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Temperature-nutrient interactions exacerbate sensitivity to warming in phytoplankton

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Temperature and nutrients are fundamental, highly nonlinear drivers of biological processes, but we know little about how they interact to influence growth. This has hampered attempts to model population growth and competition in dynamic environments, which is critical in forecasting species distributions, as well as the diversity and productivity of communities. To address this, we propose a new model of population growth that includes the temperature-nutrient interaction and test a novel prediction: that a species’ optimum temperature for growth, Topt, is a saturating function of nutrient concentration. We find strong support for this prediction in experiments with a marine diatom, Thalassiosira pseudonana: Topt decreases by 3-6°C at low nitrogen and phosphorus concentrations. This interaction implies that species are more vulnerable to hot, low nutrient conditions than previous models account for. The interaction dramatically alters species’ range limits in the ocean, projected based on current temperature and nitrate levels as well as those forecast for the future. Ranges are smaller not only than projections based on the individual variables, but also than projected ranges based on a simpler model of temperature-nutrient interactions. Nutrient deprivation is therefore likely to exacerbate environmental warming's effects on communities.
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Temperaturenutrient interactions exacerbate sensitivity
to warming in phytoplankton
MRIDUL K. THOMAS
1,2,3
,MAR
IA ARANGUREN-GASSIS
1,4
, COLIN T. KREMER
5,6
,
MARILYN R. GOULD
7
,KRISTAANDERSON
8
, CHRISTOPHER A. KLAUSMEIER
1,3,9
and
ELENA LITCHMAN
1,2,3
1
W. K. Kellogg Biological Station, Michigan State University, Hickory Corners, MI 49060, USA,
2
Department of Integrative
Biology, Michigan State University, East Lansing, MI 48824, USA,
3
Program in Ecology, Evolutionary Biology & Behavior,
Michigan State University, East Lansing, MI 48824, USA,
4
Department of Animal Ecology and Biology, University of Vigo, Vigo
36310, Spain,
5
Department of Ecology and Evolutionary Biology, Yale University, PO Box 208106, New Haven, CT 06520, USA,
6
Atmospheric and Oceanic Sciences Program, Princeton University, Princeton, NJ, USA,
7
Department of Ecology and
Evolutionary Biology, University of Connecticut, Storrs, CT 06269, USA,
8
Department of Biological Sciences, University of
Illinois at Chicago, 845 West Taylor Street (MC 066), Chicago, IL 60607, USA,
9
Department of Plant Biology, Michigan State
University, East Lansing, MI 48824, USA
Abstract
Temperature and nutrients are fundamental, highly nonlinear drivers of biological processes, but we know little
about how they interact to influence growth. This has hampered attempts to model population growth and competi-
tion in dynamic environments, which is critical in forecasting species distributions, as well as the diversity and pro-
ductivity of communities. To address this, we propose a model of population growth that includes a new
formulation of the temperaturenutrient interaction and test a novel prediction: that a species’ optimum temperature
for growth, T
opt
, is a saturating function of nutrient concentration. We find strong support for this prediction in exper-
iments with a marine diatom, Thalassiosira pseudonana:T
opt
decreases by 36°C at low nitrogen and phosphorus con-
centrations. This interaction implies that species are more vulnerable to hot, low-nutrient conditions than previous
models accounted for. Consequently the interaction dramatically alters species’ range limits in the ocean, projected
based on current temperature and nitrate levels as well as those forecast for the future. Ranges are smaller not only
than projections based on the individual variables, but also than those using a simpler model of temperaturenutrient
interactions. Nutrient deprivation is therefore likely to exacerbate environmental warming’s effects on communities.
