Limnol. Oceanogr., 58(6), 2013, 2076–2088
2013, by the Association for the Sciences of Limnology and Oceanography, Inc.
doi:10.4319/lo.2013.58.6.2076
E
Goldman revisited: Faster-growing phytoplankton has lower N : P and lower
stoichiometric flexibility
Helmut Hillebrand,1,* Georg Steinert,1 Maarten Boersma,2 Arne Malzahn,2,a Cédric Léo Meunier,2,b
Christoph Plum,1 and Robert Ptacnik 1,c
1 Plankton
Ecology, Institute for Chemistry and Biology of the Marine Environment (ICBM), Carl-von-Ossietzky University Oldenburg,
Wilhemshaven, Germany
2 Alfred Wegener Institute for Polar and Marine Research, Biologische Anstalt Helgoland, Marine Station, Helgoland, Germany
Abstract
In their seminal paper, Goldman et al. suggested that phytoplankton close to maximum growth rate attains a
restricted optimal N : P ratio close to the Redfield ratio of molar N : P 5 16. Recently, the presence of such a
global attractor for optimal phytoplankton stoichiometry has been questioned in models and empirical analyses.
As the chemical composition of phytoplankton is of major importance for our understanding of global elemental
cycles and biogeochemical transformations, we assembled 55 data sets of phytoplankton growth rate and biomass
N : P ratios in a meta-analysis testing (1) whether phytoplankton N : P converges at high growth rates, (2) whether
N : P ratios scale with growth rate, and (3) whether the optimal N : P ratios achieved at highest growth rates reflect
organism traits or environmental conditions. Across systems and species, phytoplankton N : P decreased with
increasing growth rate and at the same time showed decreasing variance, i.e., fast-growing phytoplankton is more
P rich and has a more confined elemental composition. Optimal N : P increased with increasing N : P of available
nutrients, i.e., with increasing P limitation. Other differences were rare, except cyanobacteria showed higher
optimal N : P than diatoms. Understanding the role of phytoplankton in biogeochemical transformation requires
modeling approaches that are stoichiometrically flexible to reflect the dynamics of growth and nutrient supply in
primary producers.
Phytoplankton is responsible for roughly 50% of Earth’s
global primary production (Field et al. 1998) and represents
a major link in biogeochemical cycles and transformations
(Falkowski et al. 1998). Through the uptake of multiple
nutritional elements such as nitrogen (N), phosphorus (P),
or iron, marine phytoplankton links the cycle of different
elements based on demand of the algae for these elements
and their relative availability. Therefore, the stoichiometry
of phytoplankton composition is a major constituent of
global and regional biogeochemical models and as a result
has received broad attention in the literature. Despite the
deep historical roots of research on phytoplankton C : N : P
ratios and renewed efforts in the last decade, open
questions remain even with respect to fundamental facts
such as the flexibility of phytoplankton stoichiometry and
the relationship of internal ratios to resource availability
and growth rates.
The cellular N : P ratio in many primary producers
tracks available nutrient ratios both at the level of single
species of microalgae (Rhee 1978) and at the community
level (Hillebrand and Sommer 1997), indicating a very high
flexibility in chemical composition and the lack of
* Corresponding author: [email protected]
Present addresses:
a Department of Marine Science & Fisheries, College of
Agricultural and Marine Sciences, Sultan Qaboos University,
Al-Khod, Sultanate of Oman
b Department of Ecology and Environmental Sciences, Umeå
University, Umeå, Sweden
c WasserCluster Lunz, Lunz am See, Austria
homeostasis (Fig. 1). Despite this flexibility, however, the
relationship between available and internal N : P ratios is
not necessarily linear. In a study of seston stoichiometry in
Michigan ponds, Hall et al. (2005) found a limited
flexibility in the N : P ratios of diverse phytoplankton
assemblages under widely varying N : P loading ratios,
indicating that physiological limits to storage or ecological
interactions attenuate the elemental flexibility of microalgae (Fig. 1). Subsequently, Persson et al. (2010) summarized multiple studies linking available N : P to microalgae
N : P and found that phytoplankton N : P responds nonlinearly to increasing supplied N : P, resulting in an average
slope of 0.5 in log : log space. This bending of the
relationship between available and incorporated N : P
indicates the presence of some regulatory processes
constraining stoichiometric variability.
One potential constraint of phytoplankton stoichiometry
is the growth rate of the species (or multiple species within
an assemblage). This awareness emerged from chemostat
experiments, which allowed the manipulation of growth
rates (m) through manipulation of dilution rates while
keeping the available N : P constant (complementary to
Rhee’s 1978 experiment, which altered N : P while keeping
growth constant). The experiments revealed a convergence
of phytoplankton N : P at high m both in marine (Goldman
et al. 1979) and in freshwater (Elrifi and Turpin 1985)
phytoplankton. At high m, phytoplankton N : P was highly
constrained to a narrow range of values, but N : P showed
broad variation at low m, reflecting P limitation (high N : P)
or N limitation (low N : P; Fig. 2A). The resulting
triangular or funnel shape of the relationship (based on
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Phytoplankton growth and N : P ratios
Fig. 1. Potential relationships between phytoplankton N : P
ratio and N : P supply. The three cases are strict homeostasis
where phytoplankton N : P stays constant independent of supply
(solid line), a confined flexibility (dotted line), and full flexibility,
where phytoplankton N : P fully reflects the N : P supply ratio
(intersected line), albeit not necessarily with a slope of 1.
whether linear or nonlinear regression was used) suggests
that the relative lack of homeostasis in phytoplankton
chemical composition is restricted to low growth rates,
whereas fast-growing phytoplankton requires a more
constrained stoichiometry. These results triggered the
question whether the point of convergence, the N : P at
maximum growth rate, is a general phenomenon across
phytoplankton taxa and whether this convergence N : P
carries any biological meaning.
Goldman et al. (1979) suggested that the point of
convergence reached at maximum growth rates is the
Redfield ratio, where molar N : P equals 16 (Fig. 2A). Ever
since Redfield’s seminal papers on the relative consistency
of seston stoichiometry in the open ocean (Redfield 1934,
1958), ecologists and biogeochemists have discussed the
ultimate cause of this observation and its biological
foundation. Redfield himself (1958) and succeeding work
on ocean stoichiometry (Tyrrell 1999; Lenton and Klausmeier 2007) related the stability of the Redfield ratio in the
ocean to the ability of phytoplankton to affect its
surroundings, based on N fixation as a major process
adjusting the N availability per unit P and thereby
stabilizing phytoplankton N : P. Following this, Goldman
et al. (1979) suggested a single global attractor for
phytoplankton stoichiometry at maximum growth rates.
Responding to statements that this optimal stoichiometry
also occurs in light-limited slow-growing phytoplankton
(Tett et al. 1985), Goldman (1986) additionally posed that
if not N or P but another resource limited growth (silicate,
light), phytoplankton N : P could stay close to Redfield
ratios along the entire range of growth rates.
A more recent assessment of N : P ratios along gradients
of growth rates (Klausmeier et al. 2004b) predicts that N : P
ratios are differentially constrained during exponential
growth and stationary equilibrium. Phytoplankton stoichiometry responds more directly to the stoichiometry of
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nutrient supply at low growth rates, but stays within a
narrow range at high growth rates. Along a gradient of
growth rates, thus, phytoplankton stoichiometry converges
on a species-specific optimal ratio at high growth rates
(Fig. 2B), but is more flexible and dependent on the
supplied nutrient ratios at low growth rates.
