. These three newtypes of information on eelgrass growth enabled us tocharacterise eelgrass depth distribution in more detailand identify major limiting factors controlling thedistribution.

Methods

Field data

EelgrassThe data set comprises approximately 1200 measure-ments of eelgrass biomass and shoot density, 200 mea-surements of cover, and 19 measurements of depthlimits. Field data originate from the Danish andSwedish Authorities’ Control- and Monitoring Pro-gramme for the Fixed Link across Øresund. Eelgrasssamples were collected in August–September 1993 and1996–1998 along 19 depth transects each comprising3–4 sampling sites (Fig. 1). Eelgrass cover (%) wasestimated at each site by Scuba divers. In 1993, above-and belowground biomass as well as shoot density werequantified by taking two sub-samples of 0.25 m2 inwell-established eelgrass populations at each station. In1996–1998, aboveground biomass and shoot densitywere determined in six sub-samples of 1/16 m2 at eachstation. In the laboratory, the shoots of each samplewere counted, and samples were dried at 105°C for 24h. The maximum depth limit of eelgrass occurrence wasassessed at each transect in 1997.

Water depth and light climateThe water depth at each station was recorded using aprecision depth recorder with an accuracy of 10 cm,and measurements were subsequently corrected accord-ing to Danish average water level. Light was measuredat six stations within the sampling area in Øresund overvarying periods from March to December 1994–1998.Photon flux density (PFD) was logged daily at 10, 11,12, 13 and 14.00 h at 1 and 3 m depth at each station.The mean vertical light attenuation coefficient Kt (m−1)for photosynthetic active photons (400–700 nm) wascalculated using the law of Lambert-Beer:

I3=I1 e(−Kt d),

234 OIKOS 91:2 (2000)

where I1 and I3 represent PFD at 1 and 3 m depth,respectively, and d represents the difference in depthlocation between the two measurements (i.e. 2 m). Thelight climate was relatively uniform at all stations.From April to October 1998, the median attenuationcoefficient for PFD varied only between 0.28 and 0.38m−1 at the six stations and the mean value was 0.32m−1, indicating that all eelgrass transects were exposedto a similar light climate, which is to be expected due tothe high advective transport and low water residencetime in the Øresund. As the monitoring programmedemonstrated no significant effects on eelgrass abun-dance of the construction works in Øresund (Krause-Jensen et al. 1999), it was reasonable to analyse alleelgrass data together and thereby obtain informationon the overall variation in eelgrass parameters inØresund and on the limits to this variation.

Data analyses

EelgrassShoot density, aboveground biomass, shoot weight, andcover were included in the analyses. Average shootweight was calculated for each sample by dividingaboveground biomass by shoot density. All parameters

were sorted according to water depth, and sampleswithout eelgrass were omitted. In order to identify theupper distribution bounds of eelgrass parameters withdepth, the sorted data set was grouped into classescontaining an equal number of observations, and foreach class of data, the 90th percentile and the maxi-mum were identified, providing two different measuresof upper bounds.

The distribution of each eelgrass parameter was plot-ted as a function of depth, and models were fitted alongthe overall depth range to characterise the depth distri-bution from the coastline to the depth limit of eelgrass.Models were fitted both for the entire data set and forthe upper bounds of the grouped data set. Parametersshowing a maximum at intermediate depths were fittedusing a second degree polynomial. The down-slopecourse of the parameters from the depth of maximumoccurrence towards the depth limit was fitted using afunction of exponential decrease, and the same fit wasperformed for the parameters showing a general de-crease or increase with depth.

Data on shoot density, biomass and shoot weightwith depth were grouped into 40 classes of 30 observa-tions, whereas data on cover were grouped into 20classes of 10 observations. The choice of an appropriatenumber of classes was based on the method describedin Blackburn et al. (1992); i.e., the 1200 observations ofshoot density were subdivided into various numbers ofclasses ranging from two classes of 600 observations to600 classes of two observations. For each class of data,the 95th percentiles were plotted as functions of depth,and the slope of the fitted linear regression line wascalculated. For small (B25) and large (\60) numbersof classes, the slope of upper bounds varied markedlywith the number of classes, whereas for intermediatenumbers of classes, the slope of upper bounds becamestable (Fig. 2). Blackburn et al. (1992) demonstratedthat the stable level of the upper bound slope obtainedat an intermediate number of classes defines the ‘‘true’’upper bound slope of the distribution. The optimalsubdivision of the present data set thus ranged from 25to 60 classes, and in all further analyses we chose togroup the data set on shoot density, biomass and shootweight into 40 classes containing 30 observations.

In order to identify yield-density relations of theeelgrass populations, biomass was plotted as a functionof shoot density for each depth interval of 1 m. Averagetrends in the data were modelled using all individualdata points, upper bounds were modelled using 90thpercentiles and lower bounds were modelled using 10thpercentiles of the grouped data set (now using groupsof 10 observations to maintain an appropriate numberof classes within each depth interval). Each of the datasets describing average trends, upper or lower boundswere fitted with a linear model and a yield-densitymodel predicting constant final yield (biomass, Y) athigh shoot density (X):

Fig. 1. Location of transects for eelgrass measurements(-) in Øresund between Denmark and Sweden.