Keywords: mechanistic species distribution model, nutrients, phytoplankton, population growth rate, R*, resources,
temperature, zero net growth isocline (ZNGI)
Received 14 October 2016; revised version received 23 January 2017 and accepted 23 January 2017
Introduction
Temperature and nutrients are among the strongest dri-
vers of biological processes, and they limit primary pro-
duction at a global scale (Falkowski et al., 1998; Enquist
et al., 1999; Behrenfeld et al., 2005; Elser et al., 2007; Lutz
et al., 2007). They are at the heart of three of ecology’s
most successful theoretical frameworks the metabolic
theory of ecology (West et al., 1997), resource competi-
tion theory (Tilman, 1982) and ecological stoichiometry
(Sterner & Elser, 2002). Despite the success of these
frameworks in explaining ecological patterns,
forecasting the dynamics of population growth and
competition in all but the simplest environments
remains a challenge. In part, this is because we cur-
rently lack a mechanistic framework integrating the
effects of multiple interacting environmental factors (or
stressors) on population growth. Because growth is a
highly nonlinear function of individual environmental
drivers, including temperature and nutrients (Fig. 1;
Monod, 1949; Kingsolver, 2009), the joint effect of multi-
ple drivers on growth is unlikely to be as simple as the
product of the separate effects. The absence of a frame-
work that accurately captures the joint effects of inter-
acting environmental factors limits our ability to
explore the dynamics of realistically complex systems
with theoretical models. Addressing this challenge is
especially urgent because temperature and nutrients
are both changing rapidly in natural environments
Correspondence: Present address: Mridul K. Thomas, Dept. of
Aquatic Ecology, Eawag: Swiss Federal Institute of Aquatic
Science and Technology,
Uberlandstrasse 133, 8600 D
ubendorf,
Switzerland, tel. +41 587655534, fax +41 587655802,
e-mail: mridul.thomas@eawag.ch
3269©2017 John Wiley & Sons Ltd
Global Change Biology (2017) 23, 3269–3280, doi: 10.1111/gcb.13641
(Vitousek et al., 1997; Barnett et al., 2005; Lyman et al.,
2010).
Temperature exerts a large effect on the growth of
organisms and populations, particularly in
ectotherms. Across species, increases in temperature
lead to exponential increases in important biological
rates, including metabolic, birth, death and popula-
tion growth rates (Eppley, 1972; Enquist et al., 1999;
Gillooly et al., 2001, 2002). In ectotherms, the growth
rate of individual species changes with temperature
following a unimodal, left-skewed function called the
thermal reaction norm (also known as thermal fitness
curve, thermal tolerance curve or thermal perfor-
mance curve; Fig. 1a). This skewness has important
implications for species performance in natural envi-
ronments (Martin & Huey, 2008; Kingsolver, 2009).
For example, small increases in temperature above
T
opt
, the optimum temperature for growth, lead to
large declines in fitness, implying that even small
amounts of environmental warming could threaten
populations adapted to current temperature regimes.
Larger temperature increases can drive growth rates
negative even when nutrients are plentiful. Studies of
the ecological effects of predicted temperature
changes have found that a number of species will be
negatively affected over the course of this century,
particularly in the tropics (Deutsch et al., 2008;
Martin & Huey, 2008; Sunday et al., 2012; Thomas
et al., 2012). Therefore, understanding how species
respond to temperature is an important step towards
forecasting species persistence and community com-
position in warming environments.
Nutrients also strongly influence growth rates
(Monod, 1949) and competitive dynamics (Tilman,
1982). The ability of species to persist under low-
nutrient concentrations is strongly predictive of com-
petitive outcomes in constant environments (Tilman,
1982). Population growth rate is a saturating func-
tion of limiting resource availability (Fig. 1b) in bac-
teria (Monod, 1949), phytoplankton (Eppley et al.,
1969), plants (Tilman & Cowan, 1989) and animals
(Holling, 1959). Recent work has shown that the
Monod equation also accurately describes bacterial
growth in environments with rapidly changing
nutrient concentrations (Bren et al., 2013), making it
a useful formulation with which to explore interac-
tions between nutrients and other factors in dynamic
environments.