The major difference between Goldman et al.’s (1979) and
Klausmier et al.’s (2004a) predictions becomes evident when
comparing multiple species (Fig. 2C,D). Goldman et al.
(1979) predict that different species converge towards the
same optimal N : P at maximum growth rate, which they
proposed to be the Redfield ratio of N : P 5 16 (Fig. 2C). In
the quest of understanding why this ratio is a global attractor,
Loladze and Elser (2011) recently suggested that the Redfield
ratio is universally rooted in the balance between protein and
ribosomal ribonucleic acid (rRNA) synthesis. Because
proteins are major determinants of cellular N content, and
rRNA is a major contributor to cellular P content, the
balance between these processes is directly related to cellular
N : P ratios, and to maximized growth rates. Their model also
predicts that N limitation reduces protein synthesis rates and
thus leads to N : P ratios , 16, whereas P limitation affects
RNA production rates, leading to N : P . 16. Thus, Loladze
and Elser (2011) explicitly state that their model and
empirical data suggest only that N : P 5 16 has an intrinsic
rooting in growth physiology, not that it is canonically
optimal for all environmental conditions.
Other researchers questioned the existence of a single
attractor for different species, as they observed considerable variation in optimal N : P ratios (Rhee and Gotham
1980; Hecky and Kilham 1988; Geider and LaRoche 2002;
Klausmeier et al. 2004a), which suggests that optimal N : P
is rather a species-specific trait (Fig. 2D). Klausmeier et al.
(2004a) modeled optimal N : P ratios for difference
scenarios (exponential growth and competitive equilibrium)
across phytoplankton taxa, addressing the cellular machinery for uptake (5 N-rich proteins) and assembly (P-rich
ribosomes). Their results indicated that optimal ratios are
species-specific traits, such that the Redfield ratio of N : P
5 16 would not have any intrinsic biological meaning, but
simply happens to be a ratio averaging across environmental and phylogenetic constraints of N and P incorporation
(Quigg et al. 2003; Weber and Deutsch 2010). Theoretically
derived optimal N : P ratios at highest growth rates ranged
from 8 to 45 across different species of phytoplankton
(Klausmeier et al. 2004a), which incidentally reflects the
range of seston N : P ratios observed at single stations
throughout time (Karl et al. 2001) and across lakes and
oceans worldwide (Guildford and Hecky 2000). Weber and
Deutsch (2010, 2012) even more radically argued that
biogeographic variations in phytoplankton N : P ratios are
purely driven by phylogenetic differences between low N : P
in diatoms and high N : P in other groups of phytoplankton
(Fig. 2E). At this scale, differences in limitation scenarios
and growth rates are negligible according to their
assessment, and the stability of the Redfield ratio in the
ocean is based on surface currents mixing low N : P
(diatom-rich) and high N : P (diatom-poor) phytoplankton.
A potential synthesis of these seemingly contradicting
predictions of a global biochemically mediated optimal
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Hillebrand et al.
Fig. 2. Predicted relationships between phytoplankton N : P ratio and growth rate when addressing single species (A, B) or when
comparing different species (C–F). (A) Funnel-shaped relationship of cellular N : P to growth rate in phytoplankton, predicting a
convergence on a single global attractor, i.e., slow-growing phytoplankton shows flexibility in N : P, but fast-growing phytoplankton
converges on an optimal N : P ratio. This funnel shape reflects predictions by Goldman et al. (1979), Elrifi and Turpin (1985), and
Loladze and Elser (2011). The shape of the relationship has been proposed as linear (gray lines; cf. fig. 2 in Goldman et al. 1979) or
curvilinear (black lines; cf. fig. 3 in Goldman et al. 1979 and figures in Elrifi and Turpin 1985). (B) Relationship of cellular N : P to growth
rate in phytoplankton as predicted by Klausmeier et al. (2004b). (C) Goldman et al. (1979) predicted that different species (identified by
different colors) converge on a single optimal N : P ratio, the Redfield ratio. (D) Klausmeier et al. (2004b) showed that different species
show different optimal N : P ratios, reflecting species-specific resource requirements. (E) Weber and Deutsch (2010, 2012) advocated a
more stringent differentiation between phytoplankton groups, which is not influenced by phytoplankton growth rate. (F) The different
viewpoints in (C–E) could be merged if the relationship between phytoplankton N : P and growth rate shows systematic variation with the
growth rate, as predicted by the GRH (Sterner and Elser 2002).
ratio and different species-specific optimal ratios might
exist in the form of a scaling relationship between
maximum growth rate and elemental demand. Fastgrowing species are more P-rich because maintaining high
growth rates requires high concentrations of rRNA, and
thus P, as stated in the growth rate hypothesis (GRH;
Sterner 1995; Elser et al. 2000). Thus, if species differ in
their species-specific mmax, the optimal N : P ratios should
decrease with increasing mmax (Fig. 2F). This would allow
both species-specific differences in optimal N : P ratios and
Redfield ratios being a global attractor at a certain range of
growth rates. Hence, there is considerable scope for
unification into one theorem, but unfortunately this has
not been achieved yet. The evidence for or against the GRH
is mixed for microalgae (for a thorough review, see Flynn
et al. 2010). Especially the physiological basis linking
rRNA to growth is not well established for microalgae,
which partly reflects shortcomings in measurements of
rRNA. Flynn et al. (2010) also argue that growth rate can
be independent of P if another resource is limiting and P is
stored in excess in the cells. In consequence, P storage might
mask a relationship between overall P demand and growth
rate in situations where N, silicate, or light are limiting.
As straightforward as the different predictions on
phytoplankton N : P might seem, they are highly dependent
on assumptions and definitions. Resolving the question of
global vs. species-specific convergence of N : P ratios and
the mechanistic basis of flexible N : P at low m and
constrained N : P at high m requires first a clear definition
of optimal ratios informed by a theoretical understanding
of nutrient uptake and storage coupled to growth. The term
optimal ratios has been used in different perspectives as the
nutrient ratio at which limitation switches from one
element to the other (Rhee and Gotham 1980), the nutrient
ratio under optimal growing conditions when species reach
mmax (Hillebrand and Sommer 1999), or the ratio of
minimum nutrient requirements for different elements
(Klausmeier et al. 2004b). Klausmeier et al. (2004b, 2007,
2008) revealed that the first and third definitions actually
map onto each other. In their model on cellular N : P in
phytoplankton (Klausmeier et al. 2004b), nutrient uptake
follows Michaelis-Menten kinetics and growth is based on
Phytoplankton growth and N : P ratios
cellular concentrations of elements, i.e., cell quotas (Q) as
outlined by Droop (1974). Klausmeier et al. (2004b) used
Droop’s minimum cell quota (qmin) as the concentration of
a resource needed for structure and defined the ratio of qmin
for N and P as the optimal N : P ratio. According to
Klausmeier et al. (2004b), this is identical to the ratio at
which N limitation switches to P limitation assuming a
strict Liebig type of single resource limitation (for
consequences of relaxing this assumption, see Discussion).
It should be noted that this equivalence only holds if the
theoretical maximum m for all resources is equal (Cherif
and Loreau 2010).
