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OCEANOLOGICA ACTA 1986- VOL. 9 - W 1 ~ -----~- Empirical relationship for marine primary production: the effect of environmental variables Primary production / Chlorophyll Mixing depth Light _ Temperature Production primaire Chlorophylle Profondeur de mélange Luminosité Température Yves de LAFONT AINE, Robert Henry PETERS McGill University, Department of Biology, 1205 Dr. Penfield Avenue, Montréal, Québec H 3A 1B1, Canada. Received 26/4/85, in revised form 2/9/85, accepted 5/9/85. ABSTRACT An empirical relationship to estimate daily primary production in marine environments is developed from the published literature data of 225 observations taken from 15 different studies. Chlorophyll a alone is of little value (r 2 =0.42) in predicting daily production integrated over the euphotic zone among different areas. The depth of the mixed layer, surface temperature, water extinction coefficient and the mean light level within the mixed layer significantly contribute in reducing the variability of the production-chlorophyll relationship. Incident solar radiation and critical depth do not directly account for much of the variability of integrated primary production. The overall predictive equation (r 2 =O. 67) is very similar to a theoretical model developed by Smith (1980). The empirical relationship is based on variables which can be easily and routinely measured in the field. Future field studies should consider these variables as weil as other physical parameters not commonly reported in previous studies but considered important in explaining the residual variation of the present relationship. Oceanol. Acta, 1986, 9, 1, 65-72. RÉSUMÉ Relation empirique pour la production primaire marine : effet des variables de l'environnement. Une relation empirique pour estimer la production primaire journalière en milieux marins est développée à partir de 225 observations tirées de 15 études préalablement publiées. La concentration de chlorophylle a n'a que peu de valeur (r 2 =0.42) pour la prédiction de la production journalière intégrée sur la zone euphotique entre les différentes régions à une grande échelle spatiale. La profondeur de la couche homogène, la température de surface, le coefficient d'extinction de la lumière, et le niveau moyen d'éclairement à l'intérieur de la couche homogène, contribuent de façon significative à réduire la variabilité de la relation entre la production et la chlorophylle. La lumière solaire incidente et la profondeur critique n'affectent pas directement la variabilité de la production primaire intégrée. L'équation prédictive générale (r 2 =O. 67) est très similaire au modèle théorique développé par Smith (1980). La relation empirique se fonde principalement sur des variables physiques facilement mesurables en routine. Il est suggéré que les études futures prennent ces variables en considération, ainsi que d'autres paramètres peu fréquemment rapportés lors des études antérieures, mais considérés comme importants pour expliquer la variabilité résiduelle de la présente relation. Oceanol. Acta, 1986, 9, 1, 65-72. INTRODUCTION (Ryther, 1969; Koblentz-Mishke et al., 1970). The estimation of primary production requires the incubation of water samples; this is time consuming if large oumbers of estimates are necessary and thus minimizes the temporal and spatial extent of production estimates. For predictive purposes, primary production integrated over the euphotic zone has been related empirically to surface chlorophyll and chlorophyll integrated through the water column (Lorenzen, 1970; Smith, Baker, 1978; The prediction of primary production and of its impact on the productivity of higher trophic levels are important goals of marine biologists and oceanographers. Since the advent of the carbon-14 technique, phytoplankton production has been estimated in many parts of the world' s oceans and large scale comparison of different marine ecosystems has become possible 0399·1784/86/01 65 08/$ 2.80/<0 Gauthier-Villars 65 Y. DE LAFONTAINE. R. H. PEYERS Table 1 Sources and data summary for the present analysis. Ranges are presented for each variable and means for production, chlorophyll and temperature. Location