PII:
Wat. Res. Vol. 32, No. 12, pp. 3539±3548, 1998
# 1998 Published by Elsevier Science Ltd. All rights reserved
Printed in Great Britain
S0043-1354(98)00165-1
0043-1354/98 $19.00 + 0.00
ALGAL GROWTH IN WARM TEMPERATE RESERVOIRS:
KINETIC EXAMINATION OF NITROGEN, TEMPERATURE,
LIGHT, AND OTHER NUTRIENTS
ROBERT W. STERNER1* and JAMES P. GROVER2
Department of Ecology, Evolution and Behavior, University of Minnesota, 1987 Upper Buford Circle,
St. Paul, MN 55328, U.S.A. and 2Department of Biology, The University of Texas at Arlington, Box
19498, Arlington, TX 76019, U.S.A.
1
(First received October 1997; accepted in revised form March 1998)
AbstractÐNutrient limited growth of the phytoplankton assemblage in two Texas reservoirs was studied by a combination of nutrient addition experiments and statistical modeling. Dilution bioassays
were run to ascertain the qualitative and quantitative patterns in nutrient limitation. Algal growth was
frequently and strongly nutrient limited, particularly when temperature was >228C. By itself, N was
more often stimulatory than P, though strong additional enhancement of growth by P and trace nutrients was often detected. Monod growth kinetics indicated that half-saturation constants for N limited
growth for the entire algal assemblage were in the range 20±200 mg N/L, relatively high compared to literature values, and increased with increasing temperature. Maximal growth was also an increasing function of temperature. A single temperature-dependent model was ®t to the growth dynamics for all
experiments showing N-limitation. The model m = 0.0256T([DIN]/66.0 + [DIN]) where m is speci®c
growth rate (dÿ1), T is temperature (8C) and [DIN] is dissolved inorganic N (mmol/L) ®t the experimental results reasonably well (r2=0.82). However, only a modest predictive power for growth in the controls (our best estimate of growth in situ) was achieved (r2=0.26). Thus, even with unusually detailed,
site-speci®c ®tting of model parameters, accurately modeling algal growth in natural ecosystems can
remain a challenge. # 1998 Published by Elsevier Science Ltd. All rights reserved
Key words: phytoplankton, nitrogen, phosphorus, trace-nutrients, temperature, light, Texas, monod,
water-quality, model.
INTRODUCTION
Accurate portrayal of algal growth is one of most
dicult and poorly understood areas in deterministic water quality modeling. Algal growth is inherently complex, in general showing nonlinear
responses to various environmental parameters such
as temperature, light, and several nutrients, as well
as demonstrating poorly understood interactions
among these separate factors (Bowie et al., 1985;
Thomann and Mueller, 1987). Site-speci®city also
makes extrapolation from lab or other ®eld studies
inherently problematic. Finally, the diverse multispecies algal community may resist being treated as
a single homogeneous unit. Thus, in spite of the
existence of simple, well validated models for nutrient-limited growth (Droop, 1983), accurately treating the kinetics of algal growth in water quality
models remains a signi®cant challenge.
In simpli®ed systems at steady state, algal growth
as a function of a limiting nutrient is usually represented by the Monod (1942) model (see
*Author to whom all correspondence should be addressed.
[E-mail: [email protected]].
equation 1, below), a model constructed from two
parameters: a nutrient-saturated growth rate and a
half-saturation constant. However, in situations
where more than one resource can be limiting, or
when species abundances shift, or when the physical±chemical environment is dynamic, a single
Monod model will likely fail to describe algal
growth kinetics over the whole possible parameter
space (Rhee, 1982). Situations such as these inevitably arise in water quality modeling. Hence, exploring in detail how the Monod model interacts with
these di€erent factors is important.
Parameter ®tting is one of the most important
aspects of deterministic modeling. Even when a
model faithfully describes mechanisms in the prototype, poor results may be obtained when insucient
data are available to estimate rate constants and
coecients (Bowie et al., 1985). In freshwaters, Pdependent growth kinetics of freshwater algae have
been described often enough to allow for systematic
examination of these parameters (Grover, 1989a,b).
However, N is at least an important secondary limiting nutrient in freshwaters (Elser et al., 1990), and
unfortunately most of the information available on
N-dependent growth kinetics in algae derives from
3539
3540
James W. Sterner and Robert P. Grover
Table 1. Physical and chemical conditions at the start of each of the bioassay experiments
Site
CC-L
EM-L
CC-C1
EM-U
EM-C
CC-U
CC-L
EM-L
CC-C2
EM-U
CC-U
EM-C
EM-L
CC-U
EM-U
CC-L
EM-C
CC-C2
Date
14-Jan
21-Jan
28-Jan
4-Feb
11-Feb
18-Feb
8-Apr
15-Apr
22-Apr
29-Apr
6-May
20-May
24-Jun
1-Jul
8-Jul
15-Jul
22-Jul
29-Jul
#
1
2
3
4
5
6
7
8
9
10
11
12
14
15
16
17
18
19
zmix (m)
Temp (8C)
13
13
5
6
2
4
13
12
28
6
6
2
4
5
6
9
2.5
2.5
9.4
7.1
9.0
7.3
6.4
8.9
15
18
22
21
19
25
29
29
29
28
30
28
Light (mE mÿ2 sÿ1)
60
78
110
109
360
132
50
93
213
125
78
222
269
93
85
107
162
212
DIN (mg N/L) TDP (mg P/L)
221
63
242
9
2
197
147
6
25
50
248
ÿ
19
12
29
36
38
66
20.3
18.7
21.6
9.8
12.3
24.0
34.6
13.1
28.1
20.6
48.6
ÿ
18.6
31.0
40.1
2.0
18.3
34.6
Sites are given as either CC (Cedar Creek) or EM (Eagle Mountain) together with an indication of site within the lake, either L (lower,
near dam), U (upper, near main in¯ow), or C (cove). Two sites in Prairie Cove were studied in CC reservoir. The depth represents
either the depth of the whole water column when temperature pro®les were isothermal, or the depth of the mixed layer when strati®cation was present. Light is the mean light in the relevant water column, calculated as described in the text. Bioassay 13 was lost due
to incubator failure; the original numbering scheme is preserved in this paper. Chemistry data for EM-C on May 20 is unavailable.