The definition of optimal ratio as the ratio of qmin for N
and P can be aligned to the definition of optimal ratios as
the N : P ratio under optimal growing conditions, when
available ratios exactly match demands and uptake is
directly channeled into growth without storage (Klausmeier et al. 2007, 2008; Cherif and Loreau 2010). However, the
definition of optimal N : P based on mmax raises the question
whether this maximum growth rate is absolute or relative
(Cherif and Loreau 2010). Absolute mmax would be a single
species-specific value achieved at optimal resource supply
and optimal abiotic conditions regarding temperature, pH,
or other factors. In this case, it reflects the maximal growth
rate physiologically possible. Relative mmax values are
achieved in the absence of resource limitation but under
the prevailing conditions; thus, they represent the contextspecific (ecological) maximum growth rates, which could
differ, e.g., for different temperatures, but also for different
limitation history of the population. Physiological adaptation of species can modify optimal N : P ratios by changing
macromolecular composition (Geider and LaRoche 2002),
e.g. by down-regulation or up-regulation of gene expression
under nutrient stress, leading to switches in amino acids or
reduction in protein synthesis (Martiny et al. 2006; Gilbert
and Fagan 2011). This implies that dependent on the
growing conditions of the algae, there might be different
N : P ratios related to the same highest growth rates
depending on previous resource supply conditions. Framing this in the context of the Droop model, this means that
different minimum cell quotas can arise in different
resource supply situations based on regulation processes
in the cell.
Here, we aim to unify these different arguments and
conduct a meta-analysis of phytoplankton stoichiometry
and growth rates across freshwater and marine systems. We
searched the literature for studies reporting algal cellular
N : P ratios and growth rates. In total 55 datasets were
obtained, spanning the major phylogenetic groups of
phytoplankton (cyanobacteria, diatoms, dinophytes, chlorophytes, chrysophytes, prymnesiophytes), with more than five
orders of magnitude difference in cell size and three orders of
magnitude difference in N : P supply. We used these data to
address the following questions:
(1) Do phytoplankton N : P ratios diverge at low growth
rate towards higher N : P under P limitation and lower N : P
under N limitation? If so, we expect negative correlations
between N : P and growth rate under P limitation and
positive correlations under N limitation (Fig. 2A,B). (2) Do
phytoplankton N : P ratios converge at high absolute
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growth rates across species and conditions? If so, we expect
decreasing variance in N : P with increasing m across all
data sets (Fig. 2C). (3) Does the average N : P ratio of
phytoplankton change with increasing absolute growth rate
as predicted by the GRH? If so, we expect a significant
(negative) trend of tissue N : P with increasing m (Fig. 2F).
It should be noted that we do not attempt to test the
physiological basis of the GRH here, but test whether its
main prediction regarding the relationship of growth rate
and N : P ratio holds across diverse phytoplankton data sets
and limitation scenarios. (4) Does N : Popt, the N : P ratio of
the highest growth rate under the experimental conditions,
converge on a single global attractor across species (at the
Redfield ratio of 16 : 1; Fig. 2C) or does it show broad
variance across species (Fig. 2D)? (5) If the latter is the
case, does N : Popt differ systematically between phytoplankton groups (Fig. 2E) or with different nutrient
limitation scenarios, organism body size, or other environmental conditions?
The data we obtained measured phytoplankton N : P in
response to gradients of growth rates, which were most
often obtained by manipulating dilution rates in chemostats. Whether the highest dilution rates are actually
corresponding to the highest attainable growth rate of this
species (absolute mmax) is beyond our control. Therefore, we
differentiate between N : PMAX, the N : P ratio at the
highest possible growth rate, and N : Popt, the N : P ratio
of the highest growth rate under the experimental
conditions. We base our analyses on the latter, which is
analogous to the approach by Goldman et al. (1979).
However, in contrast to his analyses scaling the realized
growth rate to the experimental maximum (m : mmax), we use
the absolute growth rate m, as we hypothesized that the
absolute growth rate drives nutrient demand (question 3).
Our meta-analysis synthesizes the existing information
showing that phytoplankton N : P consistently responds to
N limitation vs. P limitation at low growth rates but
becomes less variable at high growth rates. Moreover, we
provide first general evidence that phytoplankton N : P
consistently decreases with increasing growth rate and that
this is driven by P limitation. We corroborate that N : Popt
ratios are species specific and show a phylogenetic signal.
In addition, we show a systematic response of N : Popt to
the limitation history of the culture, with P-limited cultures
showing a higher N : Popt than N-limited cultures.
Methods
Data collection—We searched Web of Science by the
Institute for Scientific Information for studies reporting the
N : P ratios of phytoplankton species or assemblages along
gradients of growth rates. Search terms were ‘‘phytoplankton’’ and (‘‘nutrient ratio*’’ or ‘‘N : P ratio*’’ or ‘‘stoichiometr*’’) and ‘‘growth.’’ From the returned studies, we
screened the abstracts and display items to search for
suitable data sets. A dataset was suitable if it provided
estimates for growth rates and N : P ratios in phytoplankton. Selection threshold was a minimum of five different
growth rates assessed per dataset. A single publication
potentially gave rise to multiple datasets if independent
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Hillebrand et al.
experiments were reported, e.g., by growing the same algae
under different conditions, or by growing different algae.
We observed a tendency to use the same data set in
different publications; therefore, we paid careful attention
to use the same underlying data set only once. In total we
retrieved 55 data sets from 22 publications (see Web
Appendix, www.aslo.org/lo/toc/vol_58/issue_6/2076a.html).
For each data set, we transformed all N : P ratios to molar
ratios and all growth rates to natural log–based estimates
of m (d21). We used this data set to perform three
complementary analyses. The first two analyses (questions
1–3) use measured N : P ratios at different growth rates;
each data point is a single measurement. In order to answer
the first question, we used a correlation analysis between
N : P and growth rate for each study. For questions 2 and 3,
we performed a generalized additive model for location,
scale, and shape (GAMLSS) on the entire data set. In order
to answer questions 4 and 5, we performed a meta-analysis
on estimates of optimal N : P ratios (N : Popt), which we
derived from a regression model individually fitted for each
data set. Thus, here each estimate reflects an entire data set.
Correlation analysis and GAMLSS—Both analyses were
performed on natural log–transformed phytoplankton
N : P values. This transformation led to two desirable
properties. First, log transformation linearizes the relationship between N : P and m. Second, log transformation
equilibrates the change in ratio by changes in the
denominator compared to changes in the numerator. As
an illustrative example, consider changes in the N : P of a
culture starting at N : P 5 16. A fourfold increase in the N
content would yield an N : P of 64 (absolute difference 5
48), but a fourfold increase of the P content results in a
N : P of 4 and thus an absolute decrease by 12 only. Logtransformed N : P ratios show the same response to both
changes.
To answer question 1 on consistent response of
phytoplankton N : P to nutrient limitation, we obtained a
correlation coefficient between natural log–transformed
phytoplankton N : P and growth rate for each data set. Our
expectation was that N : P and m correlated negatively if P
was limiting, as N : P ratios should increase with decreasing
growth rate (cf. Fig. 2A,B). Correspondingly, we expected
a positive correlation under N limitation. To test this
expectation, we compared the correlation coefficient to the
supply ratio of N : P in the experiment.
Because questions 2 and 3 explicitly address the trend of
the mean and of the error variance in the relationship
between N : P ratio and m, we performed multiple regressions using GAMLSS, which represents a general framework for univariate regression-like analyses that is highly
flexible with regard to the distribution of the response
variable and additionally allows fitting distribution parameters as a function of the independent variable. Thus, both
the mean and the variance of the dependent variable can be
modeled as linear functions of the predictor(s), allowing us
to address questions 2 and 3 within a single flexible
regression model.
