Carbon-to-chlorophyll ratio and growth rate of phytoplankton in the sea

Sathyendranath et al.: Carbon-to-chlorophyll ratio and growth rate of phytoplankton75Table 1. Details of the 16 shelf and open-ocean cruises (offshore data)where samples were collected for chlorophyll and carbon measurements,showing geographic area, sampling dates and total number of samples(n) collectedon each cruiseArea Dates nArabian Sea (Tyro Cruise) 13 Jan–4 Feb 1993 17Arabian Sea (Arabesque 1 Cruise) 28 Aug–30 Sep 1994 110Arabian Sea (Arabesque 2 Cruise) 17 Nov–15 Dec 1994 95Labrador Sea (JGOFS Cruise) 15 May–30 May 1996 45Labrador Sea (JGOFS Cruise) 24 Oct–17 Nov 1996 28Scotian Shelf (Hudson Cruise) 18 Apr–28 Apr 1997 16Labrador Sea (JGOFS Cruise) 12 May–9 Jun 1997 50Scotian Shelf (Hudson Cruise) 8 Apr–21 Apr 1998 26Scotian Shelf (Hudson Cruise) 3 Oct–20 Oct 1998 30Scotian Shelf (Hudson Cruise) 9 Apr–17 Apr 1999 39Scotian Shelf (Hudson Cruise) 24 Oct–12 Nov 1999 37Scotian Shelf (Hudson Cruise) 9 Apr–22 Apr 2000 49Scotian Shelf (Hudson, Cruise) 1 Oct–15 Oct 2000 98Scotian Shelf (Hudson, Cruise) 2 May–16 May 2001 105Labrador Sea (Hudson Cruise) 31 May–13 Jun 2001 42Scotian Shelf (Hudson Cruise) 24 Oct–7 Nov 2001 60Total 847prymnesiophytes, Prochlorococcus, other cyanobacteria(e.g. Synechococcus) and green algae. The pigmentcriteria used to identify these algal groups are shownin Table 2.Since, for the same particulate carbon samples, correspondingchl a estimates were available using boththe Turner fluorometric method (B F ) and the HPLCmethod (B H ), the relationships between particulatecarbon and chl a were explored separately for the 2chlorophyll estimates, especially because some systematicdifferences were often encountered betweenthe chl a values estimated by the 2 methods (e.g. r 2 =0.89, slope = 1.39, n = 814, for linear regression ofHPLC chlorophyll and Turner fluorometric chlorophyllfor our offshore data set). Both particulate carbon andchl a data were log-transformed to linearise the relationshipand to reduce the weight of the stations withhigh values of particulate carbon and chl a in theregression analysis (see also Legendre & Michaud1999). Ordinary least-squares regression analysis wascarried out with particulate carbon as the dependentvariable and B F or B H as the independent variable. Ifwe represent total particulate carbon by C T , then thefitted equations have the form: log (C T ) = log m + p (logB i ), where i = H or F, and log m and p are the fittedparameters. The results can then be expressed as:CpT = mB iTokyo Bay data: Particulate carbon and pigmentdata were collected at 3 stations in Tokyo Bay everymonth from August 1997 until July 2000. Water sampleswere collected, using 5 l Van-Dorn bottles, at 7 to8 depths throughout the water column (maximum(4)depth 30 m). Particulate carbon, fluorometricchl a concentration and HPLC pigment compositionwere measured at each samplingdepth as described above (HPLC sampleswere collected within the top 10 m only). Inthe offshore dataset, HPLC pigments wereused to identify samples dominated by any 1of 6 phytoplankton functional types. Itemerged that, when our criteria wereapplied to identify algal groups, this set ofobservations included samples dominatedby diatoms and dinoflagellates, but none ofthe other types (Table 2). Again, the relationshipsbetween carbon and chl a wereestimated for Turner fluorometric chl a andHPLC chl a separately.Satellite data: Local-area coverage Sea-WiFS data collected during the period from1997 to 2006 at the Bedford Institute ofOceanography were used to generate bimonthlycomposite maps of chlorophyllusing the NASA OC4 algorithm (O’Reilly etal. 2000) and SeaDAS software. The composites for thesecond half of May for all years were then combined tocreate a climatological chlorophyll map for this timeinterval, which was then used to illustrate how theresults established from the field data could be used toarrive at first-order estimates on the distribution of particulatecarbon, phytoplankton carbon, carbon-tochlorophyllratios (χ) and carbon-based growth ratesfor phytoplankton.Quantile regression: For a given observation of particulatecarbon in the ocean, the result may be partitionedinto