Latitude # Obs. Production (mgC/m- 2/day) (mg/m- 2 ) (C") 137.5-206.3 173.5 56.4-794.9 200.5 9.0-673.0 295.3 114.3-3474.3 715.0 72.7-2921.5 591.9 202.5-472.1 323.9 12.0-1020.0 556.3 70.0-212.0 148.1 144.0-294.0 243.8 160.0-1295.0 454.4 93.0-1108.0 497.8 18.0-35.0 27.9 17.5-75.0 32.8 1.5-29.1 13.3 12.0-209.0 82.7 6.7-196.6 56.0 14.5-18.7 16.1 18.3-33.3 23.7 12.8-28.7 19.6 9.0-24.6 15.6 2.5-25.9 11.2 7.0-98.0 34.7 19.8-20.1 19.9 18.0-25.6 21.6 6.7-12.0 9.5 1.5 20 162.2-1405.4 598.1 16 9.5-802.1 250.7 68.8-562.5 263.1 23.7-1349.4 514.2 9.0-3474.3 432.3 Oceanic zones A. Sargasso Sea 32N 4 B. Sargasso Sea 32N 35 C. Loch Ewe 58N 11 D. Bansfield Sts. Antarctica E. Chukchi Sea 63S 32 67-70N 10 F. Ross Sea 51-14S 4 G. Tropical Eas 4S-10N tern Pacifie H. Eastern Pacifie 17-18N 4 1. North Pacifie 30N Oyre J. Gulf of Panama SN 4 K. Monterey Bay 17 36N Estuarine zones L. Port Hacking 34S estuary M. St. Lawrence 48N estuary N. Beaufort estuary34N ChlorophyiiTemperature 7 23 10 O. Bedford Basin 44N 28 Ali data combined 225 0.1-6. 7 2.7 -1.5-7.1 1.6 18.7-27.0 24.2 23.5-24.0 23.7 n.a. Radiation Extinction Mixing Source coefficient . depth (langleys) (m- 1) (m) 425 0.046 114-750 0.050 29-595" n.a. 25 Ryther et al., 1961 20-100 Menzel & Ryther, 1960,1961 Steele & Baird, 1968 10 248-276" 0.159-0.691 25 164-464 15-31 Mandelli & Buckholder, 1966 Hameedi, 1978 620-635" 0.044-0.271 n.a. EI-Sayed et al., 1983 480-505" n.a. 20-30 Holmes et al., 1951 580" 30-60 Bennett & Schaefer, 1960 70-80 Eppley et al., 1973 0.122-0.418 n.a. 300-350" 0.031 21.0-29.0 27.2 11.0-13.5 12.0 221-621 0.090-0.280 5.25 260-625 4 n.a. 15-30 Garrison, 1976 11.0-66.7 29.5 14.8-22.2 17.8 232-625 0.230-0.739 2-20 2.3-75.0 24.1 1.6-9.6 5.1 6.0-132.9 41.5 1.5-209.0 35.6 3.9-11.1 7.6 7.4-28.6 19.3 -0.1-17.2 7.2 -1.5-29.0 13.5 79-447 0.330-1.200 5-20 232-625" 0.875-2.063 2 49-694 0.209-0.715 5-60 29-750 376 0.031-2.063 0.334 Forsbergh, 1963 Scott, 1979 Sinclair, 1978 Thayer, 1971 Taguchi et al., 1975 2-100 25 n.a. - data not available a - taken from Sverdrup et al., 1942 1968; Fee, 1969; Bannister, 1974; Jassby, Platt, 1976; Smith, 1980). Many of these theoretical models rely on parameters (maximum photosynthetic rate, maximum quantum yield, initial slope value of the production light relationship) derived from the light-saturation curve obtained by incubation. Moreover, these parameters depend on environmental conditions (Platt, Jassby, 1976; Coté, Platt, 1983; 1984). Thus application of existing models may therefore be time-consuming and site-specifie. 1 Hayward, Venrick, 1982; Eppley et al., 1985). These empirical relationships were however established from studies of specifie areas, at specifie time periods. Lorenzen's (1970) data were mainly collected in upwelling systems (Southwest Africa, Peru-Ecuador and Baja California) while ali the data of Hayward and Venrick ( 1982) and most (80 %) of those used by Smith and Baker (1978) were collected in surveys of the North Central Pacifie and along the California coast. Recent! y Eppley et al. ( 1985) compiled data from different areas and suggested that part of the variability in the relationship is regional and that the existing relationships should be applied as predictive tools with caution in different environments. Field studies have shown that the production cycle of phytoplankton in the temperate oceans (Sverdrup, 1953; Parsons et al., 1970) and in estuaries (Sinclair et al., 1981) is largely determined by the depth of the mixed layer relative to the critical depth, a parameter dependent on transparency of the water and level of incident radiation. Physiological studies show that incident radiation, temperature and nutrients can also affect photosynthesis and thus primary production. Following the pioneer works of Riley (1946) and Ryther and Yentsch (1957), severa} theoretical models have been developed to estimate production as a function of environmental variables (Steele, 1962; Patten, The empirical relationships for primary production are characterized by considerable variability and although, it has been emphatically suggested that environmental variables may influence the relations (Small et al., 1972; Smith, Baker, 1978; Hayward, Venrick, 1982), no attempt bas been made to demonstrate their compound influence. Eppley et al. (1985) indicated that environmental variables contribute to the observed variabiIity but their analysis was restricted to the Southern California Bight area. This paper examines the relationships between phytoplankton biomass, expressed as chlorophyll a concentrations, and daily primary production, both integrated over the euphotic zone and evaluates the effects of sorne easily measured environmental variables, to develop a general relationship for the estimation of marine primary production. 