We first fitted models with growth rate (m) as potential
predictor and log-transformed N : P as dependent variable,
and performed model selection based on the generalized
Akaike information criterion (GAIC; Stasinopoulos and
Rigby 2007). After model selection, we tested whether the
best model could be improved by including an additional
link function, which models the error variance as a function
of m, again using the GAIC criterion. In case of significant
improvement by this link function (i.e., nonconstant error
variance), growth rate predicts not only the average N : P
ratio, but also the error variance around this trend. We
report the difference in GAIC values between models
(DAIC) in the results. As in quantile regression, changes in
data density across the predictor variable do not influence
the outcome. Model fitting and model selection were
performed using functions gamlss and stepGAIC from the
R package gamlss (Stasinopoulos and Rigby 2007).
We performed three sensitivity analyses for the
GAMLSS. (1) We added study identity (as random
variable) to reflect the data structure with multiple
observations from single papers and to test whether results
were based on study characteristics rather than by
associations to growth rate. (2) We included the limiting
nutrient in each study (N-limited, P-limited, other limitation) as an additional variable, as we expected phytoplankton N : P to reflect the nutrient limitation scenario. (3) In an
even more refined sensitivity analysis, we also tested
whether any significant trend in N : P might appear from
the fact that more P- than N-limited experiments were
present in the data set (see also below). Therefore, we
bootstrapped the data set with 110 observations from Nlimited and P-limited studies, and repeated the analysis
1000 times.
Meta-analysis—For each data set, we calculated N : Popt
by fitting a Michaelis-Menten type of equation to the data:
NP~
NPopt |m
kzm
Here, NP is the observed N : P ratio, m the observed
growth rate, and NPopt and k are two fitted parameters,
NPopt being the N : P ratio at m 5 ‘ and k being the growth
rate at which half of the optimum N : P was reached. The
advantage of the Michaelis-Menten formulation for this
nonlinear regression is a direct estimate of NPopt, which
then can be used for further analysis. For 43 out of 55 data
sets (78%) we retrieved significant estimates for NPopt,
which we used in subsequent tests (see Web Appendix).
We calculated an overall average NPopt across all
studies, for which we used these estimates and their
standard error (SE) in a weighted mixed-effect metaanalysis (Rosenberg et al. 2000). We also retrieved an
estimate for the 95% confidence interval around this
average based on 9999 bootstraps. We categorized each
of the 43 data sets with significant estimates of NPopt
according to system (marine [n 5 18] or freshwater [n 5
25]), manipulation of growth rate (chemostats [n 5 31],
light or resource supply [n 5 6], abiotic conditions [n 5 6]),
limiting resource (based on statements in the original
publication, N [n 5 13], P [n 5 18], or other [n 5 12]),
organism group (Cyanobacteria [n 5 16], Dinophyta [n 5
Phytoplankton growth and N : P ratios
Fig. 3. Correlation coefficients (r) between natural log–
transformed phytoplankton N : P and growth rate scaled to the
natural log–transformed supply ratio of N : P. Each data point is
one study. Symbols separate significant and marginally nonsignificant correlations (p , 0.1) from nonsignificant correlations.
5], Bacillariophyta [n 5 6], Prymnesiophyta [n 5 2],
Chlorophyta [n 5 8] and polycultures of several species [n
5 6]), culture (monoculture [n 5 37] or polyculture [n 5 6]),
and the ability to fix atmospheric N (yes [n 5 2] or no [n 5
41]). We obtained further information on temperature (uC),
light supply (mmol photons m22 s21), available dissolved
inorganic N and P (mmol L21, ln-transformed), molar ratio
of available N : P (ln-transformed), cell size of the algae
(mm3, ln-transformed), maximum growth rate (mmax)
obtained in the respective experiment, duration of the
experiment (days, ln-transformed), and size of the experimental units (liters, ln-transformed).
We used these variables in separate weighted analyses of
heterogeneity, which are comparable to analyses of
variance in the case of categorical variables, and to
weighted regressions in the case of continuous variables
(Rosenberg et al. 2000). We conducted separate tests, as
joining the different variables in a single non-weighted
analysis, e.g., a general linear model, would reduce the
number of studies dramatically as information on the
different variables was often incomplete and different
studies lacked different aspects of information. All calculations for the meta-analysis were performed with MetaWin 2.0 (Rosenberg et al. 2000).
Results
Under N limitation, phytoplankton N : P increased with
increasing growth rate, whereas under P limitation,
phytoplankton N : P decreased with increasing growth rate.
Correspondingly, the correlation coefficient r between m
and ln-transformed phytoplankton N : P showed a clear
bimodal pattern along the N : P supply gradient (Fig. 3).
Significant positive correlations occurred at low N : P
supply ratios, negative correlations (with one exception)
at high N : P supply ratios.
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Across all studies, we observed a significant negative
trend of N : P with increasing growth rate, as well as a
decrease in variance (Fig. 4A). The GAMLSS including a
function for variance had a clearly lower Akaike information criterion (DAIC 5 228.7) than the model describing
the mean only. Thus, in addition to having a higher relative
P content, fast-growing phytoplankton was more confined
in its stoichiometry (Table 1). The significant trend of N : P
ratios on growth rates translates in a reduction from N : P
5 20 at m 5 0 to N : P 5 9.1 at the maximum observed
growth rate m 5 2.5 when back transforming the analyses in
arithmetic space (Fig. 4A). These results were not driven by
a group of very–fast-growing cultures, as removing all
studies with m . 2.0 resulted in virtually the same model
(Fig. 4B, Table 1).
Adding study identity as a random term to the model did
not alter these results (Table 1). Both the negative trend of
N : P with growth rate and the concomitant reduction in
variance remained significant. The results are thus not
based on the data structure, i.e., do not reflect the results of
a single study or variation of growth rate with study.
Adding the identity of the limiting nutrient enhanced the
model fit (DAIC 5 2408.2 comparing models with and
without identity of the limiting nutrient). Again, the negative
trend in N : P with growth rate remained highly significant
(Table 1). However, including variance as a function of m did
no longer improve this model (DAIC 5 +2.0). Standardizing
the number of observations from N- and P-limited cultures,
respectively, confirmed a significant negative trend of N : P
with growth rate, i.e., the slopes based on bootstrapped
datasets were significantly different from zero (Fig. 5).
Based on these differences, we also analyzed N- and Plimited cultures separately and found that the reduction in
variance was mainly based on N-limited cultures (Fig. 6A)
whereas the trend in N : P with growth rate was based on Plimited cultures (Fig. 6B). Thus, only the variance function was
retained in the GAMLSS for N-limited experiments and only
the trend was retained in the P-limited experiments (Table 2).
Estimates for N : Popt varied within an order of
magnitude between 4.5 and 54.5 (Fig. 7A), which reflects
the range of estimates by Klausmeier et al. (2004a). The
distribution showed a mode around 16, but the median was
20.3 (Fig. 7A). The weighted average N : Popt was 21.4
(95% confidence interval 18.1–25.0) and thus significantly
higher than the Redfield ratio (Fig. 7B). Estimates for
N : Popt were significantly higher in P-limited situations
than in experiments with N-limitation or limitation by
another resource (Fig. 7B). The limiting resource explained
22.4% of the heterogeneity in N : Popt (analysis of
heterogeneity, p 5 0.0002, Q(2 degrees of freedom) between
groups 5 16.7, Q(40 df) within groups 5 57.8). Also, the
organism group (algal class) explained significant heterogeneity in N : Popt (22.3%, p 5 0.015, Q(5 df) between groups
5 14.1, Q(37 df) within groups 5 49.0), mainly because
cyanobacteria showed higher N : Popt than diatoms
(Fig. 7C). Weighted averages for group-specific N : Popt
were lowest for diatoms (14.9) and dinophytes (15.1) and
highest for cyanobacteria (25.8) and chlorophytes (27.0).