a portion that corresponds to the livingorganic carbon contained in phytoplankton and aresidual that includes contributions from heterotrophsand various sources of detritus. Addition of any ofthese components other than phytoplankton wouldincrease total particulate carbon without increasingchlorophyll. Therefore, we assumed that, at any givenchlorophyll concentration, the lowest particulate carboncontent observed represents the phytoplanktoncarbon associated with that chlorophyll concentration.Given such data over a range of chlorophyll concentrations,we sought the relationship between the phytoplanktoncarbon concentration (as opposed to totalparticulate carbon) and the chlorophyll concentration.This relationship can be represented as a line forminga lower envelope to the values of total particulate carbonplotted as a function of chlorophyll concentration.The appropriate method to find this relation is quantileregression (Koenker & Bassett 1978). At the same time,we want to exclude any outliers that, through measurementerror, are biased too low to belong to theparent distribution.

76Mar Ecol Prog Ser 383: 73–84, 2009Table 2. Criteria used to omit samples from the database in orderto identify various phytoplankton types. These criteria requirethat the concentrations of pigments diagnostic for a particulartype of phytoplankton should be high relative to theconcentration of chlorophyll a, while, at the same time, therelative concentrations of diagnostic pigments for other typesof phytoplankton should be low. Collectively, the criteriaidentify those samples in which a single phytoplanktontype may be assumed to dominate, based on the chemotaxonomicsignature. Chl: chlorophyll; Hex: 19’-hexanoyloxyfucoxanthin;But: 19’-butanoyloxyfucoxanthinPhytoplankton typeCriteria for omitting samplesnot belonging to a typePrymnesiophytes Chl c 3 /Chl a < 0.035% Divinyl Chl a and b >10%Zeaxanthin/Chl a > 0.01Peridinin/Chl a > 0.1Alloxanthin/Chl a > 0.01Chl b/Chl a > 0.1Hex/Chl a and But/Chl a < 0.05Prochlorococcus sp. % Divinyl Chl a and b < 50%Fucoxanthin/Chl a > 0.01Chl c 3 /Chl a > 0.01Hex/Chl a > 0.2Diatoms Fucoxanthin/Chl a < 0.4Chl c 1, 2 /Chl a < 0.1Chl c 3 /Chl a > 0.01Zeaxanthin/Chl a > 0.01Hex/Chl a > 0.1Chl b/Chl a > 0.1Diadinoxanthin/Chl a < 0.01Cyanobacteria Zeaxanthin/Chl a < 0.1% Divinyl Chl a > 20%Fucoxanthin/Chl a > 0.1Chl b/Chl a > 0.2Peridinin/Chl a > 0.03Hex/Chl a > 0.2Chl c 3 /Chl a > 0.035Green algae Chl b/Chl a < 0.1% Divinyl Chl b and b > 10%Fucoxanthin/Chl a > 0.01Chl c 1, 2 /Chl a > 0.1Hex/Chl a > 0.2Alloxanthin/Chl a >0.05Dinoflagellates Fucoxanthin/Chl a < 0.25Peridinin/Chl a < 0.4Hex/Chl a > 0.2Chl b/Chl a > 0.1For example, the 50th percentile (median, q = 0.5)regression is a fitted line for which half the observationsof the dependent variable lie above and halfbelow. The line represented by the 5th percentileregression lies below 95% of the observations. Clearly,to find the desired lower range, we sought such a loworderquantile regression. In fact, we sought theregression for the lowest quantile consistent with thecriterion of robustness. Rogers (1992) advises that theminimum quantile q should satisfy the condition q >5/N, where N is the total number of observations. Withsome 800 observations, this working rule would allowa regression at the first percentile (q = 0.01), but notmuch lower.The other fitting criterion is derived from inspectionof the (log-transformed to base 10) data. It is clear thatthey are convergent from lower to higher values ofchlorophyll, an indication that phytoplankton carbonconstitutes a higher proportion of particulate carbon aschlorophyll concentration increases and approachesthat characteristic of bloom conditions. In fitting the q =0.01 regression, we required that the fitted slopereflected this evident convergence. Therefore, if thefitted slope for the q = 0.01 regression was smaller thanthat of the q = 0.02 regression, we omitted the observationwith the largest residual and refitted the lines. Theprocedure was repeated iteratively until the slopeexceeded or equalled that of the q = 0.02 regression. Inthis way, 3 (HPLC) to 8 (Turner fluorometer) datapoints were identified as outliers in the