OIKOS 91:2 (2000) 235

Fig. 2. Relationship between estimates of upper bound slopesand number of depth classes. For each depth class, 95thpercentiles of eelgrass shoot density were used to characteriseupper bounds of shoot density as functions of depth. The lownumber of depth classes in the left panel ‘‘A’’ creates a largevariation in the slope, an intermediate number of depth classesin the central panel ‘‘B’’ creates a stable estimate of the slope,while a high number of depth classes in the right panel ‘‘C’’creates increasingly high estimates of the slope.

I(z−0.5h)=I0 eKt (z−0.5h)−kc 0.5B

Results

Patterns of eelgrass growth from shallow towardsdeep water

Eelgrass grew within the depth range from 0.5 to about7 m in Øresund, but shoot density, shoot weight,biomass and cover followed markedly different patternsalong the depth gradient (Fig. 3). The large data setallowed us to describe both average trends of the entiredata set and bounds of distribution, as expressed bymaximum values and 90th percentiles of the groupeddata set (Fig. 3). Both average trends and distributionbounds were analysed from the coastline to the depthlimit of eelgrass and from the depth of maximumoccurrence to the depth limit.

Shoot densityThe 1200 observations of eelgrass shoot density variedmarkedly over the depth gradient, and variations werealso large at specific depths, especially in shallow water.Shoot density had a distinct maximum of approxi-mately 2500 shoots m−2 at 0–2 m depth, and thendeclined steeply with depth down to the depth limit atabout 7 m (Fig. 3A), where approximately 11% ofsurface PFD remained.

The model of exponential decline described the de-crease in eelgrass shoot density with depth. The averagetrend in shoot density over the entire depth rangeshowed a highly significant exponential decline due tothe large number of data points included, but the modelonly explained up to 39% of the variations, and thushad little predictive power (Table 1, Fig. 3a). Themodel describing upper bounds of shoot density ex-plained 72–88% of the variations with depth.

Considering the down-slope course of eelgrass shootdensity at water depths exceeding 2 m, the exponentialmodel explained 37% of the variation in average trends,but up to 90% of the variation in upper bounds (Table1). Of the two measures of upper bounds, the modelsfitted 90th percentiles better than maxima (Table 1, Fig.3a), probably because maxima were more likely toinclude outliers.

BiomassThe 1200 observations of eelgrass abovegroundbiomass also showed large variations over the depthrange and at specific water depths, but the distributionhad distinct upper bounds which were clearly differentfrom those of eelgrass shoot density. Eelgrass biomasspeaked at about 400 g m−2 at intermediate depths ofabout 3 m, where light levels approximated 40% ofsurface PFD, and then declined gradually until 7 mdepth (Fig. 3B).

Y=wX(1+aX)−b,

where w is the maximum potential biomass per shoot,and a the area necessary for obtaining w.

Quantile regression has recently been described as analternative way of identifying distribution boundaries inlarge data sets (Scharf et al. 1998, Cade et al. 1999).Quantile regression reduces the subjective decision-making on the part of the investigator in that themethod does not require separation of the data set intoclasses. Also, the requirements of multiple data pointsare less strict in quantile regression, and the method hasa low sensitivity to outliers. In the ecological literature,quantile regression has been described only in its linearform, however, which is not applicable to humpeddistributions such as the ones we have treated here. Forhumped distributions, curvilinear quantile regressionand, thus, more sophisticated statistics would be re-quired (Koenker and Park 1996).

Light outside and within eelgrass standsPhoton flux density at a given depth, z, in the watercolumn can be calculated from subsurface PFD, I0, andKt :

Iz=I0 e−Kt z

Photon flux density at the centre of eelgrass standsdepends on light attenuation in the water column andlight attenuation in the stands, as influenced by averageshoot height (h), average aboveground biomass (B) andthe eelgrass specific attenuation coefficient (kc : 0.00986m2 g−1 dw, Borum 1980):

236 OIKOS 91:2 (2000)

A polynomial model fitted eelgrass biomass acrossthe depth gradient. Using the entire biomass data set,the model only explained 9% of the variations over theentire depth gradient and showed a maximum of 118 gm−2 at 3.1 m depth (Table 2, Fig. 3b). By contrast, themodel explained 47–67% of the variations in upperbounds of eelgrass biomass and showed a maximum of225–300 g m−2 at 2.5–2.9 m depth (Table 2, Fig. 3b).Of the two measures of upper bounds, the models fitted90th percentiles markedly better than maxima.

The exponential model described the down-slopecourse of eelgrass biomass from the depth of maximumoccurrence (3 m) towards the depth limit. The modelexplained only 10% of the variations in the overall dataset, but up to 66% of the variations in the upper boundsof biomass (Table 2). The slope of the exponentialdecline was steeper for 90th percentiles than for the

overall data set. Of the two measures of upper bounds,the models fitted 90th percentiles better than maxima(Table 2).

