LETTERS ET COMMENTS
LETTRES ET COMMENTAIRES
Phosphorus and Nitrogen Limitation of
Phytoplankton Growth in Oligotrophic Lakes:
Comment on McCauley et al. (1989)
It has proved difficult to make assessments of algal nutrient
limitation in lakes based on bioassay enrichment studies (Dodds
and Priscu 1990; Elser et al. 1990). Therefore, it was a valuable
effort by McCauley et al. (1989) to collect a large data base on
summer average chlorophyll (Chi a), total phosphorus (TP),
and total nitrogen (TN) observations from 266 lakes and to fit
a generalized linear model (sensus McCullagh and Nelder 1989)
in both TP and TN to their data. Unfortunately, I think their
conclusion regarding the relative role of TP and TN in limiting
algal growth is an artifact of their method. They found that
logTP, (logTP)2, (logTP)3, and the product (logTP)-
(log TN) had highly significant partial effects on the logarithm
of chlorophyll concentration. The curves log Chi a = ./(log TP,
log TN) are represented in a log Chi a/log TP graph by a family
of sigmoid curves that converged at low phosphorus concen
trations. This is in contrast with results by Smith (1982), who
found a family of parallel lines. The authors claim that the con
vergence has two implications for lake management: at low
concentrations of TP (<30 mg-ncT3, e.g. in oligotrophic and
mesotrophic lakes, OECD (1982) definitions of trophy) the
chlorophyll concentration is little affected by TN; high con
centrations of TP (>1000 mg-m"3) have little or no effect on
chlorophyll concentrations. However, based on their equations,
small changes in TN and TP of the same numerical value will
give about the same change in Chi a concentration for oligo
trophic lakes. Typical changes, ATP, between years in such
lakes are 3-10 mg-m"3 (Seipet al. 1990). More important, fig.
2D in McCauley et al.'s paper, which also is the basis for their
conclusion, shows a striking feature. The curve Chi a = /(TP)
for TN = 5-TP shows that Chi a decreases with increasing TP
log Chi a
25:1
5:1
m 2.50
B 2.00
CO
1 1.50
O)
H 1 .oo
Z
1■
D)
O
0.50
0.00
-0.50
LO
o
o
in
o
o
o
CNJ
in
C\j
O
LO
CO
CO
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logTP,mg-m"3
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Fig. 1. Response surface showing summer epilimnetic Chi a concentration as a function of summer epilimnetic TP and TN concentrations in
266 lakes. The surface corresponds to the regression log Chi a = -0.83 log TP + 0.34 (log TP)2 -0.12 (log TP)3 + 0.43 (log TP)-(log TN)
+ 0.03, n = 875, found by McCauley et al. (1989). Lines show TN:TP ratio equal to 5:1 and 25:1 (by mass). The lines end approximately at
lowest observed value of TN. Lowest and highest observed values of TP are 1 and 14 095 mg-m"3 and of TN are 61 and 10 740 mg-m"3.
Can. J. Fish. Aquat. Sci., Vol. 48, 1991
2551
in the regions 1 mg-m 3 < TP < 3 mg-rn 3 and TP > 600
mg-m"3. Their calibration region for TP is 1-14 093 mg-m"3
and forTN is 61-10 740 mg-m"3.
To explore this feature further, I depicted the response sur
face for Chi a to changes in both TP and TN (Fig.
1) corre
sponding to McCauley et al.'s equation for the version "com
bined model" (literature data as source). The response surface
underscores the nonsigmoid particularities of the curves shown
by McCauley et al. Since the author's management advice with
regard to TP and TN depends upon the characteristics of Ihe
log Chi a = /{log TP, log TN) curves close to an apparently
anomalous domain, one should probably either give a theoret
ical justification for the anomaly or examine if the anomalies
are artifacts of the method. It is difficult to explain that for
(1989) evaluated the relative role of the two nutrients by exam
ining their empirical relationship with chlorophyll concentra
tion among lakes throughout the Northern Hemisphere, thereby
extending the initial work of Smith (1979). Seip has questioned
one of the conclusions presented in McCauley et al, regarding
the asymmetrical effect of phosphorus and nitrogen in lakes of
different trophic status. McCauley et al. concluded that the
effect of these nutrients varies depending on the level of phos
phorus in the lake. This conclusion was drawn from two sets
of analyses; (1) a model-free inspection of the data showing
that the phosphorus-chlorophyll relationship is sigmoidal (a
result independently established by Prairie et al. (1989)) and
constant TN, chlorophyll may decrease with increasing TP (cf.
