Ecology, 92(11), 2011, pp. 2085–2095
Ó 2011 by the Ecological Society of America
Evidence for a three-way trade-off between nitrogen and
phosphorus competitive abilities and cell size in phytoplankton
KYLE F. EDWARDS,1,4 CHRISTOPHER A. KLAUSMEIER,2
2
AND
ELENA LITCHMAN3
1
Kellogg Biological Station, Michigan State University, Hickory Corners, Michigan 49060 USA
Kellogg Biological Station and Department of Plant Biology, Michigan State University, Hickory Corners, Michigan 49060 USA
3
Kellogg Biological Station and Department of Zoology, Michigan State University, Hickory Corners, Michigan 49060 USA
Abstract. Trade-offs among functional traits are essential for explaining community
structure and species coexistence. While two-way trade-offs have been investigated in many
systems, higher-dimensional trade-offs remain largely hypothetical. Here we demonstrate a
three-way trade-off between cell size and competitive abilities for nitrogen and phosphorus in
marine and freshwater phytoplankton. At a given cell size, competitive abilities for N and P
are negatively correlated, but as cell size increases, competitive ability decreases for both
nutrients. The relative importance of the two trade-off axes appears to be environment
dependent, suggesting different selective pressures: freshwater phytoplankton separate more
along the N vs. P competition axis, and marine phytoplankton separate more along the
nutrient competition vs. cell size axis. Our results demonstrate the multidimensional nature of
key trade-offs among traits and suggest that such trade-offs may drive species interactions and
structure ecological communities.
Key words: allometric scaling; ecological stoichiometry; nutrient uptake; resource competition; resource
ratio theory; trait-based ecology.
INTRODUCTION
Trade-offs are fundamental to ecological and evolutionary processes. They are assumed to underlie the
maintenance of non-neutral species diversity (Kneitel
and Chase 2004); within a species they constrain the
trajectory of phenotypic evolution (Blows and Hoffmann 2005). However, relatively little is known about
which trade-offs structure phenotypic diversity in
different groups of organisms. Recent reviews have
emphasized that, by quantifying important functional
traits across species, trade-offs can be detected and
linked to changes in species composition along environmental gradients (McGill et al. 2006, Litchman and
Klausmeier 2008). Much of the recent progress using
this approach has focused on terrestrial plants. For
example, a global analysis of leaf traits revealed a single
dominant axis of trait variation, along which leaves with
high metabolic rates have high specific leaf area and
short leaf lifespans (Wright et al. 2004). This fast-slow
continuum in leaf traits correlates with a fast-slow
continuum in tree life histories, and an interspecific
trade-off in performance under high and low light
regimes (Poorter and Bongers 2006).
A key insight from these analyses is the importance of
a multivariate approach to functional traits. Species
differ in an immense number of ways, but a multivariate
analysis often reveals that the effective dimensionality of
Manuscript received 1 March 2011; revised 20 May 2011;
accepted 20 May 2011. Corresponding Editor: P. R. Leavitt.
4 E-mail: [email protected]
trait variation is much smaller than the number of traits
measured (Wright et al. 2004, Edwards and Stachowicz
2010). Furthermore, part of the historical difficulty in
detecting interspecific trade-offs may be due to the fact
that trade-offs occur in multiple dimensions. For
example, a functional constraint between two fitnessenhancing traits may not be observable as a negative
trait correlation, if there is substantial variation in a
third, correlated trait that is unaccounted for (van
Noordwijk and de Jong 1986). However, although
trade-offs among multiple performance axes have been
postulated to explain high species diversity, current
evidence for trade-offs in more than two dimensions is
indirect (e.g., Harpole and Tilman 2007). In this study,
we have conducted a multivariate analysis of functional
traits across phytoplankton species, and combined this
analysis with a theoretical framework that relates these
traits to performance in interspecific competition. This
allows us to test for trade-offs that occur among more
than two trait dimensions.
Phytoplankton are a diverse, polyphyletic group of
microscopic, photosynthetic eukaryotes and cyanobacteria. They account for roughly half of global primary
production, and affect the biogeochemical cycling of
many elements, including carbon, nitrogen, and phosphorus (Falkowski et al. 2004). Phytoplankton species
composition can impact global climate (Falkowski et al.
1998), the trophic dynamics of aquatic ecosystems
(Sterner and Elser 2002), and water quality (Anderson
et al. 1998). Therefore, a variety of applications could
2085
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KYLE F. EDWARDS ET AL.
benefit from an understanding of the functional basis of
phytoplankton community structure.
When studying interspecific trait variation, a primary
challenge is to link functional traits to measures of
ecological performance, such as population growth rate.