offshoredataset. The final fit was judged to be free of bias byoutliers and to be the best available linear descriptionof the lower edge of the scatter plot for the log-transformeddata.RESULTSOffshore dataThe straight-line fits to the log-transformed offshoredata are shown in Fig. 1 for particulate carbon plottedas a function of both Turner fluorometric chl a andHPLC chl a (see also Table 3). The method of Legendre& Michaud (1999), who also analysed the relationshipbetween POC and chl a, is slightly different from oursin the sense that they integrated POC and chl a over afinite depth of the water column and then used averagevalues of the variables over the depth of integrationin the regression analysis. Our analyses, on theother hand, are based on discrete-depth samples. Ourresults for the parameters log m and p for the offshoredata are remarkably close to the values reported byLegendre & Michaud (1999) for all station depths(Table 3) for POC.The particulate carbon field data incorporate alltypes of carbon in the system, including that fromphytoplankton, detritus, bacteria and viruses that areretained on the filter. We can assume that the minimumcarbon amount associated with each concentrationof chl a represents the phytoplankton carbon, anyother particulate carbon serving to increase the measuredcarbon over the minimum. Using quantileregression (for q = 0.01), we therefore fitted a line(Fig. 1) that follows the minimum values of particulate

Sathyendranath et al.: Carbon-to-chlorophyll ratio and growth rate of phytoplankton77Particulate carbon (CT) (mg m –3 )a100010010b100010010C T = 180 (B H ) 0.48 (n = 847)1% QR: C p = 79 (B H ) 0.650.1 1 10HPLC chlorophyll a (B H) (mg m –3 )C T = 157 (B F ) 0.45 (n = 839)C p = 83 (B F ) 0.69 (Buck et al. 1996)1% QR: C P = 64 (B F ) 0.630.1 1 10Turner chlorophyll a (B F) (mg m –3 )carbon associated with any given chl a concentration(ignoring identified outliers). Since phytoplankton contributionto total particulate carbon may be expected toincrease from oligotrophic to eutrophic waters, weanticipated that the lines representing total and phytoplanktoncarbon would approach each other at highchlorophyll concentrations. The equations for estimatingphytoplankton carbon from chl a concentration arealso given in Table 3 for both Turner fluorometric andHPLC pigment data. From these equations, one canestimate χ, the carbon-to-chlorophyll ratio of phytoplankton,and its variation with chl a.Since the data set contains information on the pigmentcomposition of phytoplankton, samples dominated by asingle phytoplankton type could be identified based ontheir diagnostic pigments. These phytoplankton typesare fairly well separated along the chlorophyll axis, withAll dataDiatomsPrymnesiophytesCyanobacteriaProchlorococcusGreen algaeAll dataDiatomsPrymnesiophytesCyanobacteriaProchlorococcusGreen algaeFig. 1. Particulate carbon (C T ) as a function of chlorophyll a for offshoredata. Chlorophyll a estimated by (a) HPLC and (b) Turner fluorometer.Least-squares fits to log-transformed data are shown, as well as minimumcarbon estimates (C p , by quantile regression [QR] q = 0.01), whichmay be interpreted as the upper limits for phytoplankton carbon in thesystem. The relationship between phytoplankton carbon and chlorophylla in field data (Buck et al. 1996) is also shown in (b). The samplesidentified as being dominated by a particular type of phytoplankton areidentified by different colourssamples dominated by Prochlorococcus,other cyanobacteria and green algae appearingin oligotrophic waters, and diatoms andprymnesiophytes becoming more dominant inhigh-chlorophyll waters. No dinoflagellatedominatedsamples were identified from thisdata set according to the criteria outlined inTable 2. Using the chlorophyll concentrationsof the samples and Eqs. (7) & (8) from Table 3for HPLC and Turner fluorometer data, respectively,one can compute χ for these samples.The averages and ranges of χ for the 5 phytoplanktontypes identified are presented inTable 4. These numbers are consistent withvalues in the literature on the carbon-tochlorophyllratios for various phytoplanktontypes (Malone 1982, Geider 1987, Campbell etal. 1994, Kuninao et al. 2000, Schoemann et al.2005, Veldhuis et al. 2005), providing indirectvalidation of our method.The shape of the cloud of points above theminimum relationship (Fig. 1) is consistentwith the interpretation that there would be amore variable contribution to the particulatecarbon from material other than phytoplanktonin oligotrophic waters, whereas the relationshipbetween particulate carbon andphytoplankton carbon would be tighter athigher chlorophyll concentrations. Note alsothat the parameter p is