This difference was not based on the ability to fix
atmospheric N, which had no significant influence on
2082
Hillebrand et al.
Fig. 4. (A) Observed N : P ratios plotted as a function of growth rate m for the entire data set. The bold line gives the fit for the mean
of the GAMLSS model without random term (see Table 1, model 1). (B) Observed N : P ratios plotted as a function of growth rate m for
studies with m , 2. The bold line gives the fit for the mean of the GAMLSS model. For orientation, the untransformed N : P ratios are
given on the secondary y-axis. The gray lines indicate percentiles of the error variance in steps of 5%.
N : Popt (p 5 0.103). Neither system (freshwater vs. marine,
p 5 0.073), culture (single species vs. polyculture, p 5
0.092), nor the type of growth rate manipulation (p 5
0.107) had significant effects on N : Popt.
From the continuous predictors, only dissolved N
concentrations and the ratio of supplied N : P related
significantly to N : Popt. N : Popt increased with available
N : P (Fig. 8, slope 6 SE 5 3.05 6 0.92), a relationship
explaining 16.1% of heterogeneity in N : Popt (p 5 0.0009,
Q(1 df) between groups 5 11.0, Q(34 df) within groups 5
57.2). For most studies, supplied N : P below the Redfield
ratio results in estimates for N : Popt that are at or below
N : P 5 16, whereas higher-availability N : P ratios also
increase shifted estimates for N : Popt above the Redfield
ratio (Fig. 8). The relationship of N : Popt to supplied N : P
was reflected by an almost identical relationship to
Table 1. GAMLSS model output modeling mean ln (N : P) and its variance as linear functions of growth rate (each with intercept
and slope), without and with different random variables. ns: nonsignificant.
Modeled distribution
parameters
Coefficients
Estimate (6 SE)
t-value
p
Model 1—without random variable
Mean
Intercept
Slope
Variance
Intercept
Slope
2.99(0.05)
20.31(0.06)
0.08(0.05)
20.42(0.07)
55.12
25.43
1.60
26.02
,0.001
,0.001
0.110
,0.001
Model 2—without random variable, m,2.0
Mean
Intercept
Slope
Variance
Intercept
Slope
3.07(0.06)
20.45(0.07)
0.10(0.05)
20.48(0.09)
50.68
26.17
1.95
25.68
,0.001
,0.001
0. 05
,0.001
Model 3—with random variable ‘‘study ID’’ (categorical, n522)
Mean
Intercept
3.1(0.05)
Slope
20.17(0.05)
Variance
Intercept
20.11(0.05)
Slope
20.40(0.07)
68.1
23.47
22.4
25.83
,0.001
,0.001
0.016
,0.001
70.53
24.17
216.4
,0.001
,0.001
,0.001
Model 4—with random variable ‘‘limiting nutrient’’ (categorical, 3 levels [N, P, other])
Mean
Intercept
3.0(0.04)
Slope
20.25(0.06)
Variance
Intercept
20.46(0.03)
Slope
ns
Phytoplankton growth and N : P ratios
2083
Fig. 5. Sensitivity analysis of N : P ratios vs. growth rates. (A) Distribution of N-limited and
P-limited phytoplankton in the diagram of N : P and growth rates. Gray symbols have other
limiting resources. (B) Frequency distribution of slopes of phytoplankton N : P on growth rates
for 1000 estimates derived from bootstrapped data sets with equal number of N-limited and Plimited observations.
dissolved N concentrations (p 5 0.0052, Q(1 df) between
groups 5 7.8, Q(30 df) within groups 5 39.6, slope 6 SE 5
1.89 6 0.68 ).
As the raw N : P data, estimates of N : Popt decreased
with increasing maximum observed growth rate (slope 6
SE 5 22.36 6 3.43), but this relationship was not
significant (p 5 0.49). Neither metabolic constraints of
algae such as cell size (p 5 0.50) or temperature (p 5 0.43)
nor the scale of the experiment (duration: p 5 0.38, volume:
p 5 0.25) were significant predictors of N : Popt.
Discussion
This meta-analysis of published work on the relationship
between phytoplankton growth and stoichiometry allows a
Fig. 6.
Fig 4A.
number of important conclusions. Generalizing already
existing information, we found that phytoplankton stoichiometry becomes more restricted at higher growth rates;
thus, fast growth requires a more confined chemical cell
composition, whereas N : P shows more variation under
slow growth. Although phytoplankton converges to a more
restricted range of stoichiometry, it does not converge to a
general attractor. Generally, N : P ratios became lower at
higher growth rates, which corroborates predictions from
the GRH and was mainly driven by P-limited experiments.
Estimates for optimal N : P ratios at mmax were mainly
influenced both by species phylogeny and by the environment (N : P supply, limiting resource). Below, we discuss
the support for these conclusions and their consequences in
turn, and then discuss the consequences of these findings
Observed N : P ratios plotted as a function of growth rate m for (A) N-limited studies and (B) P-limited studies. Details as in
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Hillebrand et al.
Table 2. GAMLSS model output for the models with N- and P-limited studies, separately, modeling mean ln (N : P) and its variance
as linear functions of growth rate. ns: nonsignificant.
Modeled distribution
parameters
Model N-limited only
Mean
Variance
Model P-limited only
Mean
Variance
Coefficients
Intercept
Slope
Intercept
Slope
Intercept
Slope
Intercept
Slope
Estimate (6 SE)
2.19(0.04)
t-value
p
53.2
,0.001
ns
0.03
,0.001
20.16(0.07)
20.40(0.08)
22.23
24.7
4.23(0.08)
21.21(0.12)
20.58(0.05)
57.1
210.33
212.1
with respect to global biogeochemical models and concepts
of multiple resource limitation.
Phytoplankton stoichiometry becomes more restricted at
higher growth rates—Our finding of decreasing variance in
phytoplankton N : P at higher growth rates provided
corroborative but highly general evidence for a more
confined stoichiometry of fast-growing phytoplankton
(Fig. 2C,D; Goldman et al. 1979; Klausmeier et al.
2004b). As predicted by the Klausmeier et al. (2004b)
model, phytoplankton N : P tracked supply N : P broadly
under stagnant and slow growth, whereas there was only a
limited change in elemental composition during fast
growth. Consequently, the reduction of variance in
ln(N : P) with growth rate was retained in the GAMLSS
and also remained as a significant trend when study
identity was added as a random variable. The continuous
reduction in variance we observed across species differs
slightly from the Klausmeier et al (2004b) model of N : P in
a single species, which predicted constantly high flexibility
of N : P ratios over a large part of the model parameter
range (Fig. 2B,D). Our data, which comprise a broader
range of growth rates than the model, suggest that variance
declines directly with increasing m already between low and
intermediate growth rates. This reduction in variance
reflects that in the different studies, phytoplankton N : P
either increased at reduced m under P limitation or
decreased at reduced m under N limitation (Fig. 3).
On top of this corroborative evidence, however, our
analyses provide novel insight into different mechanisms
driving these patterns under different limitation scenarios.