In primary producers, including phytoplankton, nutrient acquisition traits and nutrient requirements for
growth are among the major functional traits affecting
fitness. In phytoplankton, a variety of studies have
linked nutrient physiology to population dynamics
through simple mathematical models (Droop 1973,
Tilman 1982, Grover 1991a). The parameters of these
models can be measured in the laboratory, and then
used to predict the outcome of interspecific competition
as a function of nutrient supply (Tilman 1982, Grover
1991a). Therefore, these parameters can be considered
as informative functional traits that relate directly to
population growth. By comparing parameters across
species, we can ask how nutrient niches vary across
species, and whether there are important trade-offs in
the components of nutrient competition.
We compiled a database of freshwater and marine
phytoplankton to compare physiological parameters for
two nutrients: nitrate and phosphate. In both freshwater
and marine systems, nitrogen and phosphorus are
thought to be among the most common growth-limiting
factors (Smith 2006, Elser et al. 2007). If the strength of
competition for nitrate and phosphate varies in space
and time, any functional constraints on the use of these
nutrients will affect community composition. A prior
analysis of nitrate traits in marine phytoplankton has
revealed a number of significant trait correlations that
should constrain the evolution of competitive ability for
that nutrient (Litchman et al. 2007). In this study, we
expand the multi-trait analysis by looking at both
nitrogen and phosphorus, and including marine and
freshwater species. We ask whether competitive ability
for nitrate is correlated with competitive ability for
phosphate across species. This fundamental question
remains unresolved not only for aquatic but for
terrestrial primary producers as well. Nitrogen and
phosphorus also commonly limit the growth of terrestrial plants (Elser et al. 2007), but the available evidence
that species differ in their relative abilities to compete for
these nutrients is limited (Tilman 1982, Güsewell and
Bollens 2003). Therefore, our analysis may also yield
insights into how to test for trade-offs related to nutrient
competition in terrestrial primary producers.
Based on existing theory and data, we can make two
different predictions for how competitive ability for
nitrate may relate to competitive ability for phosphate.
The first prediction derives from the pervasive effect of
cell size on resource acquisition. Theory predicts that
when nutrient acquisition is limited by molecular
diffusion, smaller cells have a strong advantage in the
rate of acquisition, relative to the amount of nutrient
required for growth (Pasciak and Gavis 1974, Yoshiyama and Klausmeier 2008). This prediction is supported
Ecology, Vol. 92, No. 11
by lab studies of uptake affinity (Tambi et al. 2009), by
mesocosm studies showing an increase in large-celled
species with increased nutrient loading (Agawin et al.
2000), and by large-scale data showing that the relative
abundance of picophytoplankton increases as total
production decreases (Agawin et al. 2000, Bell and
Kalff 2001). Therefore, based on the effect of cell size,
we would predict that competitive abilities for phosphate and nitrate should be positively correlated,
because smaller cells will be superior at acquiring both
resources.
A different prediction results if we assume that some
constraint creates a trade-off in the ability to compete
for nitrate vs. phosphate (Tilman 1982, Klausmeier et al.
2007). One plausible mechanism is the allocation of
limited energy, materials, or cell surface to uptake
proteins, which can be ion-specific (Gouaux and
MacKinnon 2005). A variety of studies have found
trade-offs under competition for two nutrients, although
the nutrients in question are usually silicate and
phosphate (Tilman 1982), or silicate and nitrate
(Sommer 1986). Some support for a nitrogen vs.
phosphorus trade-off comes from lab experiments
showing that species composition varies as the N:P
supply ratio changes (Tilman et al. 1986, Suttle and
Harrison 1988). If such a trade-off occurs, then there
may be two opposing factors structuring the relationship
between nitrate competitive ability and phosphate
competitive ability: a positive size-based correlation,
and a negative correlation due to an unknown functional constraint in competing for multiple resources.
Furthermore, there is evidence that large cell size is itself
beneficial, e.g., by reducing grazing mortality (Cottingham 1999, Steiner 2003, Chen and Liu 2010). Therefore,
if competitive ability for both nutrients declines with cell
size, while at a given size there is a trade-off in nutrient
abilities, this can be interpreted as a three-way trade-off
between competing for N, competing for P, and the
advantages accrued from large size.
In order to test these predictions, we analyze a
database, compiled from the literature, of nutrient traits
measured in the laboratory. Because every trait of
interest was not measured for every species, we use
statistical techniques for quantifying multivariate patterns in the presence of missing data. The relevance of
missing data techniques for ecology and evolution has
recently been reviewed by Nakagawa and Freckleton
(2008). As they discuss, these methods are rarely used in
ecological studies, but show widespread potential.
Statistical power is increased by using all the available
data, and the patterns detected using only complete-case
data may be biased. The approach we take here may be
useful for future multivariate trait analyses.