78Mar Ecol Prog Ser 383: 73–84, 2009Table 3. Fitted relationships between log carbon and log chlorophyll in the field for Turner fluorometric chlorophyll a (B F ) andHPLC chlorophyll a (B H ). Total particulate carbon is represented as C T , and C p is the estimated phytoplankton carbon. The fits tolog C T are by standard linear least-squares regression. The fits to estimate log C p are the results of 1% quantile regression, afterelimination of outliers. Results from Morel (1988), Legendre & Michaud (1999) and Buck et al. (1996) are also given, for comparison.Number of observations (n) and r 2 values are also given for log–log regressions. Note that the fitted relationships are of theform log(Y) = log (m) + p[log(X)]. POC: particulate organic carbonx y log (m) p n r 2 Eq. No. SourceOffshore (HPLC) B H C T 2.26 ± 0.006 0.48 ± 0.014 847 0.58 5 In situ dataOffshore (Turner) B F C T 2.20 ± 0.006 0.45 ± 0.013 839 0.59 6 In situ dataOffshore (HPLC) B H C p 1.90 0.65 844 7 In situ dataOffshore (Turner) B F C p 1.81 0.63 831 8 In situ dataTokyo Bay (HPLC) B H C T 2.43 ± 0.014 0.64 ± 0.017 469 0.76 9 In situ dataTokyo Bay (Turner) B F C T 2.41 ± 0.010 0.60 ± 0.011 811 0.78 10 In situ dataNorth Atlantic B F C p 1.92 0.69 0.60 12 Buck et al. (1996)Euphotic layer B F POC 1.95 0.57 409 0.68 11 Morel (1988)All station depths B F POC 2.21 ± 0.0140 0.505 ± 0.021 510 0.54 13 Legendre & Michaud (1999)Station depth < 200 m B F POC 2.29 ± 0.0194 0.353 ± 0.033 222 0.34 14 Legendre & Michaud (1999)Station depth > 300 m B F POC 2.16 ± 0.0213 0.614 ± 0.029 240 0.65 15 Legendre & Michaud (1999)Table 4. Mean and range of the carbon-to-chlorophyll ratios(χ) of different phytoplankton types, using the results of the1% quantile regression (QR). Chl a was determined using aTurner fluorometer and HPLCPhytoplankton typeMean χ (g/g) Range χ (g/g)1% QR 1% QRTurner fluorometerDiatoms (Offshore) 39 21–75Diatoms (Tokyo Bay) 29 15–55Dinoflagellates (Tokyo Bay) 34 22–62Prymnesiophytes 65 44–82Cyanobacteria 93 74–126Green algae 99 80–126Prochlorococcus sp. 125 123–126All diatoms together 34 15–75HPLCDiatoms (Offshore) 56 31–107Diatoms (Tokyo Bay) 39 20–68Dinoflagellates (Tokyo Bay) 45 27–80Prymnesiophytes 85 65–111Cyanobacteria 130 95–176Green algae 137 122–159Prochlorococcus sp. 145 143–147All diatoms together 47 20–107The mean (±SD) fraction of phytoplankton carbon inparticulate carbon estimated by this method is 45 ±21% using Turner fluorometric chlorophyll data (or 46± 20% using HPLC data), which is on the high side, butwithin the range of values reported in the literature(Eppley et al. 1992, Buck et al. 1996, DuRand et al.2001, Oubelkheir et al. 2005). On the other hand, χ valuesobtained by this simple method (Table 4) comparereasonably well with values in the literature on differentphytoplankton types. Furthermore, the relationshipis also consistent with that observed by Buck et al.(1996), suggesting that the estimates of the phytoplanktoncarbon-to-chlorophyll relationship in themarine environment provided here are reasonable.Note that, based on the equations for phytoplanktoncarbon and total particulate carbon, the fraction ofphytoplankton carbon in the total particulate carboncan be estimated as a function of chlorophyll concentration(C p /C T = 0.44 B H 0.17 for HPLC data and C p /C T =0.41 B F 0.18 for Turner fluorometer data).Tokyo Bay dataThe Tokyo Bay data yielded higher values of boththe parameters m and p for particulate carbon C T as afunction of chl a, compared with the offshore data(Fig. 2, Table 3). This suggests the influence of a higherbackground of non-phytoplankton carbon. The relationshipsbetween phytoplankton carbon and chl aestablished for the offshore data by