When the limiting resource was added as a categorical
factor to the model, variance was no longer related to
growth rate, as variance was driven mainly by presence of
N or P limitation in the first place. Separate analyses for Nand P-limited experiments revealed that the variance
reduction observed across all studies reflected two mechanisms: in N-limited cultures, increasing growth rates led to
more confined N : P without changing the mean N : P,
whereas in P-limited cultures N : P declines with growth
rate without changing the variance. In consequence, the
increasing stoichiometric variance at low m across all
,0.001
,0.001
,0.001
ns
studies reflects both increasing N : P in P-limited and more
flexible N : P in N-limited cultures. The lack of a trend in
N : P with m under N limitation potentially reflects the
capacity for luxury consumption of P (see Flynn et al. 2010
and discussion below), which—depending on storage
capacity of the species and P supply—allows N : P to
decline differently around the average N : P for N-limited
cultures. Please note that the N-limited average < 9 in
Fig. 6A is well below the overall average < 24 across all
studies in Fig. 4A. Thus, N-limited phytoplankton has low
N : P ratios with higher flexibility in adjusting the P content
at low m. By contrast, P-limited phytoplankton contributes
to the higher flexibility by showing a constant increase in
N : P with decreasing m.
The reduction in N : P variance at high m can also be seen
in the meta-analysis when comparing estimates of N : Popt
to the supplied N : P ratios. Whereas supplied N : P ranged
from 2 to 400 and is closely tracked by the internal
phytoplankton N : P ratios close to stagnant growth (cf.
Fig. 4A), the estimate for N : Popt is merely doubling to
tripling (cf. Fig. 8). Therewith, our analysis corroborates
previous analyses (Hall et al. 2005; Persson et al. 2010) in
finding a monotonic yet confined response of cellular
stoichiometry to changes in available N : P.
Phytoplankton N : P does not converge to a single optimal
N : P—Both the GAMLSS and the meta-analysis corroborate the conclusion that phytoplankton does not converge
to a single optimal N : P ratio at highest growth rate but to
a range of N : P ratios. Whereas this point has already been
made (Klausmeier et al. 2004a), we show that this pattern is
strongly related to the actual growth rate achieved (see
below, Phytoplankton N : P scales to growth rate) and
modified by the available nutrient ratios (Figs. 6, 7B, 8),
and algal phylogeny (Fig. 7C). Thus, we corroborate with
the largest available data set across ecosystems that
phytoplankton stoichiometry does not converge towards
the Redfield ratio as had been suggested by Goldman et al.
(1979; see Fig. 2C). The Redfield ratio does not emerge as a
global attractor, but may rather represent a median in the
range of structural N : P ratios found in phytoplankton
species and different optimal allocation strategies of N-rich
Phytoplankton growth and N : P ratios
2085
Fig. 7. Optimal N : P ratio of phytoplankton. (A) Frequency distribution of fitted estimates from 43 studies on phytoplankton. (B)
Average optimal N : P ratio (6 95% confidence intervals) for all studies and separated for studies imposing limitation by N, P, or other
(iron, light) resources. (C) Average optimal N : P ratio (6 95% confidence intervals) for different phytoplankton groups. Cyan 5
cyanobacteria, Dino 5 dinoflagellates, Diat 5 diatoms, Prym 5 Prymnesiophyceae, Chlo 5 chlorophytes, Poly 5 polycultures of
multiple species.
cellular machinery for uptake (proteins) to P-rich cellular
machinery for assembly (ribosomes) during exponential
growth (m 5 mmax) and under competitive equilibrium (net
growth rate 5 0; Klausmeier et al. 2004a).
The importance of available nutrient ratios for our
estimates of N : Popt may seem counterintuitive at first
glance if N : Popt is seen as a fixed trait of species or strains,
whereas we detected that P-limited algae did not converge
to the same N : Popt as N-limited algae. However, most
studies in the data set grew algae under different supply
ratios at different chemostat dilution (5 growth) rates,
which allows physiological adaptation of the species
modifying their nutrient requirements, e.g., by adapting
biochemical composition (Geider and LaRoche 2002) and
by down-regulation or up-regulation of gene expression
under nutrient stress (Martiny et al. 2006; Gilbert and
Fagan 2011). As a consequence of such adjustments, the
imbalance of nutrient supply is reflected in the cellular
content of nutrients even at highest experimental growth
rates, and N : Popt bears an imprint of the limitation history
of the algae. It should be noted that if algae could
potentially grow faster than the maximum experimental
growth rate, we have no means to exclude the possibility
that estimates for N : Popt narrow even further. Here, more
research at maximum growth rates could reveal potential
differences between the operationally defined estimates for
N : Popt and the N : PMAX.
We found differences in N : Popt between algal phyla,
which were significant only for the comparison of low N : P
in diatoms vs. high N : P in cyanobacteria. The overall
pattern (low N : P in diatoms, intermediate in dinoflagellates, and a tendency towards higher N : P in chlorophytes)
is consistent with previous analyses of phylogenetic
correlates of phytoplankton stoichiometry (Ho et al.
2003; Quigg et al. 2003). However, our data across
ecosystems do not corroborate a clear divergence between
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Hillebrand et al.
Fig. 8. Relationship between optimal N : P ratio of phytoplankton and available N : P in the environment. Increasing N : P
in the media triggers increasing estimates for N : Popt (Spearman
rank correlation, n 5 36, R 5 0.463, p 5 0.004). Dashed lines are
Redfield ratios.
low N : P in diatoms and high N : P in all other
phytoplankton as proposed for oceanic phytoplankton
(Weber and Deutsch 2010, 2012). Finally, neither cell size
nor temperature, the two major components of the
metabolic theory of ecology (Brown et al. 2004), proved
to be significant predictors of phytoplankton stoichiometry.
Phytoplankton N : P scales to growth rate—Phytoplankton with higher growth rate on average had lower cellular
N : P ratios. This trend across all studies was mainly driven
by P-limited experiments, where a strong decline in N : P
ratios with increasing m became evident. This pattern is
both consistent with the GRH (Sterner 1995) and with
increasing depletion of storage P at more severe P
limitation under slow growth (Klausmeier et al. 2004a).
Both mechanisms can act independently or simultaneously,
and we have no independent data on how much P was
structural and how much was stored (sensu Klausmeier
et al. 2004a) to separate between higher demand in
minimum P (qmin) with increasing m (GRH) and higher
storage of P with m. The restriction of the trend to P-limited
experiments can also be aligned to both hypotheses, as
luxury uptake of P could mask a growth rate–dependent
decrease in N : P of N-limited algae (Flynn et al. 2010). It
should be noted that the initial formulation of the GRH did
not separate between different limiting nutrients (Sterner
and Elser 2002), whereas later publications (e.g., Flynn et
al. 2010) proposed that the GRH holds for P-limited
conditions only. In fact, in their review on the suitability of
the GRH for microalgae, Flynn et al. (2010) found little
support for the GRH and only for P-limited cultures, as Nlimited cultures showed higher N : P with higher m,
contrasting the prediction from GRH. Our analysis does
not present a test of the GRH sensu stricto, as we lack data
on rRNA content and cannot test underlying assumptions
as pointed out by Flynn et al. (2010).
Thus, the significant reduction in N : P with growth rate
we observed across marine and freshwater phytoplankton
does follow predictions from GRH, but this pattern needs
mechanistic underpinning in future experiments. The GRH
is based on the fundamental link of growth to protein
synthesis and rRNA content (Vrede et al. 2004). Vrede
et al. (2004) modeled this link for consumer species and
predicted a decrease in N : P with increasing growth rate.
Although autotrophs have a higher flexibility in stoichiometric composition than most metazoan heterotrophs, we
find a similar negative trend of N : P on m here, which was
not an artifact of the data set structure, as the negative
slopes remained significant when including study identity
or limiting resource into the model (cf. Table 1) and when
bootstrapping the data set with equal numbers of
observations for N- or P-limited situations (cf. Fig. 5).
Thus, when including N or P limitation as a factor in the
model across all studies, we detected an overall significant
decrease of N : P with m, whereas this trend was restricted to
P-limited experiments in the separate analyses for N- and
P-limited cultures. This divergence reflects that in our
datasets N-limited cultures show a lower N : P and higher
maximum growth rates than P-limited cultures.