marine studies. Though there have been important
examinations of N-limited growth in freshwater
algae (Gotham and Rhee, 1981; Rhee and Gotham,
1981; Elri® and Turpin, 1985; Sommer, 1989, 1991;
Watanabe and Miyazaki, 1996), there have been
relatively few reports of Monod growth kinetic
terms of freshwater algae under N limitation.
Systematic examinations of these parameters have
apparently not yet been possible. Rhee and Gotham
(1981) reported that increasing temperature tended
to decrease cell N requirements, but few studies if
any have dealt seriously with the dependence of Nlimited growth kinetic terms on environmental factors such as temperature and light.
In the laboratory, growth kinetic terms can be
measured under highly controlled conditions of
constant temperature and light, well-de®ned chemical concentrations, and known preconditioning.
Hence, growth kinetics determined in the laboratory
can be considered ``fundamental'' measurements
that tell a great deal about physiological and community ecology (Tilman et al., 1982). Nevertheless,
there may be problems transferring measurements
like these to the ®eld. In nature, the phytoplankton
assemblage is diverse and often is dominated by
species poorly represented or dicult to grow in
laboratory cultures. Furthermore, it may be the
exception, not the rule, when a single nutrient is
rate limiting to all the species in any single natural
environment. The water quality modeler requires information on how the concentration of a particular
nutrient will in¯uence the growth of natural algae
in a complex physical and chemical background
where conditions may not be ideal for the species
present. Hence, here we would like to contrast laboratory-based Monod parameters with those from a
mathematically identical ``dose±response'' model,
where the latter is a physiological derivative of the
former, and it may occur in the presence of greater
than one limiting resource.
Given these many potential impediments to accurate modeling of algal growth, the purpose of this
study was to undertake a detailed investigation of
the dose±response relationships between nitrogen,
phosphorus, and algal growth in two reservoirs to
see if an improvement to water quality model parameters could be recommended. We wished to see
how well a Monod model or modi®ed Monod
model would describe algal growth dynamics.
MATERIAL AND METHODS
Sites and chemical analysis
Eagle Mountain Lake (32852' N, 978 28' W) is located
in Tarrant County, Texas. It has an area of 3638 ha, a
volume of 0.22 km3, a mean depth of 6.1 m, and a hydraulic retention time of 198 d. Its watershed area is 5100 km2,
just over half of which drains into Bridgeport Lake, the
only upstream reservoir on the major tributary (West
Fork Trinity River). Over a two-year period ending at the
end of the study period, average annual loading rates were
79.1 kg DIN haÿ1 yrÿ1, 390 kg total N haÿ1 yrÿ1 (excluding
DON), 23.7 kg DIP haÿ1 yrÿ1, and 77.4 kg total P
haÿ1 yrÿ1 (based on data provided by M. Ernst, Tarrant
Regional Water Authority). The dissolved inorganic N:P
loading ratio for Eagle Mountain Lake is thus 3.33 by
weight, while the total N:P loading ratio is 5.04 (excluding
dissolved organic N). Cedar Creek (328 14', 968 08'W) is
located in Henderson County, Texas. It has an area of
13950 ha, a volume of 0.84 km3, a mean depth of 6.1 m,
and a hydraulic retention time of 275 d. Its watershed area
is 2607 km2, and there are no reservoirs on its major tributaries (Kings Creek and Cedar Creek). Over a two-year
period ending at the end of the study period, average
annual loading rates were estimated as 36.9 kg DIN
haÿ1 yrÿ1, 113 kg total N haÿ1 yrÿ1 (excluding DON),
14.1 kg DIP haÿ1 yrÿ1, and 26.5 kg total P haÿ1 yrÿ1. The
dissolved inorganic N:P loading ratio for Cedar Creek
Lake is thus 2.62 by weight, while the total N:P loading
ratio is 4.29 (excluding dissolved organic N).