66 MARINE PRYMARY PRODUCTION: AN EMPIRICAL MODEL DATA AND ANALYSES biomass as independent variables. The second analysis related the productivity ratio, expressed as production over biomass (P/B), to environmental conditions. The second mode! assumes a linear relationship between production and biomass and evaluates how the slope of this relationship is altered by environmental conditions (Platt, Jassby, 1976; Harrison, Platt, 1980). Apart from the environmental variables described earlier, the distinction between oceanic and estuarine observations was evaluated by assigning a dummy variable (Dl) taking the value of 0 and 1 respectively. Since primary production was measured by two different techniques (in situ and deck incubation), a second dummy variable (D2), assigned as 0 and 1 respectively, tested the effect of method. Estimates of daily primary production and chlorophyll a concentrations integrated over the euphotic zone were compiled from literature. Only measurements of primary production based on C-14 techniques were used in the analysis. Observations of dai! y incident radiation, water extinction coefficient, sea surface temperature and mixed layer depth were also recorded when reported (Tab. 1). Observations of incident radiation missing from original data sources were substituted by the average radiation conditions at the study site given the latitude and time of the year (Sverdrup et al., 1942). From the above variables, the depth of the euphotic zone, the critical depth and the mean light leve! within the mixed layer were calculated (Tab. 2). The ratio of mixing depth to critical depth was calculated and considered as a variable. The data set is not exhaustive but covers a large range of observed values from a variety of areas from estuaries to offshore oceanic zones. Model-1 least-squares regression and correlation analyses (Sokal, Rohlf, 1981) were used to examine the relationship between production and biomass. A Kolmogorov-Smirnov normality test revealed that the data were not normally distributed for production and chlorophyll (D: 0.162, p<O.OOl and D: 0.196, p<O.OOl respectively). Different transformations (square root, Iogarithmic, inverse) of data were tested but normality was achieved only with the logarithmic transformation (D: 0.052, p>0.05 and D: 0.058, p>0.05 for production and biomass). The influence of environmental factors was assessed through a stepwise multiple regression that selected the best predictors at the 0.05 level of significance. Two analyses were performed. First, production, the dependent variable, was related to environmental factors and RESULTS The relationship between production and biomass Within the range of values analysed, daily primary production integrated over the eup ho tic zone was positive! y related to the integrated chlorophyll concentrations (Fig. 1). The predictive regression equation is significant (F-test, p < 0.001) and explains 42% of the variance observed (Tab. 3). The slope of the equation issignificantlyless than 1(t = 5.48, p<0.001) and suggests a curvilinear relationship between the two variables. The computed value of O. 700 is similar to the previously reported values O. 728 (Smith, Baker, 1978) and O. 766 (recalculated from Lorenzen's 1970; Tab. 3). The results of Hayward and Venrick (1982) are not directly comparable principally because they used a simple linear mode! based on untransformed data. Their analysis suggests however that hourly production estimates, vary in direct proportion to chlorophyll with an appro- Table 2 Estimation of derived physical parameters Euphotic zone depth (Zeu) Critical depth (Zcr) Mean light level