METHODS
Trait database.—We compiled a database of parameters, measured in the lab, that describe nutrient uptake
and nutrient-limited growth. The parameters we com-
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THREE-WAY TRADE-OFF IN PHYTOPLANKTON
piled derive from the Michaelis-Menten model of
nutrient uptake, and the Droop model of phytoplankton
growth:
Uptake ¼ Vmax
R
KþR
Qmin
Net growth ¼ l‘ 1 m
Q
ð1Þ
ð2Þ
where Vmax is the maximum cell-specific nutrient uptake
rate ([lmol nutrient]cell1d1), K is the half-saturation
constant for nutrient uptake ([lmol nutrient]/L), R is the
external nutrient concentration ([lmol nutrient]/L), l‘ is
the specific growth rate at infinite quota (d1), Q is the
internal nutrient concentration or quota ([lmol nutrient]/cell), Qmin is the minimum quota at which growth
rate equals zero, and m is the specific mortality rate
(d1).
According to resource competition theory (Tilman
1982), competitive ability for a particular nutrient at
equilibrium can be characterized by the break-even
nutrient concentration for a given species in monoculture, R*. For the model above (Eq. 1), it can be shown
that as mortality m approaches zero, R* approaches the
following (Litchman et al. 2007):
K
R !
Qmin m
Vmax
ð3Þ
Because there is little data for m, which can be highly
variable, we focus on Vmax, K, and Qmin as determinants
of competitive ability at equilibrium. As m ! 0, for
competing species with equal mortality, the superior
competitor will be the species with the greater value of
the quantity Vmax/KQmin. The ratio Vmax/K is a
commonly used measure of the ability to take up
nutrients at limiting concentrations, or ‘‘uptake affinity’’
(Healey 1980). Therefore, the quantity Vmax/KQmin can
be understood intuitively as the ability to uptake
nutrients at low concentration, scaled by the amount
of nutrient needed for growth (Qmin). We will refer to
this quantity as ‘‘competitive ability’’ for the purposes of
our analysis, and we will denote competitive ability for
nitrate and phosphate respectively as CN and CP.
Our database includes 60 marine species and 69
freshwater species, for each of which at least one of the
N
, KN, QN
following parameters was measured: Vmax
min ,
P
P
P
Vmax , K , Qmin (see Appendix A: Tables A1 and A2 for
species and parameters measured; superscripts indicate
the corresponding nutrient, N for nitrate and P for
phosphate). Although phytoplankton utilize ammonium
as well, we only analyzed nitrate uptake traits here, as
they are measured more frequently than ammonium
uptake traits, and thus we were able to acquire data for
more species. All parameters were collected from
published studies (see the list of source references in
Appendix A). As temperature and light affect these
parameters, we used studies at or near 208C, without
2087
severe light limitation. The maximum rate of nutrient
uptake (Vmax) often declines as cellular nutrient content
increases (Morel 1987). Therefore, we only included
estimates of Vmax measured under conditions of
intracellular nutrient depletion. Most ecologically important taxa are represented, including diatoms, dinoflagellates, chlorophytes, cyanobacteria, haptophytes,
raphidophytes, cryptophytes, xanthophytes, chrysophytes, and pelagophytes. We also recorded cell volume,
which was determined from the literature if not reported
in the focal study.
Multiple imputation.—A primary goal of our analysis
was to compare CN and CP across species. However,
there are relatively few species for which all six nutrient
parameters have been measured (12 freshwater species
and 13 marine species). Nonetheless, entries with some
missing parameter values still contain valuable information about how traits covary. Therefore, we analyzed
this data set using multiple imputation, a statistical
technique for quantifying multivariate patterns in the
presence of missing data (Rubin 1996, Schafer 1997). A
variety of methods are available to perform multiple
imputation (Nakagawa and Freckleton 2008). In our
analysis, we followed the method described by Schafer
(1997) and implemented in the R package norm, using R
2.11.0 (R Development Core Team 2010; norm package
available online).5 We found very similar results when
estimating trait covariances by full information maximum likelihood, with the R structural equation modeling package OpenMX (Boker et al. 2011). We present
the results of multiple imputation here, as this method
allows us to visualize the estimated trait relationships for
CP and CN.
The method we used for testing hypotheses via
multiple imputation can be described in four steps (see
Schafer 1997: chapters 5–6; a flowchart of the method is
shown in Appendix B: Fig. B1). We began with log10 N
, KN,
transformed values for all seven variables (Vmax
P
N
P
P
Qmin , Vmax , K , Qmin . and cell volume). Visual analyses
showed that on the log scale, the variables were
approximately linearly related, with normal residuals.
In the first step, we used the expectation–maximization
(EM) algorithm to find the multivariate normal
distribution that maximizes the likelihood of the
observed data. The multivariate normal distribution is
termed the imputation model, because it is assumed that
the missing data follow the same multivariate normal
distribution as the observed data. However, simulations
have shown that the multivariate normal model robustly
detects patterns in the data even for non-normal data
with a large proportion of missing data (Graham and
Schafer 1999).