N-limited algal kinetics
3541
Table 2. Concentrations of nutrients in bioassay bottles
Bottles
1±3
4±6
7±9
10±12
13±15
16±18
19±21
22±24
25±27
28±30
31±33
34±36
37±39
P addition (mg P/L)
0
1
10
50
100
1000
0
0
0
0
0
0
1000
N addition (mg N/L)
0
0
0
0
0
0
1
10
100
200
2000
0
2000
Trace nutrientsa
0
0
0
0
0
0
0
0
0
0
0
+
+
Trace nutrients are detailed below.
a
Trace nutrients consisted of (concentrations in ®nal bottles given as mg/L): Na2EDTA (0.80), FeCl36H2O (0.34), MnSO4H2O (0.061),
ZnSO47H2O (0.017), Na2MoO42H2O (0.005), CoCl25H2O (0.002), H3BO4 (0.10), biotin (0.00005), vitamin B-12 (0.00005), and thiamine (0.01).
Several sites were examined in each reservoir. ``Upper''
sites, located near the main in¯ow, were turbid and did
not permanently stratify (mean site depths 7 and 6 m in
EM and CC, respectively). ``Lower'' sites were near the
dam, were less turbid, and exhibited summertime strati®cation (mean site depths 14 and 12 m). ``Cove'' samples
were located in small bays (Walnut Creek Cove in EM
and Prairie Cove in CC), had variable turbidity, and did
not permanently stratify (mean site depths 2 and 4 m).
1±18 and 37±39, and measuring the concentrations of
NO3 and NH+
4 in bottles 1±3, 19±33, and 37±39.
Chlorophyll was analyzed following extraction in 90%
acetone overnight (no grinding). A ¯uorometric means of
separating chlorophyll a from chlorophyll b and phaeopigments (Welschmeyer, 1994) was used. This method was initially compared with various procedures using extraction
in methanol, extraction by grinding, and acidi®cation steps
and was found to give reliable results.
Sampling
Data analysis
On a set of eighteen dates in 1994 (Table 1), water
samples were collected from several depths within the
upper mixed layer and combined into a single sample.
Temperature and irradiance were measured every meter.
Water was ®ltered in the laboratory (0.2 mm), and NO3,
NO2, NH+
4 , SRP and TDP were measured with methods
following Strickland and Parsons (1972), except for TDP
which used the method of Menzel and Corwin (1965).
Dissolved inorganic nitrogen (DIN) was calculated as the
sum of the three inorganic N species.
The speci®c growth rate (dÿ1) in each bioassay bottle
was calculated from linear regressions of the natural logarithm of chlorophyll a vs time. Some small deviations from
linearity were observed in the last day of some bioassay
bottles (lower than expected biomass). However, to maintain consistency and because it did not appear that the regression slopes would be greatly altered, we did not
selectively eliminate these points.
To perform a qualitative assessment of whether P or N
limitation was present, and to assess the presence of trace
nutrient limitation or colimitation, we analyzed growth
rates from a subset of the bioassay bottles (1±3, 16±18,
31±33, 34±39, Table 2) with a one-way ANOVA consisting
of ®ve treatments: Control (no nutrients added), +P
(highest level of P alone), +N (highest level of N alone),
+TN (addition of trace nutrients alone), and +All (addition of N, P and trace nutrients). Bonferroni correction
for 18 tests (the number of bioassays) was used to get an
experiment-wide error rate of 0.05. When signi®cant treatment e€ects were identi®ed by ANOVA, Tukey's HSD
(Kleinbaum et al., 1988) was used for multiple comparisons. If the growth rate from a single nutrient addition
was found to be statistically greater than the growth rate
for the control, the result was taken to indicate limitation
by that nutrient. Bioassay experiments such as these can
detect two types of colimitation of multiple nutrients. In
one type, algae respond to more than one nutrient when
added individually, such that statistically, there would be
two main e€ects and no interaction term. In the other
type of colimitation, algae in the presence of more than
one nutrient addition show greater growth than predicted
by the linear combination of main e€ects. If response to
more than one single nutrient addition was seen, or if the
growth rate in the +All treatment exceeded that of all
single nutrient additions, colimitation was inferred. A
quantitative index to nutrient limitation (INL) was calculated from the ratio of growth in control ¯asks to growth
in +All ¯asks (0 < 1). Growth in the +All treatments
will be referred to as mmax (dÿ1).
Dose±response kinetics of algal growth vs P and N were
determined by analysis of bioassay bottles 1±18 (P) or 1±
Bioassay experiments
Though ``bottle e€ects'' can never be totally overcome
in experiments in small volumes, one way to minimize
some of the problems inherent in bottle bioassays is to dilute the community suciently to allow for several days'
growth under uncrowded conditions. Dilution also minimizes consumption of algae by protozoan and other
microconsumer grazers. Such a ``dilution bioassay''
method has been used to determine the nature of limiting
substances for natural, in situ algae (Sommer, 1989;
Sterner, 1990). Here, algae were diluted in a ratio 9:1 (®ltered:whole) using 0.2 mm ®ltered water. Triplicate samples
for initial chlorophyll were taken. Aliquots of 120 mL
from the diluted preparation were dispensed into 500 mL
acid-washed erlenmeyer ¯asks. Nutrient treatments were
then applied (Table 2). Bioassay bottles were incubated
with constant shaking at light and temperature conditions
representative of the mixed layer of the reservoir at the
time of the experiment (Table 1). For light, a mean value
for the mixed layer for the reservoir on that date was calculated from extinction coecients measured on the day
of the sample collection, together with the depth of the
thermocline (or the depth of the whole water column
when unstrati®ed), and with an estimate of average incident light for that latitude at that time of year.