within the mixed layed (lm) Lorenzen, 1972 Zeu : 4.605/Ke 0.5Io Zcr:-- Û. Parsons et al., 1977 ffo (1- e- KeZml) Parsons et al., 1977 lm:-____;_ _ _....:. KeZml Io: Incident radiation Ke: Extinction coefficient of water Zml: Depth of the mixed layer. Table 3 Relationship between production and chlorophyll. Sa and Sb are the standard e"or of the intercept and the slope respective/y. Production (P) values are in mg Cfm 2 fday and chlorophyll (Chf) in mgfm 2 except for Smith and Baker's data which are average values in mg Cfm 3 fday for P and in mgfm 3 for Chi. Regression equation # Obs. F-value r2 Sa Sb Reference ln P: 3.427+0.700 ln Chi. ln P: 4.663+0.766 ln Chi. ln P: 1.254+0.728 ln Chi. 225 87 126 164.45 0.42 0.179 0.055 P: ""2-3 Chi. P: ""2-3 Chi. P: 411.23 + 206.25 Chi. ln P: 6.444 + 0.488 ln Chi. 58 35 11 11 This study Lorenzen, 1970 Smith, Baker, 1978 Hayward, Venrick, 1982 Ryther, Yentsch, 1957 0.73 0.83 0.50 0.46 0.46 67 Y. DE LAFONTAINE, R. H. PEYERS nearity and the poor fit of the general mode] reflect the influence of other factors on the production-chlorophyll relationship between areas. ,., ..,. .. ' . E ' ' Effects of environmental variables '0 "' E The correlation matrix of production, biomass and productivity ratio with environmental factors (Tab. 5) cao be summarized as follows: 1) Production is negatively correlated with temperature, euphotic depth, critical depth and mixing depth. 2) Biomass is negatively correlated with temperature, euphotic depth, critical depth, incident radiation and ~ean light leve] within the mixed layer. 3) Productivity ratio is positive! y correlated with temperature, incident radiation, extinction coefficient and mean light leve! within the mixing depth and negatively correlated with mixing depth and euphotic depth. Correlation coefficients are greater between composite parameters and production or biomass than for single variables. For example, critical depth and mean light leve] in the mixed layer are more strongly correlated to production or biomass than incident radiation or mixing depth alone. Significant intercorrelations exist among physical factors, the strongest cases being between variables and derived parameters as one would expect. z 0 1(.) :::) 0 0 a: a. 3 30 10 CHLOROPHYLL 100 1000 300 (mgim2l Figure 1 Relationship between dai/y integrated production and chlorophyll. Letters refer to individual studies reported in Table 1. ximative slope of 2.5; this agrees with reported assimilation numbers (Harrison, Platt, 1980) which are essentially hourly productivity ratios at depth. The frequency distribution of the productivity ratios (P/B) shows a wide range (Fig. 2) with a mode between 10 and 12. A similar skewed-left distribution was also reported for assimilation numbers (Harrison, Platt, 1980). The distributions appear identical despite the difference in units between assimilation number, based on hourly estimates at discrete depths, and productivity ratios, based on integrated daily estimates. Based on the r 2 criterion, the general fit of our equation is Jess those previously reported (Tab. 3). As this variability could be due to differences among the various sources of data, the relationship between production and chlorophyll was exarnined for each study included in the global analysis. Significant positive relationships are found in the majority of cases where the number of observations is sufficient (n>4; Tab. 4). The individual r 2 values are much higher than that calculated for the general mode!. The log-log slopes of these individual relations are not significantly different than 1, indicating direct proportionality between the two variables. As the individual studies refer to regional observations, these results suggest that the curvili- 18 16 14 )(.) z w :::) 0 w a: Il.. 12 10 8 6 4 2 0 10 0 30 20 50 40 so> P/B RATIO Figure 2 Histogram of frequency distribution of productivity ratios (P/B). Values greater than 60 are pooled. + Table 4 Relationships between production and chlorophyll for individual studies used in the general analysis. Letters identify the separate studies in Table l. Underlined slopes are significantly different than Ofor /inear models and not significantly different than 1 in log-log