In the second step, we used data augmentation to
generate multiple imputations of the missing data from
the multivariate normal model. Data augmentation is an
5
hhttp://CRAN.R-project.org/package¼normi
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KYLE F. EDWARDS ET AL.
algorithm similar to Markov chain Monte Carlo that is
useful for generating multiple imputations (Schafer
1997). The goal in generating imputed data sets is to
allow visualization of the patterns in the multivariate
normal fit, and to allow statistical analyses that require
complete data sets, while at the same time properly
quantifying the uncertainty in patterns of interest due to
missing data. Multiple estimates are generated for each
missing value, with the variation among those estimates
representing the uncertainty of the model in predicting
that value (Rubin 1996). We initiated each augmentation chain at the MLE of the multivariate normal model;
plots of the traces of the covariance parameters showed
that autocorrelation vanished by the 100th step, and we
conservatively saved the 500th step in the chain, to
ensure there was no autocorrelation between the initial
and final chain states (Schafer 1997). This was repeated
200 times, yielding 200 imputations for each missing
value, to ensure that our conclusions had maximal
statistical power (Graham et al. 2007).
In the third step, the statistical model of interest is
fitted separately to each of the imputed data sets. For
example, we may fit a multiple regression testing
whether CN is predicted by CP, cell volume, or both
variables. The point estimates and standard errors for
each of these predictors is saved, for each of the 200
imputations. Finally, in the fourth step, the coefficient
estimates and standard errors from all the imputations
are combined to yield proper significance tests. In
essence, there are two sources of uncertainty or error
that must be combined: within each imputed data set,
there is residual variation that affects the standard errors
of the coefficients fitted to that data set; across imputed
data sets, there is variation among the coefficient
estimates for those data sets, which quantifies the
uncertainty in that coefficient due to uncertainty about
the true values of the missing data. Therefore, a ‘‘total
variance’’ for each coefficient is calculated as T ¼ Ū þ (1
þ m1)B, where m is the number of imputations, B is the
between-imputation variance in that coefficient, and Ū is
the mean within-imputation variance for that coefficient
(i.e., the square of the standard error). Then a t test p
can
ffiffiffi
T,
be calculated using the approximate t statistic Q=
where Q̄ is the mean coefficient estimate over all
imputations, and the statistic is distributed with degrees
of freedom as follows:
m ¼ ðm 1Þ 1 þ
2
U
ð1 þ m1 ÞB
(Rubin 1996, Schafer 1997). Example imputed data sets
and subsequent analyses are shown in Appendix B: Fig.
B2.
Regression models.—As described in Multiple imputation, we combined multiple imputation with regression
analyses to test whether CN and CP are significantly
related, and whether these traits are also predicted by
cell volume. We also aimed to test whether these
Ecology, Vol. 92, No. 11
relationships differed between the freshwater and marine
species in the data set. Therefore, for each nutrient we fit
two models, one in which competitive ability for that
nutrient was predicted by competitive ability for the
other nutrient as well as cell volume, and one which each
of these effects is allowed to vary by system (marine vs.
freshwater). In order to better test for differences
between systems, we imputed the freshwater and marine
data separately, which is appropriate for testing
interactions because it allows the imputation model to
vary between systems (McCaffrey et al. 2001). In
addition, as described in the next subsection, we found
that fitting separate imputations for marine and
freshwater species increased our ability to predict the
missing data, as judged by leave-one-out cross-validation.
Predictive performance of the imputation models.—In
order to test the predictive ability of the imputation
models, we performed leave-one-out cross-validation.
For each observed value of each nutrient parameter, we
created a new data set in which that value was deleted.
Using that data set we then created 200 imputed values
for the deleted entry. We calculated the difference
between the deleted value and the mean of the 200
imputations for that entry. Finally, we calculated the
mean squared prediction error for each of the six
nutrient parameters. We also calculated, as a null model,
the mean squared prediction error if the deleted value
was estimated as simply the mean of the observed values
for that parameter. We performed this cross-validation
analysis for two different imputation models, one in
which all the whole data set was used to impute missing
values, and one in which freshwater and marine missing
values were imputed using only freshwater and marine
species, respectively.
Because the freshwater species had relatively many
observations of P parameters, and relatively few
observations of N parameters (Appendix B: Table B1),
we performed a power analysis of the ability to detect a
trade-off between CP and CN among freshwater species,
under the pattern of missingness in the freshwater data.
We found that despite the missing data, the imputation
method could detect a trade-off in 95% of cases at P ,
0.05, and in 88% of cases at P ,0.01, when simulated
data were generated using the covariance matrix fit to
the observed data (Appendix B: Fig. B4). In contrast,
when we performed the same regression using only the
species in the simulated data with no missing traits, a
trade-off was detected in 80% of cases at P , 0.05, and
in 61% of cases at P , 0.01 (Appendix B: Fig. B4).
CP and Monod affinity.—For 19 freshwater species, we
compared observed and imputed values of CP to the
Monod affinities for P compiled in Bruggeman (2011).