Although the interactive effects of temperature and
nutrients on growth have been previously studied,
including in phytoplankton (Rhee & Gotham, 1981;
Raven & Geider, 1988; Geider et al., 1997, 1998; Ster-
ner & Grover, 1998; Mara~
n
on et al., 2014), they have
largely focussed on temperatures below T
opt
. Below
this temperature, simple multiplicative models (i.e.
models that multiply a temperature-dependent net
growth term by a nutrient-dependent growth term)
may suffice to describe growth. However, these multi-
plicative models may not perform well above T
opt
because cellular nutrient requirements are unlikely to
change monotonically above this point. Studies
focused on understanding how nutrients affect
growth rate have also tended to ignore high tempera-
tures. Increases in intracellular nutrient (specifically
phosphorus) concentrations have been linked to
increases in growth rate (the growth rate hypothesis,
Sterner & Elser, 2002), but this body of work has
neglected the effect of temperature on nutrient
requirements. More recent work (dubbed the ‘temper-
ature-dependent physiology hypothesis’, Toseland
et al., 2013; Yvon-Durocher et al., 2015) has considered
temperature explicitly and makes the contrasting pre-
diction that phosphorus concentration should decline
with increasing temperature. This is due to increasing
protein synthesis rates reducing the need for protein-
production machinery. However, this framework has
neglected the influence of temperatures beyond T
opt
.
Most ectotherms experience temperatures exceeding
T
opt
at least occasionally (Huey & Bennett, 1990; Huey
et al., 2009; Thomas et al., 2012), and in the tropics, T
max
is exceeded as well; heat avoidance is a major driver of
Temperature (°C)
(a)
0 5 10 15 20 25 30
0.0 0.4 0.8 1.2
0246810
0.0 0.4 0.8 1.2
Nutrient concentration (µM)
(b)
Specific growth rate (per day)
Fig. 1 The independent effects of temperature and nutrients on
population growth rate. (a) Growth rate as a function of tem-
perature, from the double exponential model (Equation 1). (b)
Growth rate as a function of nutrient concentration, from the
Monod equation (Equation 2). We unite both these models in the
interactive double-exponential (IDE) model (Equation 3), illu-
strated in Fig. 2.
©2017 John Wiley & Sons Ltd, Global Change Biology,23, 3269–3280
3270 M. K. THOMAS et al.
behaviour in reptiles (Huey & Slatkin, 1976; Huey &
Bennett, 1990). These periods, however brief, may be
extremely important in determining survival (Vasseur
et al., 2014). As a result of environmental warming,
such high-temperature events are expected to become
more frequent, necessitating the development of mod-
els that capture changes in nutrient-dependent growth
rate above T
opt
. In marine ecosystems, the highest tem-
peratures coincide with the lowest nutrient concentra-
tions, in the tropics and subtropics (Bopp et al., 2001).
This is due to temperature-induced stratification of the
water column, which prevents nutrients from being
resuspended from deeper waters and sediment. There-
fore, models that capture how organisms perform
under both low nutrients and high temperatures may
provide better insight into the future of the tropical
oceans.
We have developed and empirically tested such a
model.
Model
We outline below a new model of temperature- and
nutrient-dependent population growth. This model
invokes a set of simplifying assumptions to describe
net population growth rate: (i) birth and death rates are
exponentially increasing functions of temperature
(Eppley, 1972; Savage et al., 2004; McCoy & Gillooly,
2008), (ii) birth rates are saturating functions of nutrient
concentration (Monod, 1949), (iii) death rates are inde-
pendent of nutrient concentration, and (iv) the nutrient
half-saturation constant for growth is independent of
temperature. We begin by describing the effects of tem-
perature alone on population growth rate and then
integrate nutrient effects.