Shoot sizeEelgrass shoot weight was generally lowest in shallowwater and increased with water depth (Fig. 3C). Theexponential model fitted the data for shoot size butexplained only about 25% of the variation in averageshoot weight as a function of depth (Table 3, Fig. 3c)and about 33% of the variation in upper bounds (Table3, Fig. 3c). The upper bounds of eelgrass shoot weightover the depth range were less clearly defined thanupper bounds of shoot density and biomass, possiblybecause shoot weight was calculated as a mean valuefor each sample by dividing aboveground biomass byshoot density and thereby ignoring extreme shoot sizes.

Fig. 3. Shoot density (Aa),biomass (Bb), shoot weight(Cc) and cover (Dd) ofeelgrass as functions of waterdepth in Øresund, Denmark.Left panels: all individualobservations (open circles)and 90th percentiles of thegrouped observations (filledcircles). Right panels: fits ofmaxima (solid line), 90thpercentiles (broken line) andall data (dotted line).

OIKOS 91:2 (2000) 237

Table 1. Fitted models of eelgrass shoot density as a functionof depth. A model of exponential decrease was fitted both toall individual data points and to upper bounds (maxima and90th percentiles, respectively) of the grouped data set. Thedepth distribution of shoot density was fitted both along theentire depth gradient and from the depth of maximum occur-rence towards the depth limit (down-slope course). Signifi-cance level: pB0.001:***.

Data nExponential model r2

Entire depth gradientAll data ln(Y)=7.26−0.38X 11840.39***Maximum ln(Y)=8.06−0.31X 400.72***90th percentile ln(Y)=7.93−0.38X 400.88***

Down-slope course (water depths \2 m)All data ln(Y)=7.42−0.41X 9770.37***Maximum ln(Y)=8.20−0.34X 320.72***90th percentile ln(Y)=8.17−0.43X 320.90***

Table 3. Eelgrass shoot weight as a function of depth fittedusing exponential models. Models were fitted for all individualdata points, upper bounds (maxima and 90th percentiles,respectively) and lower bounds (minima and 10th percentiles,respectively) of the grouped data set. Significance levels: pB0.05:*, pB0.01:**, pB0.001:***.

r2Exponential modelData

Entire depth gradientln(Y)=−2.31+0.26XAll data 0.23***

0.24**Maximum ln(Y)=−0.81+0.15X0.33***ln(Y)=−1.23+0.16X90th percentile

ln(Y)=−3.90+0.30XMinimum 0.16*10th percentile ln(Y)=−3.26+0.34X 0.77***

100%. The polynomial model described the course ofcover with depth and explained 22% of the variations inthe overall data set, and 28–32% of the variations inthe upper bounds (Fig. 3d, Table 4). The exponentialmodel described the course of cover from the depth ofmaximum occurrence towards the depth limit and ex-plained 25% of the average down-slope trend in eelgrasscover. The upper bounds were not clearly defined, andthe exponential model only explained 36% of the varia-tions in 90th percentiles (Table 4).

Relations between eelgrass shoot density andbiomass with depth

Because eelgrass shoot density and biomass exhibitedmarkedly different depth distributions (Fig. 3A, B), weanalysed the relations between biomass and shoot den-sity in more detail for particular depth intervals toidentify how yield-density patterns varied with depth.The relation between eelgrass biomass and shoot den-sity changed markedly with depth and exhibited bothupper and lower bounds (Fig. 5).

At shallow and intermediate water depths of 0–3 m,the relation between shoot density and biomass wasquite variable; i.e. at a given shoot density there was a

The distribution of shoot weight with depth alsoformed a lower bound, of which the exponential modelexplained up to 77% of the variations (Table 3). Upperand lower bounds of shoot weight thus showed differ-ent patterns of depth distribution, with the lower boundbeing more clearly defined, and increasing more steeplywith depth than the upper bound, suggesting that thegeneral increase in shoot weight with depth was largelydetermined by increases in lower bounds.

The increase in shoot weight with depth was paral-leled by an increase in shoot height. Thus, when rootingdepth increased by 1 m, shoot height increased onaverage by 10 cm (Fig. 4A). The shoot/rhizome ratioalso increased with depth; i.e. more resources wereallocated to photosynthetic tissue when water depthincreased and light and wave exposure decreased (Fig.4B).

Co6erEelgrass cover was extremely variable and showed anyvalue between zero and 100% at all depths (Fig. 3D).The measure of cover differs from the measures ofshoot density and biomass in that cover has a limit of

Table 2. Fitted models of eelgrass biomass as a function of depth. Models were fitted for all individual data points as well asfor upper bounds (maxima and 90th percentiles, respectively) of the grouped data set. The distribution of eelgrass biomass alongthe entire depth gradient was fitted with a second-degree polynomial. The down-slope course of eelgrass parameters from thedepth of maximum occurrence towards the depth limit was fitted with a function of exponential decline. Significance level:pB0.001:***.

Polynomial model nData r2X at peak, Y-peak

Entire depth gradient0.09***All data 1181ln(Y)=4.08+0.44X−0.07X2 X=3.1, Y=118

X=2.9, Y=299 0.47*** 40Maximum ln(Y)=5.37+0.23X−0.04X2

X=2.8, Y=226 0.67*** 40ln(Y)=4.94+0.34X−0.06X290th percentile

nr2Exponential modelData

Down-slope course (water depths \3 m)All data ln(Y)=5.45−0.22X 0.11*** 711

240.47***ln(Y)=6.33−0.20XMaximum90th percentile ln(Y)=6.20−0.26X 0.66*** 24

238 OIKOS 91:2 (2000)

Fig. 4. Shoot height (A) and ratio between above- and below-ground biomass (B) of eelgrass as functions of depth. Data inbox are not included in the analysis. Based on data from 1993.