The Droop model (see Plate 1) and the Monod model
make equivalent predictions for competition outcomes
at equilibrium, under limitation by a single nutrient
(Appendix C). Therefore, a comparison of CP and
Monod affinity is useful to evaluate the utility of our
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THREE-WAY TRADE-OFF IN PHYTOPLANKTON
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TABLE 1. Predictive performance of the imputation method.
Model and
statistics
N
V max
KN
QN
min
P
V max
Freshwater
Null MSPE
Imputation MSPE
No. observations
Reduction (%)
1.04
0.346
14
67
0.137
0.0776
26
43
0.326
0.0848
17
74
Marine
Null MSPE
Imputation MSPE
No. observations
Reduction (%)
2.23
0.380
27
83
0.276
0.204
35
26
2.06
0.0633
25
97
KP
Q Pmin
0.639
0.421
47
34
0.446
0.363
43
19
0.544
0.150
47
73
2.84
0.466
30
84
0.48
0.0978
30
80
1.90
0.149
30
92
Notes: Parameters are minimum quota at which growth rate equals zero, Qmin; the half-saturation constant for nutrient uptake, K;
and the maximum cell-specific nutrient uptake rate, Vmax, for N and P. For all six nutrient parameters, mean-square prediction error is
reported for the imputation model (Imputation MSPE) and a null model in which missing values are imputed using the mean of the
observed values (Null MSPE). Percentage reduction in MSPE by the imputation model is also listed. This imputation model imputes
the freshwater and marine species separately; results for a model combining all species are given in Appendix B: Table B1.
‘‘competitive ability’’ approximation, as well as the
imputation model.
RESULTS
Predictive performance of the imputation model.—
Cross-validation results indicate that the imputation
model has substantial success in predicting known trait
values (Table 1). Mean squared prediction error was
reduced 19–97% compared to a null model in which
deleted values were imputed using the mean of the
observed trait values. The most accurately predicted
trait for both nutrients tends to be Qmin, followed by
Vmax and then K. The results in Table 1 were derived
with an imputation method in which the freshwater and
marine species were imputed separately. This method
was superior at predicting all traits, when compared to
an imputation model in which the entire data set was
used simultaneously (Appendix B: Table B1). Therefore,
unless otherwise noted, all the following results are
derived from the method that separately imputes the two
groups.
Competitive abilities and cell volume.—In order to
visualize the multivariate patterns of trait variation, we
plot observed values in combination with the mean
imputed values of the missing data. We then properly
test for significant trait relationships using regression
analyses that incorporate uncertainty in the values of the
missing data. There is evidence for two independent
relationships involving CN, CP, and cell volume. CN and
CP both tend to decline as volume increases, and this
pattern is driven by the marine species (Fig. 1A, B). At
the same time, when volume is held constant there is a
negative relationship between CN and CP, and this
pattern is driven by the freshwater species (Fig. 1C–E).
These patterns are confirmed by multiple regression; CN
is significantly negatively related to both cell volume and
CP, and likewise CP is significantly negatively related to
both cell volume and CN (Table 2, Models A and B; R 2
¼ 0.19 and 0.27 for CN and CP, respectively). We also
performed an analysis in which these effects are modeled
separately for the freshwater and marine species. The
results show that the volume effect on CN and CP is only
significant for the marine species, and the trade-off
between CN and CP is only significant for the freshwater
species (Table 2, Models C and D). Furthermore, the
variation in CN and CP explained by these regressions is
greater (R 2 ¼ 0.70 and 0.89, respectively). Principal
components analysis using the mean imputed values for
both marine and freshwater species shows that 90% of
the variation in these three traits is explained by the
plane defined by the first two PC axes (Fig. 1D, E). The
first axis (which explains 50% of the variation)
corresponds primarily to variation associated with
volume, and the second axis (which explains 40% of
the variation) corresponds primarily to a trade-off in CN
vs. CP that is orthogonal to volume-driven variation.
Therefore, the dominant axes of trait variation differ
between marine and freshwater species, but trait
variation among all species can be effectively summarized by a single plane relating CN, CP, and cell volume.
A similar plane of trait variation is found when
analyzing only the 25 species for which all seven traits
were measured (Appendix B: Fig. B3).
CP and Monod affinity.—For the 19 species shared
between our data set and the compilation by Bruggeman
(2011), CP was positively correlated with Monod affinity
(Pearson r ¼ 0.61, P ¼ 0.006; Fig. 1F; Appendix C). This
supports the utility of our competitive ability approximation, and the imputation model.
Multivariate nature of the variation in CN and CP.—
Because CN and CP are composite metrics that combine
multiple parameters, there are multiple ways to have
high or low values of these traits. Therefore, variation in
competitive ability depends upon the pattern of covariation in the component parameters, and the emergent
patterns described above may not be evident when the
components are analyzed in isolation. This can be seen
from a comparison of uptake affinity (Vmax/K ) for N
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KYLE F. EDWARDS ET AL.