Each day, duplicate samples for chlorophyll analysis
were withdrawn, ®ltered and frozen for later analysis. On
the ®nal day (4), chemical analysis was also performed,
measuring the concentrations of SRP and TDP in bottles
3542
James W. Sterner and Robert P. Grover
3, 19±33 (N) (Table 2) in bioassay experiments found to
show stimulation from either P or N alone. A Monod
equation (equation 1) was ®t to the data using nonlinear
regression (all statistics used Statistica, Statsoft, Inc., Ver
5):
‰RŠ
m ˆ m0
…1†
K ‡ ‰RŠ
where m is the realized growth rate (dÿ1); m' the growth
rate (dÿ1) saturated by the single experimental nutrient;
[R] the concentration of dissolved nutrient (mg P/L or mg
N/L depending on the experiment); and K the half-saturation constant for nutrient-limited growth. Some nutrient
depletion occurred in some of the treatments so that concentrations on day 4 were less than day 0. For nutrient
concentration [R] in model equation 1, we used the average of the values measured on day 0 and on day 4.
Nutrient chemistries for day zero for bioassay 12 are not
available. For this experiment, initial DIN was set to zero,
thus potentially biasing the results toward low values of
K. Note that, in the case of colimitation, mmax (growth
saturated by all nutrients) need not equal m' (growth saturated by one nutrient). Asymptotic standard errors of the
parameters m' and K were calculated and are reported
here, but it is important to note here that such standard
errors from nonlinear regression are very approximate,
Fig. 1. Qualitative patterns of nutrient limitation (chlorophyll growth rates, mean2SE) for twelve experiments where nutrient limitation was detected. Small case letters below ®gures identify treatments
not signi®cantly di€erent (Tukey's HSD, p = 0.05). Treatment types are identi®ed by uppercase letters
at the bottom of the ®gure.
N-limited algal kinetics
and probably underestimate the true error (Seber and
Wild, 1989).
RESULTS
Nutrient limitation of algal growth was detected
in twelve of eighteen bioassays (Fig. 1). Seasonal
patterns di€ered in the two sites. In Cedar Creek
reservoir, presence of nutrient limitation was distinctly seasonal. All experiments with water tem-
3543
perature <208C did not show nutrient limitation,
and all experiments above this temperature did. On
the other hand, in Eagle Mountain all experiments
but one showed nutrient limitation (and that one,
bioassay 10, had growth rates suggestive of nutrient
limitation, though not statistically di€erent). In
both sites, colimitation by multiple nutrients was
observed. In fact, all twelve of the bioassays with
nutrient limitation showed some form of colimita-
Fig. 2. Growth rates vs nutrient concentrations for bioassays showing single nutrient limitation. Kinetic
parameters and statistical summaries are given in Table 3. Note that one plot shows responses to P
(Bioassay 14, bottom right) and the remainder show responses to N.
3544
James W. Sterner and Robert P. Grover
tion (Fig. 1). Of all the single nutrient additions, N
was the most important, with detectable response to
N alone in almost 40% (7/18) of all experiments. P
and TN alone were found to be signi®cant in only
11% (2/18) and 6% (1/18) of experiments. When
nutrient limitation was present, it was quantitatively
strong. Mean INL in experiments showing nutrient
limitation was only 0.12 (max = 0.21), indicating
realized growth of only 12% of nutrient-saturated
growth. These qualitative patterns of nutrient limitation indicate that N, in combination with either P
or TN, had a strongly regulating e€ect on algal
growth in both reservoirs in the summer and in
Eagle Mountain reservoir often in the cold season
as well.
In all cases where qualitative macronutrient limitation was detected, the Monod model equation 1
provided a reasonable ®t to the data (Fig. 2,
Table 3). Asymptotic standard errors and t-statistics
of m' indicated that this parameter was well determined statistically. In contrast, for K, asymptotic
standard errors were often large, and t-statistics
were not all signi®cant.
Estimates of m' ranged from 0.19 dÿ1 early in the
season to 0.82 dÿ1 later (Table 3). There was only
one estimate of the half-saturation constant for
growth for P limitation, thus precluding more
analysis of this parameter. For nitrogen-limited
growth, the parameter K had a rather wide range
from 18.6 to 201 mg/L, but again the uncertainty associated with each of these estimates must be noted,
because it very likely contributed substantially to
this wide range. The median, an unweighted mean,
and a mean weighted by the inverse of SE are
reported in Table 3. The one bioassay with incomplete chemistries (#12) did not look unusual and so
was included in all further analyses.
Many previous studies have documented the
dependence of maximal growth rate on temperature. In this study, the parameters mmax and m' were
both signi®cantly related to temperature, but not to
light in multiple regressions (m': Temp, t7=7.1,
p < 0.01, Light, t7=0.46, p = 0.65; mmax: Temp,
t15=5.64, p < 0.01, Light, t15=1.6, p = 0.13) (note
that more estimates of mmax are available since this
was estimated in every bioassay). The two measurements of maximal growth compared favorably at
the low and high temperature, but m' was less than
mmax at intermediate temperature. The index of
nutrient limitation (INL) indicated consistently very
strong nutrient limitation in temperatures >228C
[Fig. 3(D)].