Fig. 1 at low TN:TP ratios; the ratio between the largest TN
and TP values in the data set is 0.8). However, contrary to
(2) a multivariate regression analysis of the influence of nitro
gen and phosphorus on chlorophyll levels throughout a broad
collection of lakes. Based on the parametric regression anal
ysis, McCauley et al. found that "the effect of nitrogen is much
logistic expressions, third-order polynomials have an upper and
a lower maximum and thereby negative derivatives. Further
greater at high TP concentration than at low" and that "the
phosphorus-chlorophyll relationship is a family of sigmoid
more, since the independent variables TP and TN probably are
partly colinear, the coefficients of the polynomial expression
curves that converge at low phosphorus concentration." These
conclusions differ considerably from the original interpretation
may be inflated (Reckhow et al. 1987). Thus, based on a visual
assessment of the response surface in Fig. 1, and the arguments
above, 1 feel that the analysis of McCauley et al. does not prove
3.8
that "variation in TN concentration in oligotrophic systems has
little, if any, consequence to algal biomass" — Knut L. Seip,
Senter for industriforskning (Center for Industrial Research),
Forskningsvn 1, P.O.Box 124 Blindern, N-0134 Oslo 3,
Norway.
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References
O
Dodds.W. K.,andJ. C.Priscu. 1990. A comparison of methods for assess
ment of nutrient deficiency of phyloplanklon in alargeoligolrophic kike.
Can. J. Fish. Aquat. Sci. 47: 2328-2338.
J. J., E. R Marzolf, and C. R. Goldman. 1990. Phosphorus and
nitrogen limitation of phytoplankcon growth in the freshwaters of North
America: a review and critique of experimental enrichments. Can.
J. Fish. Aquat. Sci. 47: 1468-1477.
l
1.0
., J. A. Downing, and S.Watson. 1989. Sigmoid relationships
between nutrients and chlorophyll among lakes. Can. J. Fish. Aquat.
Sci. 46: 1171-1175.
McCullagh, P., andJ. A. NfcLDiiR. 1989. Generalized linear models. Chap
3.8
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3.4
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3.0
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2.6
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1
I
I
I
I
man and Hall, London. 511 p.
OECD. 1982. Eutrophication of waters. Monitoring assessment and control.
OECD, Paris.
Rl:ckiiow,K. H.,R. W.Black,T. B. Stockton,Jr.,J. D.Vogt.andJ. G.
Wood. 1987. Empirical models of fish response to lake acidification.
Can. J. Fish. Aquat. Sci. 44: 1432-1442.
Seip, K. L., H. Sas, and S. Vermij. 1990. The short term response to eutro
phication abatement. Aquat. Sci. 52: 199-220.
Smith, V. 1982. The niirogen ;ind phosphorus dependence of algal biomass in
lakes: a theoretical and empirical analysis. Limnol. Oceanogr. 27: I 101-
o
CD
o
1112.
Different Effects of Phosphorus and Nitrogen on
Chlorophyll Concentration in Oligotrophic and
Eutrophic Lakes: Reply to Seip
Establishing the role(s) of the many nutrients that might affect
the observed biomass and production of phytoplankton
throughout the natural domain of lakes is a daunting task.
Results from manipulation experiments along with evidence
gathered from natural variation in levels of nutrients and chlo
rophyll provide key pieces of the puzzle. While Elser et al.
(1990) synthesized and criticized experimental results on phos
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Log10 [Total
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Fig. 1. (A) Predicted lo«10 chlorophyll concentrations from McCauley
et al.'s combined model, where predictions were made only within
the range of TP, TN, and chlorophyll a observed in world lakes (cf.
Seip's fig. 1). (B) Contours of observed logH) chlorophyll concentra
tions in world lakes determined using an inverse squared distance tech
nique followed by cubic-spline smoothing. All concentrations arc
phorus (TP) and nitrogen (TN) limitation. McCauley et al.