At water depths exceeding 3 m, the range of variationbetween biomass and shoot density was gradually re-duced, and became narrow in the deepest eelgrass pop-ulations. This reduction in variation was mainly due tothe fact that the lower bound of the relation betweenshoot density and biomass became steeper and gradu-ally converged towards the upper bound as water depthincreased. In deep water, eelgrass populations showedno plateau in the relation between shoot density andbiomass, and the linear model fitted both averagetrends and upper and lower bounds best (Fig. 5, Table5).

Eelgrass growth with depth in relation to light

The slopes of the exponential decreases in eelgrassshoot density, biomass and cover from the depth ofmaximum occurrence towards the depth limit expressthe ‘‘attenuation coefficients’’ of eelgrass shoot density,biomass and cover with depth. These ‘‘attenuation co-efficients’’ of eelgrass parameters can be compared di-rectly with the attenuation coefficient (Kt) forphotosynthetic active photons (PFD). As the 90th per-centiles gave the best description of upper bounds, weused those percentiles when comparing slopes.

The upper bound of shoot density had the highestattenuation coefficient (0.43 m−1) among the eelgrassparameters, and shoot density decreased moremarkedly with depth than did PFD (0.32 m−1). Theattenuation coefficient of biomass was slightly lower(0.26 m−1) than the attenuation coefficient of PFD,whereas the attenuation coefficient of cover wasmarkedly lower (0.12 m−1).

The light climate expressed by the light attenuationcoefficient applies to a situation without eelgrass. Toobtain better comparisons between attenuation of eel-grass parameters and light attenuation with depth, we

wide range of biomass values. The yield-density modelbest fitted both the average trends in the data and theupper bounds at these depths. Upper bounds ofbiomass increased with shoot density up to a plateau ofapproximately 350 g m−2. At even higher shoot densi-ties, biomass seemed reduced, which may be an arte-fact, however, due to the low number of data points atvery high shoot density. The lower bounds tended toconverge towards the upper bounds at high shoot den-sities (Fig. 5, Table 5).

Table 4. Fitted models of eelgrass cover as a function of depth. Models were fitted for all individual data points as well as forupper bounds (maxima and 90th percentiles) of the grouped data set. The distribution of eelgrass biomass along the overalldepth gradient was fitted with a second-degree polynomial. The down-slope course of eelgrass parameters from the depth ofmaximum occurrence towards the depth limit was fitted with a function of exponential decline. Significance levels: notsignificant:ns, pB0.05:*, pB0.001:***.

X at peak, Y-peak r2 nData Polynomial model

Entire depth gradientAll data ln(Y)=1.85+1.37X−0.2X2 X=3.4, Y=66 0.22*** 240Maximum ln(Y)=4.55+0.05X−0.01X2 X=2.5, Y=105 240.31*

0.28*90th percentile 24ln(Y)=4.23+0.23X−0.04X2 X=2.9, Y=96

Data r2 nExponential model

Down-slope course (water depths \3 m)0.25*** 141All data ln(Y)=5.82−0.49X

14Maximum 0.25nsln(Y)=4.81−0.06X140.36*ln(Y)=5.00−0.12X90th percentile

OIKOS 91:2 (2000) 239

Fig. 5. Eelgrass biomass as afunction of shoot density atvarious water depths in Øresund.Left panels: all observations.Right panels: best fit of upperbounds (solid lines), the best fitof lower bounds (dotted) andthe best fit of all observations(broken line). The relationsbetween eelgrass biomass andshoot density were fitted witheither a linear model or ayield-density model to give thebest fit.

modelled the actual light climate within eelgrass standsand illustrated the relative light availability in a situa-tion without eelgrass and a situation with eelgrass (Fig.6). Light attenuation in eelgrass beds is modified bydepth-related changes in biomass, density, and shootheight. Self-shading in eelgrass stands is reduced withdepth due to the reduced shoot density and biomass,and as the shoots are taller in deep water, they receiverelatively more light than expected from calculation ofPFD at the various depths. Thus, at the centre of thedense, low eelgrass stands at about 2 m depth, only halfthe amount of light was available as compared to thesituation without eelgrass (Fig. 6). By contrast, the lightlevel in the sparse, tall eelgrass stands close to the depthlimit was almost similar to light levels outside thestands. Taking these adjustments of the light climate

within eelgrass stands into account, we can calculatethat the ‘‘true’’ PFD attenuation in eelgrass stands is0.27 m−1, which is almost the same as the biomassattenuation coefficient of 0.26 m−1.