Ecology, Vol. 92, No. 11
FIG. 1. The relationship between competitive ability for nitrate and phosphate, CN and CP, respectively, and cell volume. (A)
Scatterplot of log10CN vs. log10(cell volume), combining observed and imputed trait values. Open circles are marine species, and solid
circles are freshwater species. (B) Scatterplot of log10CP vs. log10(cell volume); symbols are as in panel (A). (C) Scatterplot of log10CP
vs. log10CN, combining observed and imputed trait values. Open circles are marine species, and solid circles are freshwater species.
Circle diameter is proportional to the cube root of the effective spherical diameter for that species. (D) Loading of CN, CP, and cell
volume (V ) onto the first two PC axes of a PCA using these three variables. Respective loading coefficients of CN, CP, and volume are
(0.17, 0.65, 0.74) on axis 1, and (0.46, 0.86, 0.21) on axis 2; percentages in axis labels are the percentage of variation explained by
each axis. (E) The plane defined by the two PC axes in panel (D) and a three-dimensional scatterplot of the trait values as in panel (C).
For reference, points are connected to the plane with a vertical line. Note that log10CP increases toward the viewer. (F) Scatterplot of
log10CP vs. log10(Monod affinity), for the 19 freshwater species in common between this study and Bruggeman (2011). Solid circles are
the six species with all six nutrient traits observed, and open circles are the 13 species with some missing trait data.
TABLE 2. Multiple regression results for the relationships between competitive ability for nitrate and phosphate, CN and CP, and
cell volume.
Coefficient
SE
P
Model A: CN response, no effect of system (mean R 2 ¼ 0.19).
Volume
CP
Predictor
0.32
0.31
0.088
0.15
0.00033
0.037
Model B: CN response, slopes vary by system (mean R 2 ¼ 0.70).
Volume, freshwater
Volume, marine
CP, freshwater
CP, marine
0.24
0.31
0.67
0.050
0.22
0.11
0.27
0.2
0.29
0.005
0.012
0.80
Model C: CP response, no effect of system (mean R 2 ¼ 0.27).
Volume
CN
0.25
0.36
0.10
0.18
0.011
0.051
Model D: CP response, slopes vary by system (mean R 2 ¼ 0.89).
Volume, freshwater
Volume, marine
CN, freshwater
CN, marine
0.050
0.36
0.63
0.076
0.17
0.14
0.23
0.26
0.77
0.010
0.0063
0.69
Notes: Four models are summarized: (A) CN as a function of volume and CP, (B) the same model with these slopes varying by
system, (C) CP as a function of volume and CN, and (D) the same model with these slopes varying by system. For each predictor, the
coefficient, standard error, and P value from a two-sided t test are listed. The coefficients and standard errors are calculated using
multiple imputation as described in Methods: Multiple imputation. The mean R 2 across all imputations is also listed for each model.
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THREE-WAY TRADE-OFF IN PHYTOPLANKTON
2091
FIG. 2. Relationships between uptake affinities and the minimum quota at which growth rate equals zero, Qmin, for freshwater
species. (A) Scatterplot of log10(uptake affinity for P) vs. log10(uptake affinity for N). Solid circles are species for which all four
N
P
, Vmax
], K is the half-saturation
traits were measured (Vmax is the maximum cell-specific nutrient uptake rate for N and P [Vmax
constant for nutrient uptake [KN, KP]), open circles are mean imputed values for species with at least one N trait and one P trait
measured, and gray triangles are mean imputed values for all other freshwater species. (B) Scatterplot of log10(uptake affinity for P)
vs. log10QPmin . Solid circles are species for which all three traits were measured, open circles are mean imputed values for species with
P
or KP measured, and triangles are mean imputed values for all other freshwater species. (C) Scatterplot of
QPmin and one of Vmax
P
N
log10(uptake affinity for N) vs. log10QN
min . Symbols are as in panel (B). (D) Scatterplot of log10C vs. log10C . Solid circles are
species for which all six traits were measured, inverted triangles are mean imputed values for species with at least two N traits and
two P traits measured, open circles are mean imputed values for species with at least one N trait and one P trait measured, and gray
triangles are mean imputed values for all other freshwater species.
and P among the freshwater species. Although uptake
affinity is often thought to indicate the ability to
compete under nutrient limitation (Healey 1980), our
P
N
data show no relationship between Vmax
/KP and Vmax
/KN
(Fig. 2A; mean Pearson correlation across imputations ¼
0.13). However, our analysis of the Droop model (Eqs.