Turner fluorometricand HPLC pigments (Fig. 1) are also extended herefor the higher chlorophyll concentrations encounteredin the semi-enclosed bay. The separation between theextrapolated phytoplankton–carbon–chlorophyll linesand the data points in Fig. 2 also suggest that nonphytoplanktoncontributions to the POC are higher inthe coastal environment than in the open ocean, whichmay be expected for areas influenced by river outflowand land drainage. Analyses of HPLC data revealedthat this data set contained samples dominated bydiatoms and dinoflagellates. Those samples are identifiedin Fig. 2, and their carbon-to-chlorophyll ratios arepresented in Table 4.

Sathyendranath et al.: Carbon-to-chlorophyll ratio and growth rate of phytoplankton79Particulate carbon (C T ) (mg m –3 )a100001000100b100001000100C T = 268 (B H ) 0.64 (r 2 = 0.76, n = 469)1% QR: C p = 79 (B H ) 0.650.1 1 10 100HPLC chlorophyll a (B H ) (mg m –3 )C T = 256 (B F ) 0.60 (r 2 = 0.78, n = 811)1% QR: C p = 64 (B F ) 0.630.1 1 10 100Turner chlorophyll a (B F ) (mg m –3 )Satellite-based mapsTo illustrate the potential applications of this work,the results presented above were used in conjunctionwith chl a estimates derived from SeaWiFS to mapparticulate carbon, phytoplankton carbon and carbonto-chlorophyllratios of phytoplankton (Fig. 3) in Mayin the NW Atlantic. This is the spring bloom season,and the chlorophyll distribution is highly variable(Fig. 3a), ranging from oligotrophic Gulf Streamwaters to high chlorophyll waters off SW Greenland.The map of particulate carbon is based on Eq. (6)(Table 3) for offshore data, which relies on a largenumber of observations from the area. It is an alternativeapproach to that based on back-scattering (e.g.Loisel et al. 2002) or the method of Gardner et al.(2006), which is based on relationships between beamattenuation, POC and the diffuse attenuation coefficientat 490 nm. Our method is designed to capturethe particulate carbon that covaries with chl a. It is notAll dataDiatomsDinoflagellatesAll dataDiatomsDinoflagellatesFig. 2. Particulate carbon (C T ) as a function of chlorophyll a for a semienclosedbasin (Tokyo Bay). Chlorophyll a estimated by (a) HPLC and(b) Turner fluorometer. Least-squares fits to log-transformed data areshown, as well as the minimum carbon estimates (C p ) from Fig. 1capable of identifying variations in particulatecarbon that are independent of chl a. Onthe other hand, our method is unlikely to beinfluenced by phenomena such as coccolithblooms or bubbles, which can increase backscatteringor the attenuation coefficient withoutincreasing chlorophyll concentration. Themaps of particulate carbon and phytoplanktoncarbon reveal similarities with the chlorophyllmap, given the correlation betweenthese properties. The phytoplankton carbonmap (using Eq. 8; Table 3) relies, in addition,on a simple conceptual model, which hasbeen tested indirectly by comparison withvalues from the literature (Buck et al. 1996).The ratio χ estimated here has a conservativerange (10 to 150) and is low in high-biomassareas and high in low-biomass areas. InFig. 3, we also show the assimilation numberP Bm computed using the Nearest-NeighbourMethod of Platt et al. (2008) and the maximum,light-saturated growth rate, which iscomputed as P B m /χ (see Eq. 3). Note that bothP Bm and the maximum growth rate peak infrontal areas, possibly because of associatedhigh nutrient supply.DISCUSSIONRelationship between particulate carbonand chl a concentrationThe data presented here show a strong correlationbetween particulate carbon and chl aconcentration. The results are remarkably close tothose presented by Legendre & Michaud (1999) for anindependent data set on POC and chl a. They notedthat, since chl a is readily estimated from satellite data,such relationships provide a simple avenue for estimatingPOC from satellite data. They also pointed out theimportance of POC in ecosystem models as the foodsource for zooplankton. Our data also show that ourmethod is robust, even though it straddles a broadrange of trophic conditions, ranging from oligotrophicto eutrophic. Such macro-ecological patterns, whichappear to transcend boundaries of biogeochemicalprovinces and even biomes, can also serve as usefultools for testing the performance of marine ecosystemmodels. Typically, particulate carbon or POC is notrepresented explicitly in ecosystem models, but can beestimated as the sum of the computed particulate carbonin the various elements of the model, includingdetritus. If the models were able to reproduce the bulkproperties of the ecosystem, as shown here, we would