models (**: p<0.001; *: p<0.01). Data source # Obs. A. 4 Il 35 32 10 4 4 7 4 23 17 20 16 10 28 B. c. D. E. F. G. H. 1. J. K. L. M. N. O. Log-log mode) Linear mode) SI ope rz SI ope r2 0.07 0.91 1.47 0.84 0.02 0.51** 0.85** 0.88** 0.88** 0.17 0.41 0.09 0.71 0.29* 0.65** 0.66** 0.86** 0.63* 0.68** 0.68 5.71 20.66 0.03 0.40** 0.50** 0.59** 0.96** 0.26 0.53 0.13 0.58 0.16 0.54** 0.80** 0.95** 0.44* 0.61** 1:09 1.55 4.93 0.46 0.69 0.62 0.95 m ill 0.95 1.23 68 732 15.38 36.32 47.24 3.58 8.20 22.73 9.63 23.82 IT.46 39.79 11.73 MARINE PRYMARY PRODUCTION: AN EMPIRICAL MODEL Table 5 Correlation matrix ofphysical variables and production (P), chlorophyll (B) and productivity ratio (P(B). Physical variables are temperature (Temp), incident radiation (Jo), water extinction coefficient (Ke), mixed layer depth (Zml), euphotic depth (Zeu), critical depth (Zcr) and mean light leve! within the mixed layer (lm) (***p<0.00l,**p<O.Ol,*p<0.05). lo Temp. lo. Ke Zml Zeu Zcr lm p Ke 0.386*** -0.125 0.026 Zml Zeu Zcr lm p B P/B 0.200** -0.203** -0.437*** 0.441*** 0.022 -0.590*** 0.718*** 0.444*** 0.375*** -0.533*** 0.458*** 0.868*** 0.468*** 0.751*** -0.197* -0.262** 0.288** 0.578*** -0.200** 0.100 0.093 -0.175** -0.301*** -0.236*** 0.098 -0.413*** -0.165* -0.039 0.076 -0.138* -0.176* -0.291*** 0.723*** 0.359*** 0.331*** 0.345*** -0.323*** -0.224** -0.115 0.275*** 0.218** -0.260*** B Table 6 Results of the stepwise regression analysis for models describing production (P) and productivity ratio (P(B). Symbols are defined in Table 5. Dependent Variable Ln P Step 1. 2. 3. 4. 5. 6. Selected Variable Rz ln Chi. lnZml Temp Zeu Dl ln lm 0.41 0.53 0.58 0.61 0.65 0.67 Multiple Equation: r 2 : 0.67 n: 202 P(Chl Overall 41.0 13.1 4.5 3.5 4.3 1.4 139.7 113.2 89.9 77.5 74.1 65.4 F ln P: 2.385+0.808 ln Chl+0.0306 Temp+0.260 ln lm -0.291 Dl -0.015 Zeu 1. 2. 3. 4. Multiple Equation: r 2 : 0.45 n: 202 %Variance Explained lnZml Temp 0.20 0.36 0.40 0.45 Dl ln Ke 20.2 16.2 3.8 5.0 50.8 47.4 44.7 40.8 P/Chl: 46.9+0.874 Temp+7.60 ln Ke-7.588 ln Zml-14.584 Dl DISCUSSION Stepwise regression analyses indicate that chlorophyll, depth of the mixed layer, temperature and depth of euphotic zone significantly contribute to the variance in daily primary production (Tab. 6). The difference between estuarine and oceanic environments, as defined by dummy variable Dl, was also significant. In the final step of the analysis, the mixing depth was replaced by the mean light level within the mixed layer, which is a composite parameter of the mixing depth (Tab. 2). This "best" predictive multiple model accounted for 67% (p<0.001) of the variance. The depth of the mixed layer, the most significant variable, explains 20% of the variability in the productivity ratio (Tab. 6). Temperature, depth of euphotic zone and the difference between estuaries and oceanic zones (Dl) contribute to 16.2, 5.0 and 3.8% respective) y. The final equation is significant and explains 45% of the variance. Although productivity ratios were significantly correlated with incident radiation (Tab. 5), the variable was not selected (p>0.05) in the multivariate model. The second dummy variable D2 was never selected by any regression models; this suggests that methodological techniques for C-14 analyses used in the various studies do not contribute to the overall variability observed. The ratio of mixing depth to critical depth was not selected in either regression analyses. Ryther and Yentsch (1957) first suggested the use of chlorophyll a as a predictor for primary production in the ocean. The present analysis shows that, despite the significant relation between production and biomass, chlorophyll atone is of little value in predicting daily primary production among different areas. The very strong correlations between chlorophyll and production in different studies indicate however that, within areas, chlorophyll can predict production. This is consistent with previous conclusions that the seasonal pattern of chlorophyll at one site generally reflects the seasonality in productivity but cannot account for variability among sites (Cadée, Hegeman, 1974; Cole, Cloern, 1984). Although variations in measurements associated with the productivity technique among different sources of data might contribute to the scatter observed in the general relationship, the slope value and the general fit are in fact very close to previous empirical relations (Lorenzen, 1970; Smith, Baker, 1978; Hayward, Venrick, 1982) for which problems in measurement and calculation are probably minimized. This strongly supports the argument that other factors, primarily environmental, are largely responsible for the observed variability (Hayward, Venrick, 1982). 