Download Empirical relationship for marine primary production : the

OCEANOLOGICA ACTA 1986- VOL. 9 - W 1
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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.
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72