Though many biological reactions depend on the
reciprocal of temperature, in a manner described by
the Arrhenius equation, and some algal growth studies support this formulation for temperaturedependence of maximal growth (e.g. Goldman and
Carpenter, 1974), there is in fact no standard representation of growth and temperature (Rhee, 1982;
Bowie et al., 1985; Ahlgren, 1987). Here, the relationship between both mmax and m' vs temperature
was explored in more detail by examining regressions of ln-transformed growth and reciprocaltransformed (1/T) temperature in all possible combinations with the untransformed data. Though
some modest increases in r2 were achieved by these
transformations, the two growth parameters
required di€erent transformations to maximize r2,
so in the interest of simplicity and consistency, the
untransformed variable T was used in further analyses. The regressions for the growth rate parameters were,
m 0 ˆ0:10 ‡ 0:024T,
mmax ˆ0:21 ‡ 0:025T,
r ˆ 0:93 and
r ˆ 0:81:
In both cases, the intercepts were not signi®cantly
di€erent from zero, but the slopes were.
Temperature e€ects on K are more poorly
described than for growth, but have been reported
(Rhee and Gotham, 1981). Physical±chemical
models of uptake predict a positive relationship
Table 3. Monod kinetic parameters for algal growth in bioassay experiments showing single nutrient limitation
Bioassay
2: EM-L, Jan 21
4: EM-U, Feb 4
5: EM-C, Feb 11
8: EM-L, April 15
9: CC-C2, April 22
12: EM-C, May 20a
15: CC-U, July 1
16: EM-U, July 8
19: CC-C2, July 29
14: EM-L, June 24
Unweighted Mean
Median
Weighted Mean
Nutrient
DIN
DIN
DIN
DIN
DIN
DIN
DIN
DIN
DIN
TDP
Km (mg/L, mean 2 SE) mmax (dÿ1, mean 2SE) m' (dÿ1, mean 2SE)
58.1 236.1
24.3 28.3*
18.6 26.3*
34.7 218.0
172 2 79.5
105 2 41.8*
82.0 226.0*
109 232*
201 274*
10.1 23.1*
0.212 0.03*
0.242 0.02*
0.192 0.02*
0.312 0.04*
0.382 0.06*
0.592 0.08*
0.652 0.07*
0.772 0.09*
0.722 0.08*
0.822 0.09*
Summary of N kinetics
89.4
0.44
82.0
0.38
48.5
0.32
0.2320.02
0.4020.05
0.6820.01
0.8820.16
0.6120.03
0.9520.02
1.0620.14
0.8320.07
0.8420.08
0.9820.17
r2
0.25
0.74
0.69
0.51
0.67
0.73
0.83
0.93
0.91
0.66
0.72
0.83
0.65
For plots and ®tted functions, see Fig. 2. For the Monod parameters K and mmax (equation 1), statistical signi®cance is shown here by *
indicating p < 0.05 by t-statistic. Summary statistics at bottom include all N-limited or N-colimited cases as indicated by DIN in the
Nutrient column. Weighted means utilize the reciprocal of the SE's for weights.
a
Initial DIN set to zero.
N-limited algal kinetics
Fig. 3. Changes in kinetic parameters and intensity of
nutrient limitation with temperature. Circles: Cedar Creek.
Squares: Eagle Mountain. (A) The half-saturation constant for N-limited growth (K) vs temperature. Regression
equation for dashed line is given in the text. (B) Maximal
growth in N dose±response experiments (m') increased with
temperature. (C) Maximal growth in the presence of all
nutrients (mmax) also increased with temperature.
Regression equation given in text. (D) The index of nutrient limitation (INL) was variable below 228C but was consistently low (indicating strong nutrient limitation) above
that temperature.
between the half-saturation constant for uptake and
temperature (Aksnes and Egge, 1991). Though it is
important to remember that the half saturation constant for uptake and for growth are not equivalent
(Morel, 1987), we might expect both to increase
with temperature if one does. In this study, the parameter K was positively correlated to temperature
[r = 0.70, p = 0.03, Fig. 3(A)] but not to light
(r = 0.11, p = 0.78). Similarly, in a multiple regression, temperature was found to be signi®cant
(t6=2.7, p = 0.03) but light was not (t6=0.87,
p = 0.4). The regression equation describing the
e€ect of temperature (T, 8C) on the half-saturation
constant
for
N-limited
growth
was,
K = 0.76 + 4.6T, which suggests a trend of K from
approximately 40 to approximately 130 mg/L from
winter to summer temperatures.
Combined in¯uences of nutrients and temperature
Based upon the evidence for near linear e€ects of
temperature on m' [Fig. 3(B)] a temperature-dependent model was ®t to all N-limited bioassays,
‰RŠ
m ˆ TmT
…2†
K ‡ ‰RŠ
3545
Fig. 4. Temperature-dependent growth model (equation 2)
on maximal growth vs observed growth in experiments in
the two reservoirs. (A) Plot shows observed growth rate
(dayÿ1) from all nine N-limited bioassays vs DIN (mg/L)
and temperature (8C). (B) Residual plot showing some evidence for lack of ®t; data and model identical to (A)
above.
where mT is the coecient for temperature-dependence for growth. Nonlinear regression of this
model yielded reasonable ®t to the data [Fig. 4(A),
r2=0.82], but residuals indicated apparent overestimation of growth at low growth rates, and apparent
underestimation at intermediate growth rates
[Fig. 4(B)]. Parameters were well de®ned:
mT ˆ0:025620:001 …dayÿ1 8Cÿ1 †;
K ˆ66:027:4 …mg=L†:
Two variations of this model were also examined.