80Mar Ecol Prog Ser 383: 73–84, 2009Fig. 3. Climatological chlorophyll a data (1997 to 2006) for the second half of May for the NW Atlantic, derived from SeaWiFS (a).(b) Particulate carbon and (c) estimated fields of phytoplankton carbon (C p ) derived from (a) using Eq. (7) from Table 3. Thechlorophyll and phytoplankton carbon fields are then used to derive χ, the carbon-to-chlorophyll ratio of phytoplankton (d). TheNearest-Neighbour Method of Platt et al. (2008) is used to map the light saturation parameter P m B (e). Finally, P m B is divided by χto estimate maximum (light-saturated) carbon growth rates (μ) using Eq. (3), and setting the terms in parentheses on theright-hand side of the equation to 1 (f)have an independent validation of the overall performanceof the model. One anticipates that macroecologicalpatterns, such as those presented here,would be modulated locally and regionally (as seen, forexample, in the differences between offshore andTokyo Bay data).Phytoplankton carbon measurement in the fieldMany ecosystem models are not based on chl a, but oncarbon, such that a suitable carbon-to-chlorophyll ratiohas to be invoked to estimate chl a for comparison withsatellite data. For phytoplankton at sea, the carbon-to-

Sathyendranath et al.: Carbon-to-chlorophyll ratio and growth rate of phytoplankton81chlorophyll ratio is a poorly known quantity. Phytoplanktoncarbon concentration is not easily measured in thefield, given the difficulty of distinguishing phytoplanktoncarbon from other types of carbon. What is often measuredis the total particulate carbon or POC, of whichphytoplankton carbon is recognised to be a variable fraction(Eppley et al. 1992, Oubelkheir et al. 2005). Linearregression of POC on chlorophyll has been used to derivethe phytoplankton fraction of the carbon from theslope of the fit, on the assumption that there is a backgroundof POC at sea that is not associated with phytoplankton(e.g. Steele & Baird 1961, Townsend & Thomas2002, Behrenfeld et al. 2005). But the method ignores thepossibility that this background might be variable andthat other types of particulate carbon might co-vary withthe phytoplankton, leading to erroneous results (Banse1977, Eppley et al. 1992, Legendre & Michaud 1999), especiallywhen dealing with large data sets from a varietyof locations covering a wide range of chl a values, as isthe case here. The non-linear approach used here overcomessome of the limitations of these earlier methods.Oubelkheir et al. (2005) used an analysis of opticaldata and phytoplankton carbon measurements in culturesto derive the fraction of phytoplankton carbon inPOC. Their method has not yet been validated bydirect measurements. Another approach to estimatingphytoplankton carbon at sea relies on measurementsof cell carbon in various types of phytoplankton in laboratorycultures, combined with cell counts of thephytoplankton types at sea (Eppley et al. 1992, Du-Rand et al. 2001, Grob et al. 2007). The limitation ofthis method is that the cell quota of carbon is a variablequantity that depends on growth conditions (Geider1987, Cloern et al. 1995), and this often introduces alevel of uncertainty into the calculations. A directmethod to estimate the carbon-to-chlorophyll ratio (χ)at sea is the pigment-labelling method (Goericke &Welschmeyer 1998). Unfortunately, this method hasnot yet been widely used.The variability observed in the relationship betweentotal carbon and chlorophyll (Figs. 1 & 2) arises from 2main sources: variability in the proportion of non-phytoplanktonicparticulate carbon and variability in thephytoplankton carbon itself. The former type of variabilityis related to the status of the ecosystem as a whole,whereas the latter may be associated with changes in thephytoplankton community itself or with its