Discussion

Boundaries of eelgrass growth with depth

The use of boundary functions in the analyses of eel-grass depth distribution in Øresund allowed us to focuson data reflecting resource limitation and providedmodels with high predictive power. The boundary func-tions were especially powerful in describing the down-slope pattern of eelgrass parameters from intermediate

240 OIKOS 91:2 (2000)

Table 5. Fitted models of eelgrass biomass as a function of shoot density at various water depths in Øresund, Denmark. Modelswere fitted for the entire data set and for upper bounds (90th percentiles) and lower bounds (10th percentiles) of the groupeddata set. Equations for the linear- or yield-density models (Y=wX(1+aX)−b) are shown depending on which gave the best fit.Significance levels: pB0.01:**, pB0.001:***.

rData set Linear model r Yield density model

0–2 m0.71***All data Y=39+0.08X 0.55*** Y=0.77X(1−0.003)−1.3

90th percentile Y=77+0.10X 0.96***0.66*** Y=1.8X(1−0.005X)−1.2

10th percentile 0.84***Y=18+0.04X 0.70*** Y=0.26X(1−0.003X)−0.97

2–3 m0.53***All data Y=83+0.07X 0.39*** Y=2.0X(1−0.02X)−0.91

90th percentile Y=140+0.1X 0.83***0.55** Y=2.8X(1−0.009X)−1.1

10th percentile Y=32+0.05X 0.67*** fit not possible3–4 mAll data Y=55+0.14X 0.54*** fit not possible90th percentile Y=96+0.17X 0.61*** fit not possible10th percentile Y=13+0.11X 0.88*** fit not possible4–5 mAll data Y=20+0.25X 0.77*** fit not possible90th percentile Y=43+0.31X 0.89*** fit not possible10th percentile Y=7.4+0.18X 0.95*** fit not possible5–6 mAll data Y=21+0.26X 0.73*** fit not possible90th percentile Y=18+0.50X 0.87*** fit not possible10th percentile Y=2+0.29X 0.95*** fit not possible

depths towards the depth limit of the plants. The highpredictability is due to the fact that boundary functionsexclusively describe the pattern produced by the majorresource limiting eelgrass abundance. In contrast, mod-els based on averages were less precise in predicting theoutcome of regulation, since they reflected the com-bined effect of the multiple factors influencing eelgrassabundance. Average values blur the response of eel-grass variables to resource limitation, because averagesare influenced by the many low values in the data setthat are due to biomass removal by physical forces andrepresent early stages of recolonisation followingdisturbance.

The upper bounds of eelgrass shoot density, shootbiomass, and cover, all of which express the abundanceof eelgrass, exhibited markedly different patterns ofdepth distribution and therefore must be differentlyaffected by the factors regulating depth distribution.The model of exponential decline gave a satisfactorydescription of reductions in upper bounds of eelgrassshoot density and biomass from intermediate depthstowards the depth limit, suggesting that light is themain regulating factor. The upper bound of shootdensity was more clearly defined and easier to modelprecisely than the upper bounds of biomass, cover andshoot weight, indicating that shoot density is regulatedin a more direct and deterministic manner than theother parameters. The well-defined upper bound ofshoot density may also reflect that shoot density proba-bly responds faster than biomass and cover to changesin the light climate and consequently more oftenreaches the upper limit.

Shoot density, shoot biomass and shoot weight weremeasured from the exact same samples taken within the

eelgrass patches. Cover, in contrast, is a more subjectivediver’s description of the percentage of sea floor cov-ered by eelgrass, reflecting both the patchiness of eel-grass stands and the cover of eelgrass within thepatches. Since eelgrass cover is estimated visually byprojecting the outline of the leaves to the sea bottom,both the dense, small shoots in shallow-water popula-tions and the more sparse, but larger shoots in deep-water populations may reach a cover of 100%. Theupper limit of eelgrass cover is therefore less sensitive tochanges in light climate compared to limits of density

Fig. 6. Relative light availability outside eelgrass stands (opencircles) and at the centre of eelgrass stands (filled circles) atvarious depths. Light availability outside eelgrass stands wascalculated from the mean attenuation coefficient (Kt=0,32) ofphoton flux density (PFD) in Øresund in 1998, using the lawof Lambert-Beer. Photon flux density at the centre of eelgrassstands was calculated similarly but corrected for average shootheight (h) and average aboveground biomass (B) of eelgrass atthe various depths (see methods).

OIKOS 91:2 (2000) 241

and biomass. The cover within patches and the propor-tion of vegetated patches may be quite differently regu-lated. While light seems to set the upper limits toeelgrass growth within patches, the proportion of vege-tated patches is probably more influenced by physicalexposure, which is suppressed within the stands (Sand-Jensen and Mebus 1996). The stochastic nature ofphysical perturbation may explain why eelgrass cover isan extremely variable parameter that is difficult topredict using simple models.

Regulation of eelgrass populations in shallowwater

In addition to providing models with high predictivepower, the use of upper and lower boundaries demon-strated the range of variability in eelgrass parametersand elucidated spatial structures of ecological relevance.Upper and lower boundaries can change at similar ordifferent rates, and thereby demonstrate whether agiven general trend reflects trends in maximum values,minimum values or both. The boundary functions thusillustrated a reduction in variability of shoot densityand biomass with depth (Fig. 3A, B). High frequency ofperturbation in shallow water is expected to provoke awide range of developmental stages and thus a largervariability in eelgrass populations. After a major distur-bance such as an ice scour, a storm, or a period ofanoxia, eelgrass populations often show extensivegrowth and survival of new shoots that would other-wise have been suppressed, and the populations becomedominated by these new, small shoots (Wium-Andersenand Borum 1984, Olesen and Sand-Jensen 1994). Thisresponse to disturbance may explain the occurrence ofhigh shoot density and cover in shallow water (Fig. 3A,D). Maximum biomass may not have time to developwhere disturbance is highest (Fig. 3B). Variability in-duced by flowering also tends to be high in sites of highlight availability where as much as 10% of the largestindividuals are lost at seed set (Backman and Barilotti1976, Costa and Seeliger 1989, Olesen 1999).