One included linear temperature dependence on the
half-saturation constant as well as on the maximal
growth rate, as suggested in Fig. 3(A). The other
model utilized an exponential term for temperaturedependent maximal growth (of form amT where a is
a constant and T is temperature). These two variations yielded only slight improvements in predictive power (r2=0.83 and 0.84, respectively) and lack
of ®t as suggested by residuals was not eliminated
(not shown). Hence, the simpler model equation 2
was chosen as best.
3546
James W. Sterner and Robert P. Grover
DISCUSSION AND CONCLUSIONS
Fig. 5. Observed vs predicted growth rates using model
equation 2. Closed circles: N-limited bioassays. Open
squares: all others. Dotted line has slope of 1 and represents perfect predictive power. Points are labeled as to
bioassay number (Table 1). Bioassay 12 is not plotted
since incomplete data precluded prediction with the
model.
Finally, it can be asked whether the temperaturedependent kinetic model equation 2 can be used to
predict algal growth in the reservoirs. To answer
this question, predicted growth rates from model
equation 2 using values in Table 1 were compared
to observed growth in the control ¯asks for seventeen of eighteen bioassay experiments (initial chemistry data not available for one experiment).
Growth in the controls represents the best estimate
available of algal growth in the reservoirs, because
the algae were simply resuspended in ®ltered, unamended water. Predicted and observed growth rates
were very signi®cantly positively correlated
(r = 0.51, p < 0.01), though the success of the
model at predicting growth was modest (Fig. 5).
The model tended to overestimate growth rate at
low growth, consistent with the residual analysis
given in Fig. 4(B). There was a major dichotomy
between observed growth under N-limitation (Fig. 5,
circles) and without N limitation (Fig. 5, squares).
N limitation prevailed when observed growth was
less than approximately 0.2 dÿ1.
Attempts to increase the predictive power of this
model were unsuccessful. Plots of residual values vs
TDP, light, zmix and site failed to demonstrate any
convincing trend. The possibility that colimitation
of DIN and other nutrients reduced the predictive
power of the model was examined by comparing
the residual variation in Fig. 5 to the magnitude of
additional stimulation by P and trace nutrients
(+All compared to +N, Fig. 1). There was no
obvious relationship between these parameters.
Note, for example, that the model is successful for
bioassays 8 and 4 (Fig. 5), but these have strong
nutrient interactions (Fig. 1). In contrast, the model
is poor for bioassays 16 and 19, but for these two,
the nutrient interaction is weak, with growth in the
presence of N alone nearly equally growth in the
presence of all nutrients (Fig. 1).
The goal of deterministic water quality modeling
is to produce a model of sucient realism to reproduce the dynamics of the relevant ®eld site, and to
allow for the exploration of di€erent management
scenarios (Thomann and Mueller, 1987). Model
validation normally occurs by con®rming that the
modeled variables reproduce the temporal dynamics
or sometimes the annual average in the prototype.
However, this method of validation risks ``getting it
right for the wrong reasons''. If subcomponents of
the model are validated instead, there can be more
assurance that the individual mechanisms in the
model accurately re¯ect nature. In this study, we
examined in detail how to use the Monod growth
model (equation 1) in combination with a great
deal of experimental and observational data from
two study sites to represent the growth of algae in
these Texas reservoirs through the year.
Half-saturation constants for N-limited algal
growth of total phytoplankton are usually modeled
in the range of 10±20 mg/L (Thomann and Mueller,
1987) but may range in speci®c instances from 1.4
to 400 mg/L (Bowie et al., 1985). Unfortunately, the
number of actual measurements of this parameter
for freshwater algae is relatively small. Values
obtained in this study were somewhat higher than
the range typically modeled. Dose±response relationships in these reservoirs suggested half-saturation constants for N-limited growth in the range
from 18.6 to 201 mg/L (Table 3), with a single
weighted mean of 48.5 mg/L. The temperature
dependent model equation 2 suggested a value of
66.0 mg/L. Clearly, the method of determination of
K has an in¯uence on the value of this parameter
that is chosen. Systematic changes in K for N-limited growth with respect to parameters such as temperature are not yet well described. In the face of
this uncertainty, and given the inherent statistical
diculties
of
determining
this
parameter
(Ratkowsky, 1983), considerable latitude is available to modelers. Additional study of the half-saturation constant for N-limited growth is clearly
needed, and its potential temperature-dependence
requires con®rmation.
Nutrient limitation as measured by the intensity
of nutrient limitation, INL [Fig. 3(D)] was strong at
some times and weak at others. Single nutrient limitation by N was often observed whereas single
nutrient limitation by P was observed only once. A
Monod model alone (equation 1) does not take into
account many factors such as temperature- or lightdependence, interactions among nutrients, and
changes in species composition, so we paid particular attention to interactions such as these. In this
study, the mean light in the mixed layer seemed to
have little in¯uence on algal community growth in
that it was neither related to nutrient-saturated
growth rates nor was it related to growth in con-
N-limited algal kinetics
trols. Temperature however had a clear and consistent e€ect on nutrient-saturated growth rate, and a
Monod model that included linear e€ects of temperature on growth provided a reasonably good
description of the experimental data (Fig. 4).