Effect of temperature on population growth rate. The ther-
mal reaction norm has been described using a variety
of empirical and partly mechanistic equations (School-
field et al., 1981; Norberg, 2004; Dell et al., 2011; Cork-
rey et al., 2012; Thomas et al., 2012). However, many of
these equations have parameterizations that are hard to
interpret biologically and difficult to expand upon to
incorporate interactions with other factors. To avoid
this problem, we introduce a model of the thermal reac-
tion norm that emerges from the difference between
two exponential, temperature-dependent rates: repro-
duction/birth (Savage et al., 2004) and mortality
(McCoy & Gillooly, 2008) (Fig. 1a). We refer to this
hereafter as the double-exponential model:
lT
ðÞ
¼b1expðb2TÞðd0þd1expðd2TÞÞ ð1Þ
where specific growth rate ldepends on temperature,
T. The first half of (1) describes the effect of
temperature on birth rates: b
1
is the birth rate at a tem-
perature of 0°C, and b
2
is the exponential change in
birth rate with increasing temperature. The second half
of (1) captures mortality rates, where d
0
is a tempera-
ture-independent mortality term, while d
1
and d
2
jointly
describe the exponential increase in mortality rate with
temperature. For certain parameter combinations, the
difference between the two exponential curves yields
the left-skewed shape typical of thermal reaction norms
(e.g. Fig 1a; Kingsolver, 2009).
Effect of nutrients on population growth rate. We used the
Monod equation to describe the effect of nutrients on
growth rate (Fig. 1b; Monod, 1949):
lRðÞ¼lmax R
RþKð2Þ
where specific growth rate ldepends on nutrient con-
centration, R, as well as the maximum growth rate,
l
max
, and a half-saturation constant, K. This standard
equation captures the saturating relationship between
nutrient concentration and growth rate (Fig. 1b).
Interactive effects of temperature and nutrients on population
growth rate. To develop a model predicting how these
two factors would interact, we assumed that reproduc-
tion rates are nutrient-dependent but death rates are
nutrient-independent. In other words, we expect nutri-
ents to be required for the construction of cellular
machinery that ultimately leads to cell division, and
assume that a decrease in the ability to produce such
machinery slows down division but is not lethal. This
allows us to combine Eqns (1) and (2), replacing l
max
in
Eqn (2) with the temperature-dependent birth term in
Eqn (1) while retaining the nutrient-dependent birth
term, R/(R+K). This results in a model of population
growth rate as a joint function of temperature and
nutrients:
lT;RðÞ¼b1expðb2TÞ R
RþKðd0þd1expðd2TÞÞ
ð3Þ
We refer to this model hereafter as the interactive
double-exponential (IDE) model (Fig. 2; Fig. S1). All of
the parameters in Eqn (3) retain their earlier meanings,
except that b
1
now refers to the birth rate at the refer-
ence temperature of 0°C only under nutrient-replete
conditions. At nutrient concentrations well above the
half-saturation level K, this model approximates to the
double-exponential model. However, the shape of the
thermal reaction norm changes in important ways at
lower nutrient concentrations (Fig. 2). We note that this
model formulation is applicable to ectotherms in gen-
eral, having no terms specific to phytoplankton.
©2017 John Wiley & Sons Ltd, Global Change Biology,23, 3269–3280
HEAT +STARVATION KILLS FASTER THAN EITHER 3271
Model predictions. Our IDE model makes an important,
novel prediction: that T
opt
is a saturating function of
nutrient concentration (Fig. 2a). This is also true of T
max
(the temperature above which population growth rate is
negative; Thomas et al., 2016) and temperature niche
width (the range of temperatures over which growth
rate is positive). T
min
(the temperature below which pop-
ulation growth rate is negative; Thomas et al.,2016)
shows the reverse pattern, increasing strongly at the
lowest nutrient concentrations. The differences in model
structure lead to very large decreases in growth rate at
temperatures above T
opt
under low-nutrient conditions,
suggesting that even occasional periods of high tempera-
ture and low nutrients could have large effects on spe-
cies and communities. In addition to these predictions,
our model captures an important property of nutrient
curves that has previously been reported: R*,thenutri-
ent concentration at which net population growth rate is
zero (and a measure of nutrient competitive abilities)
(Tilman, 1982), is lowest at intermediate temperatures
and increases sharply near T
min
and T
max
(Fig. 2a).