1 and 2) indicates that competitive ability depends upon
the ratio of uptake affinity to the nutrient requirement
for growth (Qmin). Furthermore, Vmax/K tends to be
positively correlated with Qmin for both nitrate and
phosphate (Fig. 2B, C; mean Pearson r ¼ 0.82 and 0.58,
respectively). Accordingly, a trade-off between N and P
competitive abilities only becomes apparent when
uptake affinity is scaled by Qmin (Fig. 2D; mean Pearson
r ¼ 0.65).
Analogous considerations are important for the
relationships between cell volume and CN or CP among
the marine species. Vmax, K, and Qmin all tend to
increase with volume for both N and P (Appendix B:
Fig. B5). While an increase in K or Qmin will reduce
competitive ability, an increase in Vmax will increase
competitive ability. Therefore, the ultimate effect of
volume on CN and CP depends on the relative
allometric scaling of the component parameters; for
both of these traits, the ultimate effect is negative
(Appendix B: Fig. B5).
2092
KYLE F. EDWARDS ET AL.
Ecology, Vol. 92, No. 11
PLATE 1. Michael R. Droop (1918–2011). Photo courtesy of SAMS (Scottish Association for Marine Science).
DISCUSSION
We have found that the interspecific relationship
between CN and CP is consistent with both of the
predictions outlined in the Introduction. Both traits tend
to decrease as cell size increases (Fig. 1A–C, Table 2),
leading to an axis of trait variation along which CN and
CP are positively correlated (Fig. 1D, E). At the same
time, when cell size is controlled for, there is a negative
correlation between CN and CP (Fig. 1C–E, Table 2),
leading to a trade-off in the ability to compete for these
two nutrients. The size-based trait variation is most
evident in the marine species, while the variation
orthogonal to cell size is most evident in the freshwater
species (Fig. 1A–C, Table 2). However, the data as a
whole appear to be well summarized by a single plane of
trait variation (Fig. 1C–E). Therefore, we suggest that
the marine and freshwater species are both structured by
the same underlying trade-off, which can be visualized
as a constraining plane in three-dimensional trait space
(Fig. 1E).
A potential three-way trade-off, and the advantage of
large cell size.—The plane relating CN, CP, and cell
volume can be interpreted as a three-way trade-off, in
which an increase in any single trait tends to decrease the
other two traits. This interpretation rests on the
assumption that there is a fitness advantage to large cell
size, which we have not quantified here. Two prominent
hypotheses for the advantage of large cell size are
resistance to grazers, and an advantage in nutrient
competition under fluctuating nutrient supply. Marine
studies of microzooplankton grazing have shown that
the ratio of grazing mortality : production is typically
lower for larger species (Chen and Liu 2010), and
furthermore, that grazing on large cells by larger
zooplankton such as copepods is too low to compensate
for reduced microzooplankton grazing (e.g., Sommer et
al. 2005). There is similar evidence from lakes (Hambright et al. 2007), as well as evidence that large cells
experience lower mortality from the cladocerans that
can dominate phytoplankton grazing in lakes and ponds
(Cottingham 1999, Steiner 2003). It is also possible that
large cells persist solely because larger phytoplankton
species are consumed by different kinds of grazers than
smaller phytoplankton species (Sommer et al. 2005,
Calbet 2008). If grazing on smaller species reduces their
competitive effect, while a different suite of grazers
control larger species, then large phytoplankton could
persist due to niche differentiation via specialized
consumers, in the absence of any other advantage of
large cell size (Armstrong 1994).
Large cell size has also been suggested as an
advantage under fluctuating nutrient supply (Turpin
and Harrison 1980, Suttle et al. 1987, Stolte and
Riegman 1995, Litchman et al. 2009). Larger cells tend
to have greater maximum uptake rates on a per-cell
basis (Litchman et al. 2007, this study), and may have
larger nutrient storage capacity, relative to minimum
nutrient requirements (Grover 1991b, Stolte and Riegman 1995, Litchman et al. 2009). These trends will allow
larger cells to take up nutrient pulses more quickly, or
store more nutrients under brief periods of high supply.
There is some experimental evidence in support of these
predictions (Turpin and Harrison 1980, Suttle et al.
1987). In addition, an eco-evolutionary analysis using
empirical trait allometries from diatoms has shown that
November 2011
THREE-WAY TRADE-OFF IN PHYTOPLANKTON
large size can be selected for, under pulsed nitrate supply
with a relatively long (;2–30 day) period (Litchman et
al. 2009).
Empirical support for a CN vs CP trade-off.—Nitrogen
and phosphorus are thought to be common factors
limiting phytoplankton growth, in both freshwater and
marine systems (Smith 2006, Elser et al. 2007). Our
results imply that phytoplankton species are constrained, such that an increase in competitive ability
for nitrate tends to decrease competitive ability for
phosphate. This result is consistent with prior empirical
work on community composition as a function of the
N:P supply ratio. Laboratory and mesocosm experiments have shown that even moderate changes in N:P
supply can alter community composition (Tilman et al.