Temperature also was related to the half-saturation
constant for growth, but inclusion of such a temperature dependence improved the ability to predict
realized growth rates only marginally. Interactions
between individual nutrients (speci®cally N with P
or N with TN or all three) were often observed in
the experiments.
In sorting through the various factors that potentially in¯uence algal growth in these two reservoirs,
the best model was one that included both limitation by DIN and temperature e€ects on nutrientsaturated growth (equation 2). Including other
terms either did not improve the ®t to the data, or
improved it only very slightly. The light climate
seemed not to have much in¯uence on algal growth.
Use of this model to predict the growth of the
entire algal assemblage in these two reservoirs
explained approximately 25% of the variability in
the growth rates in control ¯asks under N-limited
conditions, our best estimate of growth in situ. We
could not signi®cantly improve on this value by inclusion of other factors.
It is perhaps sobering that a detailed study on
rate kinetics such as this can do no better than
explain 25% of the variation in algal community
growth. The reasons for this lack of success need to
be discussed. First, it is possible that a considerable
amount of the residual variation is from ``uninteresting'' (or unmeaningful) sources such as analytical
precision of measuring DIN or other nutrients,
sampling error, or bottle e€ects. That is, the model
may actually do a better job of predicting algal
growth than Fig. 5 indicates. Growth in the control
bottles does not necessary equal growth in the
reservoir itself. The analytical precision of measuring DIN is a particularly problematic feature here,
since at low concentration, small di€erences in DIN
can mean large di€erences in predicted growth.
Though we cannot test this idea explicitly with the
data at hand, it is our feeling that analytical precision of measuring DIN concentrations is a large
source of the residual variation. The suitability of
DIN itself as a measure of a resource probably
bears more scrutiny too. Algae discriminate between
ÿ
NH+
4 and NO3 (Eppley et al., 1969; Stolte et al.,
1994). Unfortunately, our data cannot resolve any
di€erential growth that could be predicted by separÿ
ately studying NH+
4 and NO3 .
Other factors more fundamental to algal physiology likely contribute to the problem. Many studies have shown that instantaneous measurements
of nutrient concentrations are imperfect predictors
of growth under nonequilibrium conditions, such as
inevitably exist in nature (Burmaster, 1979;
Sommer, 1985; Grover, 1990, 1991). Algae can
3547
maintain higher than expected growth when nutrients are low if they have recently experienced a
high nutrient pulse. Patchiness such as this may
provide a sucient explanation for why observed
growth sometimes exceeds predicted growth at low
[DIN] (points below diagonal line in Fig. 5).
Models based on internal cellular nutrient concentrations can better predict growth rate than one
based on extracellular concentrations (Sommer,
1991).
Much work remains in understanding the fundamental limnology of reservoirs in arid regions. The
extent to which these sites are P-, N-, or trace nutrient-limited, or limited by combinations of these elements, needs to be systematically studied.
Bioassays conducted with methods identical to the
present study in another north Texas reservoir, Joe
Pool Lake, indicated a much greater importance of
P and trace nutrients than N (Sterner, 1994). The
two reservoirs in the present study, Cedar Creek
and Eagle Mountain, are located in the same geographic region as Joe Pool Lake. All are part of the
Trinity River drainage. Cedar Creek and Eagle
Mountain demonstrated contrasting conditions to
Joe Pool Lake in that N was much more important
than P in these two sites. Generalization about
algal-nutrient relationships in north Texas reservoirs, including the identity of the main limiting
nutrients, is clearly premature. One similarity
between these two studies though was that in all
three reservoirs, nutrients became strongly and consistently limiting when water temperature was
warm. Interestingly, the kinetic parameters for
Cedar Creek and Eagle Mountain showed no distinct site-to-site variability, as can be seen in Fig. 3
by comparing the two kinds of symbols. The data
have also been scanned manually to see if there
were consistent di€erences between or among the
three kinds of sites within the reservoir. There were
not.
In summary, we have shown that a detailed study
on parameter ®tting of the Monod algal-nutrient
model provides only modest predictive power.
Besides indicating interesting things about algalnutrient relationships, we feel these results should
sound a cautionary note about general application
of models such as these in water quality modeling.
Faithful prediction of ®ne-scale algal dynamics may
not be achievable. However, models may still be
useful for other purposes, such as heuristic exploration of management scenarios, and projections of
long-term average algal biomass. As always, those
using models must be clear about their goals, and
clear-headed about limitations.
AcknowledgementsÐWe are grateful to Mark Ernst for
advice and assistance and to the Tarrant County Water
Control District for funding. Judy Robinson, Caroll
Duhon, and Clayton Napier provided expert technical assistance. Additional funding was provided by NSF grants
9119781 and 9421925 to RWS, and grant 9418096 to JPG.
3548
James W. Sterner and Robert P. Grover
The Max Planck Institut fuÈr Limnologie provided support
for writing the manuscript.
REFERENCES
Ahlgren G. (1987) Temperature functions in biology and
their application to algal growth constants. Oikos 49,
177±190.
Aksnes D. L. and Egge J. K. (1991) A theoretical model
for nutrient uptake in phytoplankton. Marine Ecology
Progress Series 70, 65±72.