69 Y. DE LAFONTAINE. R. H. PEYERS The dominant environmental factor contributing to primary production variability is the depth of mixing. The importance of the mixed layer depth in phytoplankton dynamics was recognized very earl y by Riley ( 1946) and Sverdrup (1953) but its prime role has been stressed only recently in theoretical models (Smith, 1980; Kiefer, Kremer, 1981; Wofsy, 1983). The inverse relationship between productivity and mixing depth (Tab. 6) is consistent with other observations relating production and/or biomass to the degree of stratification of the water column (Fournier et al., 1979; Demers, Legendre, 1982; Perry et al., 1983). These suggest that a higher degree of stratification corresponds to a reduction of the mixing depth which enhanced primary production. The present analysis shows that incident radiation (lo) does not directly account for much of the variability of marine primary production, in agreement with results from previous studies (Williams, Murdoch, 1966; Harrison, Platt, 1980; Coté, Platt, 1983). The model developed by Ryther and Yentsch (1957) was based on the incident light level. Reanalysis of their data (given in their Tab. 2) reveals that the correlation coefficient (r) between production values predicted by their model and observed values drops from 0.94 (p<0.01) to 0.37 (p>0.1) if only one datum (the largest) is removed. Incident radiation per se is not sufficiently powerful to predict production as shown in our global analysis. Although light is the proximal agent of phytoplankton production, its effect is modulated by the depth of mixing (Legendre, Demers, 1984). Deeper mixing layer decreases the average light intensity available to the cells and thus decreases productivity. The fact that the mean light levet within the mixed layer was selected over Io supports the hypothesis that photosynthetic capacity is affected by the Iight history (Platt, Jassby, 1976) and probably adapts to the mean light intensity in the mixed layer (Demers, Legendre, 1982; Legendre, Demers, 1984). Temperature is the second most important factor contributing 16.2% of the explained variability in the productivity ratios. The slope (0.031) from the multiple equation is close to the value of 0.0275 in Eppley's (1972) function of growth rate on temperature and the QlO value calculated from the present analysis (2.05) agrees weil with previous estimates (2.25 - Williams, Murdoch, 1966; 2.35 - Joint, Pomroy, 1981; 2,13 Bruno et al., 1983; 2.2 - Coté, Platt, 1983) and approaches the expected value of 2 from enzymatic processes. The negative relationship between euphotic depth and production is supported by other empirical evidence (Small et al., 1972; Lorenzen, 1976; Smith, Baker, 1978). The extinction coefficient, which is the reciprocal of the euphotic depth, accounts for 5% of the overall variance of productivity ratios (Tab. 6). The dummy variable, Dl, suggests that oceanic sites are more productive than estuaries (Tab. 6). This is surprising as estuaries are generally areas where nutrients are rapidly replenished and rarely limiting (Riley, 1967). Unfortunately, nutrient concentrations were not available from the majority of studies used here. However, a very slightly significant, but negative, effect of nitrates on the variation in assimilation num- / / 3000 1000 / IY 300 0 ... w 0 0 w 100 ...a: / 30 / / / / 10 3 3 10 30 100 300 1000 3000 OBSERVED Figure 3 Plot of predicted values of dai/y integrated production (mg C/m 2 /day) from the general multiple equation (Tab 6) against observed values. Solid line represents the 1 : 1 line and dashed lines are the upper and lower 95% confidence limits of individual observations. Letters refer to individual studies in Table l. bers