Model comparison and evaluation. We tested the first pre-
diction of the IDE model (nutrient dependence of T
opt
)
experimentally, using a marine phytoplankton species,
Thalassiosira pseudonana, and two different nutrients,
nitrate and phosphate. We then used it to predict range
limits in the ocean based on temperature and nitrate,
under both present and future ocean conditions. We
compared these predictions against those made using an
existing model of temperaturenutrient interactions in
phytoplankton. This reference model uses a simple mul-
tiplicative interaction (taking the product of tempera-
ture-dependent and nutrient-dependent terms) to
characterize growth. This form of interaction is charac-
teristic of a large number of models of phytoplankton
growth (Sterner & Grover, 1998; Moisan et al., 2002;
Huber et al., 2008). The specific reference model we con-
sider here is derived from the equations currently used
in the Darwin project, which studies global patterns of
phytoplankton diversity, physiology, biogeography and
marine ecosystem function (e.g. Follows et al.,2007;Dut-
kiewicz et al., 2013). However, we made two changes:
we extracted only the temperature and nutrient compo-
nents of their equation (ignoring light and other factors),
and we fit the temperature-related parameters of the
equation to our empirical data, rather than using con-
stants from the literature. The resulting multiplicative
interaction (MI) model takes the following form:
lT;RðÞ¼sexp A1
Tþ273 1
273

exp BTTopt
4

R
RþKm:ð4Þ
Here, sand Adetermine the height and shape of (4),
while Bdetermines the range of temperatures over
510152025
246810
Temperature (°C)
Nutrient concentration (µM)
−2.5
−2.0
−1.5
−1.0
−0.5
0.0
0.5
(a)
Topt
Tmin, R* Tmax, R*
growth rate
Specific
(per day) Nutrient concentration (µM)
5°C
10°C
15°C
20°C
25°C
(b)
0246810
0 5 10 15 20 25 3 0
−0.5 0.0 0.5 1.0−0.5 0.0 0.5 1.0
Temperature (°C)
2.5 µM
5 µM
10 µM
20 µM
50 µM
(c)
Specific growth rate (per day)
0
Fig. 2 The joint effects of temperature and nutrients on population growth rate, based on the interactive double-exponential (IDE)
model (Equation 3). (a) Density plot showing variation in growth rate across both gradients and changes in important traits. T
opt
(white
line) is a saturating function of nutrient concentration and R* (black line, where growth rate = 0) is a U-shaped function of temperature
(i.e. this is the zero net growth isocline, or ZNGI). Moving horizontally across the figure, the temperatures at which the R* is reached
are also the extremes of the temperature niche, T
max
and T
min
. This plot is truncated just below the ZNGI, but untruncated and 3D ver-
sions may be seen in Fig. S1. (b) Vertical slices through 2a, showing how Monod curves change with temperature. (c) Horizontal slices
through 2a, showing how thermal reaction norms change with nutrient concentration.
©2017 John Wiley & Sons Ltd, Global Change Biology,23, 3269–3280
3272 M. K. THOMAS et al.
which growth can occur (i.e. the niche width). Mortality
occurs at a constant rate m, and all other parameters
have the same interpretation as in (3). This MI model
structure is similar to that of the IDE, but it invokes a
multiplicative relationship between temperature and
nutrient terms, thereby incorporating the weaknesses
we mentioned earlier. As a result, T
opt
is invariant
across nutrient levels in this and other such models
(Sterner & Grover, 1998; Moisan et al., 2002; Huber
et al., 2008). T
max
and T
min
are also higher in the MI
model than in the IDE model (Fig. 3).
Materials and methods
Experiment
We measured population growth rates of a marine diatom,
Thalassiosira pseudonana strain CCMP 1335 (obtained from the
Provasoli-Guillard National Center for Marine Algae and
Microbiota), across gradients of temperature and nutrients in
two separate experiments.