Bowie G. L., Mills W. B., Porcella D. B., Campbell C. L.,
Pagenkopf J. R., Rupp G. L., Johnson K. M., Chan
P. W. H. and Gherini S. A. (1985) Rates, constants, and
kinetics formulations in surface water quality modeling
(second edition). U. S. Environmental Protection
Agency, Environmental Research Laboratory, Athens,
GA. EPA/600/3-85/040.
Burmaster D. (1979) The continuous culture of phytoplankton: mathematical equivalence among three steady
state models. American Naturalist 113, 123±134.
Droop M. R. (1983) 25 years of algal growth kinetics. A
personal view. Bot. Mar. 26, 99±112.
Elri® I. R. and Turpin D. H. (1985) Steady-state luxury
consumption and the concept of optimum nutrient
ratios: a study with phosphate and nitrate limited
Selenastrum minutum (Chlorophyta). J. Phycol. 21, 592±
602.
Elser J. J., Marzolf E. R. and Goldman C. R. (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.
Eppley R., Rogers J. N. and McCarthy J. J. (1969) Halfsaturation constants for uptake of nitrate and ammonium by marine phytoplankton. Limnol. Oceanogr.
14, 912±920.
Goldman J. C. and Carpenter E. J. (1974) A kinetic
approach to the e€ect of temperature in algal growth.
Limnol. Oceanogr. 19, 756±766.
Gotham I. J. and Rhee G.-Y. (1981) Comparative kinetic
studies of nitrate limited growth and nitrate uptake in
phytoplankton continuous culture. J. Phycol. 17, 309±
314.
Grover J. P. (1989a) In¯uence of cell shape and size on
algal competitive ability. J. Phycol. 25, 402±405.
Grover J. P. (1989b) Phosphorus-dependent growth kinetics of 11 species of freshwater algae. Limnol.
Oceanogr. 34, 341±348.
Grover J. P. (1990) Resource competition in a variable environment: phytoplankton growing according to
Monod's model. The American Naturalist 136, 771±789.
Grover J. P. (1991) Algae grown in non-steady continuous
culture: Population dynamics and phosphorus uptake.
Verh. Internat. Verein. Limnol. 24, 2661±2664.
Kleinbaum D. G., Kupper L. L. and Muller K. E. (1988)
Applied Regression Analysis and Other Multivariable
Methods. Duxbury Press, Belmont, CA.
Menzel D. W. and Corwin N. (1965) The measurement of
total phosphorus in seawater based on the liberation of
organically bound fractions by persulfate oxidation.
Limnol. Oceanogr. 10, 280±282.
Monod J. (1942) La Croissance des Cultures Bacteriennes.
Hermann, Paris.
Morel F. M. M. (1987) Kinetics of nutrient uptake and
growth in phytoplankton. J. Phycol. 23, 137±150.
Ratkowsky D. A. (1983) Nonlinear Regression. Marcel
Dekker, Inc., New York.
Rhee G.-Y. (1982) E€ects of environmental factors and
their interactions on phytoplankton growth. Adv.
Microb. Ecol. 6, 33±74.
Rhee G.-Y. and Gotham I. J. (1981) The e€ect of environmental factors on phytoplankton growth: temperature
and the interactions of temperature with nutrient limitation. Limnol. Oceanogr. 26, 635±648.
Seber G. A. F. and Wild C. J. (1989) Nonlinear
Regression. John Wiley and Sons, New York.
Sommer U. (1985) Comparison between steady state and
non-steady state competition: Experiments with natural
phytoplankton. Limnol. Oceanogr. 30, 335±346.
Sommer U. (1989) Nutrient status and nutrient competition of phytoplankton in a shallow, hypertrophic lake.
Limnol. Oceanogr. 34, 1162±1173.
Sommer U. (1991) A comparison of the Droop and the
Monod models of nutrient limited growth applied to
natural populations of phytoplankton. Funct. Ecol. 5,
535±544.
Sterner R. W. (1990) Resource competition and the autecology of pennate diatoms. Verh. Internat. Verein.
Limnol. 24.
Sterner R. W. (1994) Seasonal and spatial patterns in
macro and micro nutrient limitation in Joe Pool Lake.
Texas. Limnol. Oceanogr. 39, 535±550.
Stolte W., McCollin T., Noordeloos A. A. M. and
Riegman R. (1994) E€ect of nitrogen source on the size
distribution within marine phytoplankton populations.
J. Exp. Mar. Bio. Ecol. 184, 83±97.
Strickland J. D. H. and Parsons T. R. (1972) A Practical
Handbook of Seawater Analysis. Fisheries Research
Board of Canada, Ottawa, Canada.
Thomann R. V. and Mueller J. A. (1987) Principles of
Surface Water Quality Modeling and Control. Harper
and Row, New York.
Tilman D., Kilham S. S. and Kilham P. (1982)
Phytoplankton community ecology: the role of limiting
nutrients. Annu. Rev. Ecol. Syst. 13, 349±372.
Watanabe T. and Miyazaki T. (1996) Maximum ammonium uptake rates of Scenedesmus quadricauda
(Chlorophyta) and Microcystis novackii (Cyanobacteria)
grown under nitrogen limitation and implications for
competition. J. Phycol. 32, 243±249.
Welschmeyer N. A. (1994) Fluorometric analysis of chlorophyll a in the presence of chlorophyll b and pheopigments. Limnol. Oceanogr. 39, 1985±1992.