has been reported for a coastal embayment (Harrison, Platt, 1980) as weil as for an equatorial oceanic area (Herbland, Le Bouteiller, 1983). Estuaries are generally considered more hydrodynamic than offshore oceanic zones and are characterized by higher degrees of vertical mixing and turbidity which tend to reduce primary production (Sinclair et al., 1981; Oncles, Joint, 1983). The plot of the predicted values of production from the final equation (r 2 = 0.67) against observed values (Fig. 3) shows that the 95% confidence Iimits of individual observations range over one order of magnitude. Other factors obviously contribute to the variability observed. Species composition and cell size influence phytoplankton productivity (Malone, 1971; Garrison, 1976; Coté, Platt, 1983; Gros, Ryckaert, 1983), but this information is not often reported in each phytoplankton study and could not be considered in this analysis. However species composition and cell size of phytoplankton are Iargely determined by environmental conditions, particularly the depth of mixing (Parsons, Takahashi, 1973; Ignatiades, 1979; Levasseur et al., 1984) and other physical parameters, such as the degree of stratification or vertical mixing of the water column (Demers, Legendre, 1982; Pingree et al., 1975; 1978; Levasseur et al., 1984). Sorne attempt should be made to consider these variables in future studies. The present study has developed an empirical relationship to predict daily primary production in marine systems from six independent variables that can be easily and routinely measured during fieldwork. The empirical equation derived here: log P =log B +log Io +log ( 1-e- Ke.Zml) -log Ke- log Zml +T-1/Ke -Dl is strikingly similar to a purely theoretical model develo- 70 MARINE PRYMARY PRODUCTION: AN EMPIRICAL MODEL ped by Smith (1980, his equation 27): descriptions have terrestrial (Lieth, 1975; Downing, Weber, 1984) and freshwater applications (Smith, 1979; Straskraba, 1980), yet oceanographie studies have tended to concentrate on more specifie models (Eppley et al., 1985). The present paper is therefore an attempt to extend the search for general, if crude, predictors of primary production in marine systems. log P=log B+log Io +log (1-e- Ke.Zml) -log Ke -log Zml. +log 0 max+ f (Ke.Zml) Not only the variables are common but the sign of the coefficient of these variables are identical for both expressions. The variable 0 max in Smith's equation represents the maximum photosynthetic quantum yield which can be mathematically related to the maximum growth rate, the latter being a known function of temperature (Eppley, 1972). Smith's equation is made more complex than our empirical relationship by the addition of an elaborate function of Ke and Zml [f(Ke.Zml)]. These two variables appeared 6 times in his full equation stressing the importance of the depth of mixing on phytoplankton production as found in our results. Although empirical relationships in ecology need not to reflect the mechanisms linking dependent and independent variables (Peters, 1980; Rigler, 1982), the strong correspondence between empirical and theoretical models observed here indicates that our empirical relationship is consistent with current analytical approaches to this problem. General empirical Although both observation and theory point to the importance of the depth of the mixed layer in phytoplankton dynamics, this variable is subject to a large error in determination and its definition varies among authors. Better precision of this variable coupled with information on other physical variables, such as the degree of stratification, is required for future tests of and improvements to the present empirical relationship. Acknowledgements Funds for this study were provided by the Natural Sciences and Engineering Research Council of Canada and the McGill University Computing Center. We wish to thank Mr. C.T. Taggart for his comments on an early version of the manuscript. REFERENCES Bannister T.T., 1974. Production equations in terms of chlorophyll concentrations, quantum yield and upper limit to production, Limnol. Oceanogr., 19, 1-12. Bennett E.B., Schaefer M.B., 1960. 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