acclimation tothe light or nutrient regime. Assuming that, at any givenchlorophyll concentration, the variability in the total carbon-to-chlorophyllratio is primarily due to changes inthe non-phytoplanktonic carbon, data on total particulatecarbon and chlorophyll can be used to retrieve thephytoplankton carbon, as demonstrated here. The estimateswe have given for phytoplankton carbon in thefield have been derived from measurements of particulatecarbon, invoking simple ecosystem considerations.Since there will always be some contribution to particulatecarbon in the field from material other than phytoplankton,this estimate (Eqs. 7 & 8; Table 3) represents anupper limit of phytoplankton carbon for a given chl aconcentration. Moreover, it is well known that adaptationto low light levels usually leads to an increasein chlorophyll concentration per cell (e.g. Cullen 1982,Veldhuis & Kraay 2004). Hence, we may refine the interpretationof the field estimates to state that they representmaximal phytoplankton carbon for a given chlorophyllconcentration under the prevailing ambient lightconditions. We may expect these estimates to be modulatedwith changes in the available light, e.g. the carbonto-chlorophyllratio decreasing with decreasing light.Since most of the offshore data come from depths of 40 mor less, the results presented here may be taken to berepresentative of the surface mixed layer.Carbon-to-chlorophyll ratios of phytoplanktonThe analyses presented here provide an indirectestimate of carbon-to-chlorophyll ratios in the field,based on an extensive database. They compare wellwith values in the literature (Table 4), and the estimatesof χ that emerge from the analyses (see Fig. 3)are conservative. This relationship may be modulatedby light conditions during growth, as noted above.Since most of our data are from surface and near-surfacewaters, we may anticipate lower values of χ atdepth in the ocean, where the average light levelsexperienced by the cells are lower. Carbon-to-chlorophyllratios also vary with phytoplankton group, beinglowest for the larger diatom cells and highest forsmaller species such as Prochlorococcus sp., which isalso consistent with literature values.The indirect method established here yields carbonto-chlorophyllratios for phytoplankton that are reasonable,based on our current knowledge. The field datafor various phytoplankton types separate into groupsalong the chlorophyll axis, which made it possible toestablish χ for the different groups. These estimatesmay be considered reasonable first approximations ofwhat can be expected in the field, when one of thesephytoplankton types is dominant. It remains to beestablished whether these values of χ would hold ifother phytoplankton types were dominant and if thenutrient and light regimes were different.Phytoplankton growth ratesCloern et al. (1995) used over 200 measurements ofcarbon-to-chlorophyll ratios and growth rates from

82Mar Ecol Prog Ser 383: 73–84, 2009laboratory cultures reported by various investigatorsand established an empirical model that relates carbon-to-chlorophyllratios to growth rates based onphysiological considerations. They then developed amodel for conversion between carbon-based growthrates and chlorophyll-specific photosynthesis rates.Geider (1987) and Geider et al. (1997) also proposedmodels that account for variations in carbon-to-chlorophyllratios based on algal responses to culture conditions.The method of Behrenfeld et al. (2005) for estimatingphytoplankton growth rates for remote-sensingapplications is also based on laboratory measurements.Since laboratory cultures are often maintained in conditionsthat poorly represent typical growth conditionsat sea, some uncertainty is introduced when laboratorymodels are translated for application to field models.Phytoplankton growth rates can be measured at seaindirectly, from dilution experiments on zooplanktongrazing (Landry & Hassett 1982), from chl a labellingexperiments (e.g. Welschmeyer & Lorenzen 1984), orfrom pigment budget experiments assuming steadystateconditions in the water column sampled (e.g.Welschmeyer & Lorenzen 1985, Landry et al. 1995).But such measurements are not implemented on a routinebasis