In shallow water, the upper and lower boundaries ofbiomass converge at high shoot densities, as docu-mented by the yield-density relations (Fig. 5). Thelower boundaries of the biomass-shoot density relationsimply increase with increasing shoot density, while theupper boundaries describe a competition-density effectobeying the law of constant final yield (Kira et al. 1953)up to high shoot densities. At very high shoot densities,biomass does not reach peak values. Although ourstudy does not follow the same populations over time,it still provides information on temporal aspects be-cause it includes populations in different developmentalstages. Thus, the lower biomass at very high shootdensities may represent young, recently perturbed pop-ulations, characterised by many small shoots that have

not yet reached the maximum possible biomass (Olesenand Sand-Jensen 1994), while climax populations ofmaximum biomass exhibit reduced shoot density due toself-thinning. This interpretation conforms to the self-thinning process as described for even-aged terrestrialplant populations undergoing density-dependent mor-tality but maintaining constant biomass under lightlimitation (Yoda et al. 1963, Westoby 1984). The samepattern has been identified for eelgrass stands (Olesenand Sand-Jensen 1994). It is likely that self-thinning ineelgrass stands is a short-term phenomenon becausemost stands experience only a short summer periodwith high biomass and optimal light and temperatureconditions before growth conditions deteriorate in au-tumn, and storms reduce the biomass (Olesen andSand-Jensen 1994).

Regulation of eelgrass populations in deeper water

The boundary functions showed at least two character-istic differences between deep and shallow eelgrass pop-ulations. Firstly, the variations in shoot density, shootbiomass and biomass-shoot density relations weremarkedly reduced with depth, probably as a responseto the reduced frequency of physical disturbance andthe reduced input of solar energy. Secondly, eelgrassshoot density, biomass and cover were reduced expo-nentially from intermediate water depths towards thedepth limit of the plants. An exponential decline inupper bounds of eelgrass parameters is expected if lightis the main regulating factor, and if light is linearlyrelated to the eelgrass parameter in question. The slopesof the exponential decreases in the upper bounds ofeelgrass parameters, which express ‘‘attenuation coeffi-cients’’ of eelgrass parameters with depth, demonstratedthat shoot density was more markedly reduced withdepth than were biomass and cover. We have alreadydiscussed reasons for the low sensitivity of cover tochanges in the light climate, and now discuss reasonsfor the differences in down-slope patterns of shootdensity and biomass.

The reduced shoot density with depth reduces self-shading. The light climate is therefore relatively im-proved for the remaining shoots (Fig. 6) which,consequently, may produce a relatively high biomass(Fig. 3C). Eelgrass shoots also become longer in deeperwater (Fig. 4A), and thereby obtain improved lightconditions higher in the water column than expectedfrom their rooting depth (Fig. 4A). Also, the upperbound of the biomass-shoot density relation showed nocompetition-density effect, indicating that the popula-tions do not become dense enough to create a competi-tion among individual shoots for the same resources.

Another factor that may provide a relative improve-ment of light conditions in the deeper eelgrass popula-tions, involves changes in the eelgrass-specific light

242 OIKOS 91:2 (2000)

attenuation coefficient (kc) with depth. The kc-valueexpresses the absorbance of light per unit mass ofphotosynthetic tissue, and the magnitude of kc conse-quently influences the vertical distribution of light incanopies. Specific light attenuation coefficients areknown to depend on shape, size and pigment content ofthe photosynthetic tissue (e.g. Kirk 1994). Long, broadleaves that characterise deep eelgrass populations, areexpected to exhibit smaller kc-values than short, narrowleaves (Jørgensen 1990), but measurements addressingthis aspect are not available. The factors mentionedabove should all improve the light climate relatively indeeper water, and may thereby account for the lowerreduction in biomass as compared to shoot density withdepth (Fig. 3A, B). Studies of other seagrasses alsodemonstrate that reductions in shoot density andchanges in shoot morphology with depth may counter-act the attenuation of light in the water column. Forexample, shallow (3 m) and deep (10 m) Posidoniaoceanica stands in Corsica experienced similar lightconditions below the canopies (Via et al. 1998).