Outlook—Our results unify a number of previously
separate conclusions from phytoplankton growth and
stoichiometry analyses. Phytoplankton N : P becomes more
restricted and significantly decreases with increasing
growth rate. At maximum growth rate under the present
abiotic conditions, N : P converges to an optimal ratio that
is not only different for species and phylogenetic groups,
but bears the imprint of previous nutrient supply and thus
physiological adaptation. The main results of our metaanalysis trigger new approaches in biogeochemical modeling as well as in phytoplankton ecology.
The Redfield ratio remains a standard assumption in
global assessments of nutrient limitation and production of
phytoplankton as well as biogeochemical cycles and
transformations (Howarth 1988; Falkowski et al. 1998;
Galloway et al. 2004). Congruent with Klausmeier et al.
(2004a), we concluded that the Redfield ratio does not
emerge as a universally optimal value, but appears to be the
average of current species composition and environment in
the ocean. In our data set, which reflects a nonrandom
selection of species, the average ratio of N : P across species
systematically changed with growth rate, where the Redfield ratio was found at intermediate m, whereas the average
ratios were significantly higher and lower in stagnant and
in rapidly growing cultures, respectively. Even in large-scale
models on element cycles, the dynamics of phytoplankton
stoichiometry needs to be considered explicitly, as assuming
Redfield proportions of N : P not only underestimates
variance, but neglects that Redfield proportions are not
suitable for a majority of environmental conditions
regarding the algae’s physiological scope for growth and
the relative availability of N : P. These two axes, growth
conditions and supplied N : P, can serve as dynamic
Phytoplankton growth and N : P ratios
predictors of phytoplankton N : P in stoichiometrically
explicit models. In addition to cell size, elemental stoichiometry is moreover a promising trait for predicting and
understanding changes in phytoplankton community structure in response to global environmental change (Finkel
et al. 2010).
For phytoplankton ecology, we see a demand for
disentangling the relative role of P storage vs. minimal P
requirement in understanding the trend of N : P on growth
rate. If the GRH underlies the trend of N : P on m, our
understanding of pelagic nutrient flows has to be based on
structural changes associated to the absolute growth rates
of phytoplankton. If storage of P in less P-limited
conditions drives this trend, phytoplankton stoichiometry
rather reflects the excess availability of P. Thus, in one case
the composition of phytoplankton with regard to phylogeny and achievable absolute growth rates has to be
assessed, and in the other case it is the relative availability
of nutrients.
In addition, the effect of limitation scenarios on the
estimate for N : Popt opens the discussion for questions
associated to adaptation to nutrient limitation and
changing N : P requirements over time. Optimal N : P ratios
in phytoplankton have been interpreted as the ratio where
limitation switches from N to P, assuming a strict Liebig
type of limitation (Rhee and Gotham 1980; Klausmeier
et al. 2008). However, it seems that algae can adapt their
N : Popt in certain ranges, a possibility that requires careful
experimentation along gradients of N : P supply ratios.
Liebig type of single nutrient limitation may not be the only
or the single most important type of limitation. Autotrophs
frequently experience multiple nutrient limitation (Harpole
et al. 2011), which can occur at different levels of biological
organization within individuals, populations, and communities (Danger et al. 2008). At the community level, multiple
resource limitation should be the rule rather than an
exception, as species should show trade-offs in their resource
requirements in order to coexist. More important for the
discussion here are the individual and population levels, as
most experiments in our database used monocultures. At the
level of single organisms, the deficiency of one element can
reduce the cell quota of this element, but might also impair
the uptake and cell quota of another element. In this case,
the response to N limitation might not always be a linear
decrease in N : P ratio, especially if at the population level
individuals with different genotype or physiological condition differ in their nutrient requirements. Most experiments
in our database used ratios that were chosen to clearly reflect
N or P limitation. A third recommendation from our
conclusions is therefore to analyze the response of cellular
N : P along gradients to assess potential nonlinearities in
resource use based on co-limitation.
Acknowledgments
We thank Christopher Klausmeier and James Elser for
comments on the outline of the study and the manuscript. Robert
Sterner and two reviewers additionally improved the manuscript
considerably. This manuscript was enabled by funding from the
German Science Foundation (DFG) to H.H. (project Hi848/8-1)
and A.M. (project Ma4501/1-1).
2087
References
BROWN, J. H., J. F. GILLOOLY, A. P. ALLEN, V. M. SAVAGE, AND
G. B. WEST. 2004. Toward a metabolic theory of ecology.
Ecology 85: 1771–1789, doi:10.1890/03-9000
CHERIF, M., AND M. LOREAU. 2010. Towards a more biologically
realistic use of Droop’s equations to model growth under
multiple nutrient limitation. Oikos 119: 897–907, doi:10.1111/
j.1600-0706.2010.18397.x
DANGER, M., T. DAUFRESNE, F. LUCAS, S. PISSARD, AND G.
LACROIX. 2008. Does Liebig’s law of the minimum scale up
from species to communities? Oikos 117: 1741–1751,
doi:10.1111/j.1600-0706.2008.16793.x
DROOP, M. R. 1974. The nutrient status of algal cells in
continuous culture. J. Mar. Biol. Assoc. UK 54: 825–855,
doi:10.1017/S002531540005760X
ELRIFI, I. R., AND D. H. TURPIN. 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, doi:10.1111/
j.0022-3646.1985.00592.x
ELSER, J. J., AND OTHERS. 2000. Biological stoichiometry from
genes to ecosystems. Ecol. Lett. 3: 540–550, doi:10.1046/
j.1461-0248.2000.00185.x
FALKOWSKI, P. G., R. T. BARBER, AND V. SMETACEK. 1998.
Biogeochemical controls and feedbacks on ocean primary
production. Science 281: 200–206, doi:10.1126/science.281.5374.200
FIELD, C. B., M. J. BEHRENFELD, J. T. RANDERSON, AND P. G.
FALKOWSKI. 1998. Primary production of the biosphere:
Integrating terrestrial and oceanic components. Science 281:
237–240, doi:10.1126/science.281.5374.237
FINKEL, Z. V., J. BEARDALL, K. J. FLYNN, A. QUIGG, T. A. V. REES,
AND J. A. RAVEN. 2010. Phytoplankton in a changing world:
Cell size and elemental stoichiometry. J. Plankton Res. 32:
119–137, doi:10.1093/plankt/fbp098
FLYNN, K. J., J. A. RAVEN, T. A. V. REES, Z. FINKEL, A. QUIGG,
AND J. BEARDALL. 2010. Is the growth rate hypothesis
applicable to microalgae? J. Phycol. 46: 1–12, doi:10.1111/
j.1529-8817.2009.00756.x
GALLOWAY, J. N., AND OTHERS. 2004. Nitrogen cycles: Past,
present, and future. Biogeochemistry 70: 153–226, doi:10.
1007/s10533-004-0370-0
GEIDER, R. J., AND J. LAROCHE. 2002. Redfield revisited: variability
of C : N : P in marine microalgae and its biochemical basis. Eur.
J. Phycol. 37: 1–17, doi:10.1017/S0967026201003456
GILBERT, J. D. J., AND W. F. FAGAN. 2011. Contrasting
mechanisms of proteomic nitrogen thrift in Prochlorococcus.