1986, Suttle and Harrison 1988, de Tezanos Pinto and
Litchman 2010). Large-scale observational studies have
used the ratio of total nitrogen to total phosphorus
(TN : TP) as a proxy for the N:P supply ratio; these
studies have also found that community composition
varies with TN : TP (Smith 1983, Philippart et al. 2000).
Although changes in community composition with
TN : TP may be driven in part by changes in the
abundance of nitrogen-fixing species (Smith 1983), large
changes in non-fixing taxa have been observed as well
(Philippart et al. 2000). The relative contribution of
different nitrogen forms (ammonium, nitrate, organic N
compounds and fixed atmospheric N) to TN may also
change with changing TN : TP ratios, and alter phytoplankton community composition. A future analysis of
traits associated with utilizing different forms of N could
help disentangle their contribution to structuring phytoplankton communities along the TN : TP gradient.
Our results are also consistent with an analysis of the
correlation between TP and dissolved nitrogen across
lakes (Leibold 1997). In some regions, nutrient concentrations were positively correlated across lakes, which
may indicate that among-lake variation is driven by a
combination of strong grazer pressure and variation
across lakes in overall nutrient supply; in another region,
nutrient concentrations were negatively related, as
predicted by nutrient limitation and a trade-off in
competition for N vs. P (Leibold 1997).
Multivariate constraints on trait variation.—The tradeoffs we have described occur at the emergent level of
the competitive ability approximation. Comparisons
using only the component parameters could have
indicated that such trade-offs do not occur (Fig. 2),
and in some cases could suggest opposite patterns of
trait covariation (Appendix B: Fig. B5). It is likely that
for most organisms and traits, a multivariate approach
will be essential for fully uncovering constraints on trait
variation. Studies of intraspecific genetic trait variation
have also found that constraints on trait variation, and
therefore constraints on trait evolution, may only be
evident in multivariate trait space (Blows and Hoffmann 2005). In addition, our results suggest that
2093
relating traits to population dynamic models may be an
important guide for uncovering and interpreting trait
constraints.
Potential differences in selective pressures between
marine and freshwater systems.—In our data set, there
is a striking difference between marine and freshwater
species in the regions of trait space inhabited (Fig. 1C).
This may reflect biases in the choice of species that are
used in lab studies of nutrient uptake kinetics. For
example, many of the large marine species are dinoflagellates or diatoms associated with toxic blooms.
However, the differences in trait distribution may also
reflect different selection pressures in marine vs.
freshwater environments. Marine diatoms include more
large species than freshwater diatoms (Litchman et al.
2009). If marine phytoplankton communities consistently include more very large species, this may be due to
different patterns of nutrient fluctuation in marine vs.
freshwater systems (Litchman et al. 2009), greater mixed
layer depths in marine systems (Litchman et al. 2009), or
the different dominant consumers in these systems
(Sommer and Sommer 2006).
In our data set, freshwater species not only tend to be
smaller, but appear to be more spread out along a CN vs.
CP axis (Fig. 1C). Freshwater systems are thought to
exhibit more spatial variation in the N:P supply ratio
(Sterner and Elser 2002, Sterner et al. 2008). If N:P ratio
is a dominant force in interspecific competition, and
varies greatly across environments, then this variation in
selective pressures could result in freshwater species
spreading out along the axis of CN vs. CP (Fig. 1C).
Trait-based ecology and interspecific trade-offs.—Our
results support the value of quantifying functional traits
in order to detect interspecific variation in ecological
strategies (McGill et al. 2006, Litchman and Klausmeier
2008). Despite the fundamental role of trade-offs in
ecology and evolution, there is surprisingly little
understanding of which trade-offs maintain natural
phenotypic diversity. Furthermore, although it is reasonable to expect that trade-offs involve multiple traits
or strategies simultaneously, there is very little evidence
for trade-offs that involve more than one axis of trait
variation. To our knowledge, the analysis most similar
to the constraining plane in Fig. 1E is from an analysis
of fish life histories (Winemiller and Rose 1992). They
found evidence for a general three-way trade-off among
three life history strategies, which they termed ‘‘opportunisitic,’’ ‘‘periodic,’’ and ‘‘equilibrium.’’ More such
analyses are needed, to better understand how many
dimensions of trait variation underlie the immense
natural diversity of phenotypes.
ACKNOWLEDGMENTS
This work was supported by grants from the James S.
McDonnell Foundation, and the National Science Foundation (OCE 09-28819 to E. Lichtman and C. A. Klausmeier,
and 08-45932 to E. Lichtman). This is KBS publication
#1590.
2094
KYLE F. EDWARDS ET AL.
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APPENDIX A
List of species in the data set and references for trait data (Ecological Archives E092-182-A1).
APPENDIX B
Additional methods and results for multiple imputation analyses (Ecological Archives E092-182-A2).
APPENDIX C
Competitive ability in the Monod model (Ecological Archives E092-182-A3).