Energetics may also contribute to explaining the rela-tively small reduction in biomass with depth. Largershoots in the deeper eelgrass populations may havelower energy requirements compared to smaller shootscharacteristic of shallow populations provided the in-traspecific size relations for eelgrass resemble the inter-specific relations described for terrestrial plants(Enquist et al. 1998). Also, eelgrass shoots from deepwater allocate relatively more resources to leaves thanto roots and rhizomes (Fig. 4B), thereby reducing res-piratory costs and allowing a more efficient use of thesparse light. Moreover, the larger shoots may reflect ahigher shoot age due to fewer disturbances in deepwater. Recent studies in Posidonia oceanica populationsthus suggest a decline in shoot mortality with depth(Olesen et al. 2000). The patterns of eelgrass parametersalong the depth gradients in Øresund agree with resultsof shading experiments conducted among different sea-grasses, which also demonstrate that seagrasses gener-ally adapt to low light availability by reducing shootdensity and adjusting morphology, e.g. increasing shootlength and shoot/root ratio (e.g. Dennison and Alberte1982, Bulthuis 1983, Abal et al. 1994, van Lent et al.1995).

In conclusion, upper and lower boundary functionsdefine the limits and the range of variability of eelgrassparameters with depth. The boundary functions addinformation on the regulation of eelgrass parameterswith depth both by providing models with high predic-tive power (Tables 1–4) and by revealing spatial struc-tures in the data (Figs 3, 5). There are indications thatthe general patterns of depth distribution found foreelgrass populations in Øresund may also apply toother seagrasses and other areas, and we recommendthe use of boundary functions when large data sets areavailable.

Acknowledgements – We thank ‘‘the Danish Ministry of Envi-ronment and Energy’’, ‘‘the Control and Steering Group forthe O8 resund Fixed Link’’ and ‘‘Øresundskonsortiet’’ for per-mission to use the data which have been collected in monitor-ing programmes for the Fixed Link across Øresund. Data werecollected by SEMAC JV (Sound Environmental Monitoringand Control Group) and FBC (Feedback Monitoring Centre).Anna Haxen is thanked for linguistic corrections.

ReferencesAbal, E. G., Loneragan, N., Bowen, P. et al. 1994. Physiolog-

ical and morphological responses of the seagrass Zosteracapricorni Aschers. to light intensity. – J. Exp. Mar. Biol.Ecol. 178: 113–129.

Backman, T. W. and Barilotti, D. C. 1976. Irradiance reduc-tion: effects of standing crops of the eelgrass Zosteramarina in a coastal lagoon. – Mar. Biol. 34: 33–40.

Bay, D. 1984. A field study of the growth dynamics andproductivity of Posidonia oceanica (L.) delile in Calvi Bay,Corsica. – Aquat. Bot. 20: 43–64.

Blackburn, T. M., Lawton, J. H. and Perry, J. N. 1992. Amethod of estimating the slope of upper bounds of plots ofbody size and abundance in natural animal assemblages. –Oikos 65: 107–112.

Borum, J. 1980. Biomasse og produktionsforhold hos alegræsog det tilknyttede epifytsamfund. – M.Sc thesis, Freshwa-ter Biological Laboratory, Univ. of Copenhagen.

Brown, J. H. 1995. Macroecology. – Univ. of Chicago Press.Brown, J. H. and Maurer, B. A. 1989. Macroecology: the

division of food and space among species on continents. –Science 243: 1145–1150.

Buesa, R. J. 1975. Population biomass and metabolic rates ofmarine angiosperms on the northwestern cuban shelf. –Aquat. Bot. 1: 11–23.

Bulthuis, D. A. 1983. Effects of in situ light reduction ondensity and growth of the seagrass Heterozostera tasmanica(Martens ex Aschers.) den Hartog in Western Port, Victo-ria, Australia. – J. Exp. Mar. Biol. Ecol. 67: 91–103.

Cade, B. S., Terrell, J. W. and Schroeder, R. L. 1999. Estimat-ing effects of limiting factors with regression quantiles. –Ecology 80: 311–323.

Chambers, P. A. and Kalff, J. 1985. Depth distribution andbiomass of submersed aquatic macrophyte communities inrelation to Secchi depth. – Can. Fish. Aquat. Sci. 42:701–709.

Costa, C. S. B. and Seeliger, U. 1989. Vertical distribution andressource allocation of Ruppia maritima L. in a southernBrazilian estuary. – Aquat. Bot. 33: 123–129.

Den Hartog, C. 1970. The seagrasses of the world. – Verh. K.Ned. Akad. Wet. Ser. 2. vol. 59 (1).

Dennison, W. C. and Alberte, R. S. 1982. Photosyntheticresponses of Zostera marina L. (eelgrass) to in situ manipu-lations of light intensity. – Oecologia 55: 137–144.

Duarte, C. M. 1991. Seagrass depth limits. – Aquat. Bot. 40:363–377.

Duarte, C. M. and Kalff, J. 1990. Patterns in the submergedmacrophyte biomass of lakes and the importance of thescale of analysis in the interpretation. – Can. J. Fish.Aquat. Sci. 47: 357–363.

Enquist, B. J., Brown, J. H. and West, G. B. 1998. Allometricscaling of plant energetics and population density. – Na-ture 395: 163–165.

Guo, Q., Brown, J. H. and Enquist, B. J. 1998. Using con-straint lines to characterize plant performance. – Oikos 83:237–245.

Hulings, N. C. 1979. The ecology, biometry and biomass ofthe seagrass Halophila stipulaceae along the Jordaniancoast of the gulf of Agaba. – Bot. Mar. 22: 425–430.