2552
Can. J. Fish. Aquat. Sci., Vol. 48, 1991
of Smith (1979) that the relationships consist of a parallel series
of lines.
Seip questions only the validity of the interpretation of the
parametric model presented by McCauley et al. for oligotrophic lakes and suggests that we failed to replicate Smith's
family of parallel relationships between TP and chlorophyll due
to the particular quadratic model that we chose. We disagree
with Seip that our original interpretation is incorrect, and we
support our original conclusion in two ways: (1) by showing
that the asymmetrical effect of nitrogen and phosphorus is pres
ent in the contour plot presented by Seip based on our para
metric model and (2) by examining the raw data themselves
without model fitting to provide evidence that our findings result
from the data and not from our choice of statistics.
Before proceeding, however, it is important to recognize that
the predictions of the regression model must be examined only
over the range of the independent variables. Clearly, models
can often predict spurious (and often ludicrous) results if applied
outside the range of data from which they were derived. There
fore in the analyses presented below, we restrict the contour
plots to the realistic range of log TP and log TN values.
Figure 1A shows the contour plot of predictions of chloro
phyll concentration from our combined model when limited to
the range of natural variation of log TN and log TP. Once the
contour plot is restricted to the range of data present in the
original analysis, the asymmetrical effect of phosphorus and
nitrogen on chlorophyll is readily apparent from the asymmetry
in the isoclines at both low and high phosphorus levels. A nearly
identical response to nitrogen and phosphorus is seen in a sim
ple contour plot of the data (Fig. IB). To illustrate this asym
metry at low phosphorus levels, consider an oligotrophic lake
with log TP (micrograms per litre) = 0.5. Lakes with this level
predicts an increase in chlorophyll response from the 0-0.5
range to the 0.5-1.0 range whereas a unit change in log TN
still predicts chlorophyll levels within the original range of
0-0.5. In both Fig. 1A and IB, isoclines of chlorophyll a con
centration are nearly vertical at low phosphorus concentrations,
but nearly horizontal at high phosphorus concentrations. Chlo
rophyll concentration therefore appears to vary little with TN
in oligotrophic lakes but varies greatly with TN in eutrophic
lakes. Chlorophyll concentrations are very sensitive to variation
in phosphorus concentration in oligotrophic lakes, and insen
sitive to variation in phosphorus concentration in eutrophic
lakes. These predictions are consistent with the conclusions
presented in McCauley et al. and are independent of statistical
fitting methods.
The polynomial equation presented in McCauley et al. are
one of many models that could describe the same result. No
matter what model is chosen, the result is the same: TP con
centration is correlated differently with chlorophyll at different
combinations of phosphorus and nitrogen. Chlorophyll con
centration covaries primarily with TP in oligotrophic lakes and
primarily with TN in eutrophic lakes — Edward McCauley,
Ecology Division, Department of Biological Sciences, Univer
sity of Calgary, Calgary Alta. T2N 1N4, Canada, and John
Downing, Departement de Sciences Biologiques, Universite de
Montreal, Montreal, Quebec H3C 3J7, Canada.
(JB105)
References
Elser, J. J., E. R. Marzolf, and C. R. Goldman. 1990. Phosphorus and
nitrogen limitation of phytoplankton growth in the freshwaters of North
America: a review and critique of experimental enrichments. Can.
J. Fish. Aquat. Sci. 47: 1468-1477.
of phosphorus have an average of 308 fig TN-L"' or log TN =
McCauley, E.,J. A. Downing, andS. Watson. 1989. Sigmoidrelationships
between nutrients and chlorophyll among lakes. Can. J. Fish. Aquat.
2.48 as determined from our original dataset. If you locate this
point on the log TN - log TP surface (Fig. 1) and then ask what
effect does a unit change in log TP or log TN have on the esti
mate of chlorophyll a, you observe that the change in log TP
Prairie, Y. T., C. M. Duarte, and J. Kalff. 1989. Unifying nutrient-chlo
rophyll relationships in lakes. Can. J. Fish. Aquat. Sci. 46: 1176-1182.
Smith, V. H. 1979. Nutrient dependence of primary productivity in lakes.
Limnol. Oceanogr. 24: 1051-1064.
Can. J. Fish. Aquat. Sci., Vol. 48, 1991
Sci. 46: 1171-1175.
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