at sea. The method applied here is based onin situ measurements of photosynthesis–irradianceparameters and an indirect estimate of carbon-tochlorophyllratios. It allows us to exploit the existingarchives of photosynthesis–irradiance parameters, andto reconcile chlorophyll-based and carbon-based modelsof primary production. It would be desirable to testthe performance of the method presented here byusing in situ experiments.The method developed here for estimating the carbonbasedgrowth rates of phytoplankton (Fig. 3) is based ona large body of field observations of photosynthesis–irradianceparameters and particulate carbon at sea. It is differentfrom that proposed by Behrenfeld et al. (2005),which relies on backscattering-derived POC, with theadditional assumption of a constant background contributionfrom heterotrophic organisms and detritus, to derivephytoplankton carbon. Their carbon-based growthmodel relies on culture data, whereas the photosynthesis–irradianceparameters on which our method is basedare estimated for natural seawater samples from thestudy area. Photosynthesis–irradiance parameters aredirectly observable at sea, and it is now possible to extrapolatethese observations on a pixel-by-pixel basis(Platt et al. 2008). Therefore, algorithms for primary productionthat are based on photosynthesis– irradiance formalismremain the methods of choice, compared withcarbon-based models. In the absence of routine techniquesto measure carbon-based growth rates for phytoplanktonat sea, these rates have to be either extrapolatedfrom laboratory observations or estimatedindirectly from photosynthesis–irradiance parameters,as proposed here. At present, the value of mapping carbon-basedgrowth rates by remote sensing is principallyfor comparison with growth rates used in large-scaleecosystem models. The sources of differences betweenmodels and estimates, if identified, could provide insightsthat would allow further improvements of bothmodels and remote-sensing methods.CONCLUSIONSAlmost 50 yr ago, Strickland (1960) identified limitationsof existing methods for estimating the carbon-tochlorophyllratios of natural phytoplankton. Seventeenyears later, Banse (1977, p 199) lamented ‘matters havenot improved greatly’, and identified further problemswith existing methods. Now, 30 yr later, we are stillin search of a robust method for measuring this elusiveproperty. Even though new technologies such aslabelled chlorophyll (see Welschmeyer & Lorenzen1984) have been brought to bear on the problem, suchmeasurements have yet to become routine, and fieldestimates of phytoplankton carbon still often rely onthe cell quotas of carbon measured in laboratory cultures,which bring their own uncertainties into the estimates.We still do not have a direct, accurate and routinemethod for measuring phytoplankton carbon atsea.Meanwhile, the need to quantify phytoplankton carbonhas increased. Ecosystem and climate-changemodels use carbon-to-chlorophyll ratios, which areknown to be highly variable (values reported in theliterature range from 1000; see also Table 4for a more conservative range). We need to be able tomeasure the carbon-to-chlorophyll ratio directly and tounderstand its variability if we are to improve phytoplanktongrowth models and better evaluate the role ofphytoplankton in the global carbon cycle and how itmight vary in the context of a changing climate. It is afundamental property of phytoplankton that remainsdifficult to define.The relationships between particulate carbon andchl a presented here are based on bulk-property considerationsand rely on a large body of field data. Theyreveal macro-ecological properties of use in modelsand in remote sensing. Simple ecosystem considerationsthen allow us to establish an upper limit for thecarbon-to-chlorophyll ratio of phytoplankton in thefield and its variation with chlorophyll concentration.We were also able to determine the ratios for severalparticular phytoplankton types, with results that areconsistent with earlier observations. These findingslead to first-order estimates of the ratio from remotesensing. Once the carbon-to-chlorophyll ratio is estab-

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