Jørgensen, P. 1990. Selvskygning og maksimal biomasse hossubmerse vandløbs makrofytter. – Ms.Sc thesis, BotanicalInst., Univ. of Aarhus, Denmark.

OIKOS 91:2 (2000) 243

Kira, T., Ogawa, H. and Shinozaki, K. 1953. Intraspecificcompetition among higher plants. I. Competition-density-yield interrelationships in regularly dispersed populations.– J. Polytechnic Inst. Osaka City Univ. 4: 1–16.

Kirk, J. T. O. 1994. Light and photosynthesis in aquaticecosystems. 2nd. ed. – Cambridge Univ. Press.

Koenker, R. and Park, J. 1996. An interior point algorithm fornonlinear quantile regression. – J. Econometrics 71: 265–283.

Krause-Jensen, D., Middelboe, A.L., Christensen, P.B. et al.1999. Benthic vegetation – Zostera marina, Ruppia spp.and Laminaria saccharina. – The Authorities’ Control andMonitoring Programme for the Fixed Link acrossØresund. Status report 1998.

Mann, K. H. 1982. Ecology of coastal waters – A systemapproach. Vol. 8. – Blackwell.

Odum, E. P. 1975. Ecology, 2nd ed. – Holt Rinehart andWinston.

Olesen, B. 1999. Reproduction in Danish eelgrass (Zosteramarina L.) stands: size-dependence and biomass partition-ing. – Aquat. Bot. 65: 209–219.

Olesen, B. and Sand-Jensen, K. 1994. Biomass-density patternsin the temperate seagrass Zostera marina. – Mar. Ecol.Prog. Ser. 109: 283–291.

Olesen, B., Enrıquez, S., Duarte, C. M. and Sand-Jensen, K.2000. Depth-acclimation of morphology, demography andphotosynthesis of Posidonia oceanica and Cymodoceanodosa in the Spanish Mediterranean Sea. – Mar. Ecol.Prog. Ser. (in press).

Ostenfeld, C. H. 1908. On the ecology and distribution of thegrass wrack (Zostera marina L.) in Danish waters. – Rep.Dan. Biol. Stn. 16: 1–62.

Robertson, A. I. and Mann, K. H. 1984. Disturbance by iceand life-history adaptations of the seagrass Zostera marina.– Mar. Biol. 80: 131–141.

Rørslett, B. 1987. A generalised spatial niche model foraquatic macrophytes. – Aquat. Bot. 29: 63–81.

Sand-Jensen, K. and Mebus, J. R. 1996. Fine-scale patterns ofwater velocity within macrophyte patches in streams. –Oikos 76: 169–180.

Sand-Jensen, K., Nielsen, S. L., Borum, J. and Geertz-Hansen,O. 1994. Fytoplankton og makrofytudvikling i danske

kystomrader. – Havforskning fra Miljøstyrelsen Nr. 30.Miljøstyrelsen, Miljøministeriet.

Sand-Jensen, K., Pedersen, M. F. and Krause-Jensen, D. 1997.A, legræssets udbredelse. – Vand & Jord 5: 210–213.

Scharf, F. S., Juanes, F. and Sutherland, M. 1998. Inferringecological relationships from the edges of scatter diagrams:comparison of regression techniques. – Ecology 79: 448–460.

Spence, D. H. N. 1975. Light and plant response in freshwater. – In: Evans, G. C., Cambridge, R. and Rackham,O. (eds), Light as an ecological factor. Vol II. Blackwell,pp. 93–133.

Thom, R. M. 1990. Spatial and temporal patterns in plantstanding stock and primary production in a temperateseagrass system. – Bot. Mar. 33: 497–510.

Thomson, J. D., Weiblen, G., Thompson, A. et al. 1996.Untangling multiple factors in spatial distributions: lilies,gophers, and rocks. – Ecology 77: 1698–1715.

van Lent, F., Verschuure, J. M. and van Veghel, M. L. J.1995. Comparative study on populations of Zostera marinaL. (eelgrass): in situ nitrogen enrichment and light manipu-lation. – J. Exp. Mar. Biol. Ecol. 185: 55–76.

Via, J. D., Sturmbauer, C., Schonweger, G. et al. 1998. Lightgradients and meadow structure in Posidonia oceanica :ecomorphological and functional correlates. – Mar. Ecol.Prog. Ser. 163: 267–278.

West, R. J. 1990. Depth-related structural and morphologicalvariations in an Australian Posidonia seagrass bed. –Aquat. Bot. 36: 153–166.

Westoby, M. 1984. The self-thinning rule. – Adv. Ecol. Res.14: 167–225.

Wium-Andersen, S. and Borum, J. 1984. Biomass variationand autrophic production of an epiphyte-macrophyte com-munity in a coastal Danish area: I. Eelgrass (Zosteramarina L.) biomass and net production. – Ophelia 23:33–46.

Yoda, K., Kira, T., Ogawa, H. and Hozumi, K. 1963. In-traspecific competition among higher plants. IX. Self-thin-ning in overcrowded pure stands under cultivation andnatural conditions. – J. Biol. Osaka City Univ. 14: 107–109.

244 OIKOS 91:2 (2000)