Mol. Ecol. 20: 92–104, doi:10.1111/j.1365-294X.2010.04914.x
GOLDMAN, J. C. 1986. On phytoplankton growth rates and
particulate C : N : P ratios at low light. Limnol. Oceanogr. 31:
1358–1363, doi:10.4319/lo.1986.31.6.1358
———, J. J. MCCARTHY, AND D. G. PEAVEY. 1979. Growth rate
influence on the chemical composition of phytoplankton in
oceanic waters. Nature 279: 210–215, doi:10.1038/279210a0
GUILDFORD, S. J., AND R. E. HECKY. 2000. Total nitrogen, total
phosphorus, and nutrient limitation in lakes and oceans: Is
there a common relationship? Limnol. Oceanogr. 45: 1213–
1223, doi:10.4319/lo.2000.45.6.1213
HALL, S. R., V. H. SMITH, D. A. LYTLE, AND M. A. LEIBOLD. 2005.
Constraints on primary producer N : P stoichiometry along
N : P supply ratio gradients. Ecology 86: 1894–1904, doi:10.
1890/04-1045
HARPOLE, W. S., AND OTHERS. 2011. Nutrient co-limitation of
primary producer communities. Ecol. Lett. 14: 852–862,
doi:10.1111/j.1461-0248.2011.01651.x
2088
Hillebrand et al.
HECKY, R. E., AND P. KILHAM. 1988. Nutrient limitation of
phytoplankton in freshwater and marine environments: A
review of recent evidence on the effects of enrichment.
Limnol. Oceanogr. 33: 796–822, doi:10.4319/lo.1988.33.4_
part_2.0796
HILLEBRAND, H., AND U. SOMMER. 1997. Response of epilithic
microphytobenthos of the Western Baltic Sea to in situ
experiments with nutrient enrichment. Mar. Ecol. Prog. Ser.
160: 35–46, doi:10.3354/meps160035
———, AND ———. 1999. The nutrient stoichiometry of benthic
microalgal growth: Redfield proportions are optimal. Limnol.
Oceanogr. 44: 440–446, doi:10.4319/lo.1999.44.2.0440
HO, T. Y., A. QUIGG, Z. V. FINKEL, A. J. MILLIGAN, K. WYMAN,
P. G. FALKOWSKI, AND F. M. M. MOREL. 2003. The elemental
composition of some marine phytoplankton. J. Phycol. 39:
1145–1159, doi:10.1111/j.0022-3646.2003.03-090.x
HOWARTH, R. W. 1988. Nutrient limitation of net primary
production in marine ecosystems. Annu. Rev. Ecol. Syst. 19:
89–110, doi:10.1146/annurev.es.19.110188.000513
KARL, D. M., AND OTHERS. 2001. Ecological nitrogen-to-phosphorus
stoichiometry at station ALOHA. Deep-Sea Res. II 48:
1529–1566, doi:10.1016/S0967-0645(00)00152-1
KLAUSMEIER, C. A., E. LITCHMAN, T. DAUFRESNE, AND S. A. LEVIN.
2004a. Optimal nitrogen-to-phosphorus stoichiometry of
phytoplankton. Nature 429: 171–174, doi:10.1038/nature02454
———, ———, ———, AND ———. 2008. Phytoplankton
stoichiometry. Ecol. Res. 23: 479–485, doi:10.1007/s11284008-0470-8
———, ———, AND S. A. LEVIN. 2004b. Phytoplankton growth
and stoichiometry under multiple nutrient limitation. Limnol.
Oceanogr. 49: 1463–1470, doi:10.4319/lo.2004.49.4_part_2.1463
———, ———, AND ———. 2007. A model of flexible uptake of
two essential resources. J. Theor. Biol. 246: 278–289,
doi:10.1016/j.jtbi.2006.12.032
LENTON, T. M., AND C. A. KLAUSMEIER. 2007. Biotic stoichiometric controls on the deep ocean N : P ratio. Biogeosciences 4:
353–367, doi:10.5194/bg-4-353-2007
LOLADZE, I., AND J. J. ELSER. 2011. The origins of the Redfield
nitrogen-to-phosphorus ratio are in a homoeostatic proteinto-rRNA ratio. Ecol. Lett. 14: 244–250, doi:10.1111/j.14610248.2010.01577.x
MARTINY, A. C., M. L. COLEMAN, AND S. W. CHISHOLM. 2006.
Phosphate acquisition genes in Prochlorococcus ecotypes:
Evidence for genome-wide adaptation. Proc. Natl. Acad. Sci.
USA 103: 12552–12557, doi:10.1073/pnas.0601301103
PERSSON, J., P. FINK, A. GOTO, J. M. HOOD, J. JONAS, AND S. KATO.
2010. To be or not to be what you eat: Regulation of
stoichiometric homeostasis among autotrophs and heterotrophs. Oikos 119: 741–751, doi:10.1111/j.1600-0706.2009.
18545.x
QUIGG, A., AND OTHERS. 2003. The evolutionary inheritance of
elemental stoichiometry in marine phytoplankton. Nature
425: 291–294, doi:10.1038/nature01953
REDFIELD, A. C. 1934. On the proportions of organic derivations
in sea water and their relation to the composition of plankton,
p. 176–192. In R. J. Daniel [ed.], James Johnstone memorial
volume. Univ. Press of Liverpool.
———. 1958. The biological control of the chemical factors in the
environment. Am. Sci. 46: 205–221.
RHEE, G. Y. 1978. Effects of N : P atomic ratios and nitrate
limitation on algal growth, cell composition, and nitrate
uptake. Limnol. Oceanogr. 23: 10–25, doi:10.4319/lo.1978.
23.1.0010
———, AND I. J. GOTHAM. 1980. Optimum N-P ratios and
coexistence of planktonic algae. J. Phycol. 16: 486–489,
doi:10.1111/j.1529-8817.1980.tb03065.x
ROSENBERG, M. S., D. C. ADAMS, AND J. GUREVITCH. 2000.
MetaWin version 2.0 statistical software for meta-analysis
[Internet]. Sinauer Associates. Available from http://www.
metawinsoft.com/
STASINOPOULOS, D. M., AND R. A. RIGBY. 2007. Generalized
additive models for location scale and shape (GAMLSS) in
R. J. Stat. Softw. 23: 1–46.
STERNER, R. W. 1995. Elemental stoichiometry of species in
ecosystems, p. 240–252. In C. G. Jones and J. H. Lawton
[eds.], Linking species and ecosystems. Chapman & Hall.
———, AND J. J. ELSER. 2002. Ecological stoichiometry. Princeton
University Press, Princeton (USA).
TETT, P., S. I. HEANEY, AND M. R. DROOP. 1985. The Redfield
ratio and phytoplankton growth rate. J. Mar. Biol. Assoc.
UK 65: 487–504, doi:10.1017/S0025315400050566
TYRRELL, T. 1999. The relative influence of nitrogen and
phosphorus on oceanic primary production. Nature 400:
525–531, doi:10.1038/22941
VREDE, T., D. R. DOBBERFUHL, S.A.L.M. KOOIJMAN, AND J. J.
ELSER. 2004. Fundamental connections among organism
C : N : P stoichiometry, macromolecular composition, and
growth. Ecology 85: 1217–1229, doi:10.1890/02-0249
WEBER, T. S., AND C. DEUTSCH. 2010. Ocean nutrient ratios
governed by plankton biogeography. Nature 467: 550–554,
doi:10.1038/nature09403
———, AND ———. 2012. Oceanic nitrogen reservoir regulated
by plankton diversity and ocean circulation. Nature 489:
419–755, doi:10.1038/nature11357
Associate editor: Robert W. Sterner
Received: 25 September 2012
Amended: 18 March 2013
Accepted: 22 May 2013