The first was a 5 95 factorial experiment examining tem-
peraturephosphorus interactions. The five temperatures (20°,
25°, 27.5°,30°and 32.5°C) were chosen to span the range that
previous experiments had suggested included T
opt
and T
max
(Boyd et al., 2013). The five phosphate concentrations (1, 2.5, 5,
15 and 36.2 lM) ranged from concentrations common in natu-
ral environments to those commonly used in laboratory exper-
iments and spanning moderately limiting to saturating levels.
Measurements were made in three replicate cultures at every
temperature and phosphate combination, for a total of 75
growth rate estimates.
The second experiment examined temperaturenitrate
interactions in the same strain. This was not factorial, with
slightly different temperatures being used at the highest
nitrate concentration tested. These high nitrate measurements
were performed later, and the growth chambers were stabi-
lized at a slightly different temperature when the culture accli-
mation period began (levels differed by 1.5°C or less). To be
specific, this experiment used four nitrate concentrations
(1, 15, 300 and 884 lM) and seven temperatures. At the three
lower nitrate concentrations, the temperatures used were 10°,
15.8°, 20.4°, 23.6°, 28.4°, 30.1°and 32°C, while at the highest
concentration of 884 lM, the temperatures used were 10°,
15.8°, 20.2°, 25.1°, 28.5°, 29.3°and 31°C. Measurements were
made in three replicate cultures at every temperature and
nitrate combination, for a total of 84 growth rate estimates.
Culture conditions. We grew nonaxenic cultures of T. pseudo-
nana in different media for phosphorus and nitrate experi-
ments. For the phosphorus experiments, we used autoclaved
125 mL conical flasks containing approximately 50 mL
artificial seawater medium (modified ESAW, 549 lMnitrate;
Berges et al., 2001), and for the nitrate experiments, we used
50 mL sterile culture flasks containing approximately 40 mL
artificial seawater medium (Tropic Marin salt mix, L1 med-
ium, 36.2 lMphosphate; Guillard & Hargraves, 1993). All
glassware and equipment that came in contact with the med-
ium were acid-washed to remove any residue that might
cause contamination with nutrients. Cultures were maintained
in a growth chamber at 20°C under cool white fluorescent
lights (Ecolux 20W). All growth chambers used during accli-
mation period and the experiment were set to a 14:10 light/
dark cycle, with a light intensity of approximately 100 lEm
2
s
1
. Before the phosphate experiment, all cultures were
allowed to acclimate for 23 weeks at the experimental tem-
peratures and nutrient concentrations. Before the nitrate
experiment, all cultures were exposed to 0 lMnitrate medium
for five days, and then, they were allowed to acclimate for ten
days at the experimental temperatures and nutrient concentra-
tions. In all cases, cultures were shaken every day by hand
and diluted every 25 days to keep them in exponential
growth phase.
Growth assays. Experimental assays were carried out in
50 mL conical flasks containing 3040 mL of culture. Every
0 5 10 15 20 25 30 35
012345
Temperature (°C)
Nitrate concentration (µM)
Fig. 3 Comparison of the IDE model (purple) and the MI model
(green) fits to our temperature-nitrate growth rate measure-
ments. Solid lines indicate how R* (the minimum nutrient
requirement for growth) changes with temperature and how
T
min
and T
max
change with nitrate concentration (see Fig. 2a for
explanation). The MI model would suggest greater tolerance of
high temperatures and poorer tolerance of low temperatures.
Dotted lines show how T
opt
changes with nutrient concentration
in the two model fits. T
opt
remains constant across nutrient con-
centrations in the MI model, while it is a saturating function of
nutrients in the IDE model and in our data (Fig. 4). The MI
model fit assumed a background mortality rate of 0.1, which
affects the height of the zero net growth isocline but not its
shape (see Table S1 for all parameter values). Note that the Y-
axis range was chosen to highlight the region of greatest dis-
agreement between models.
©2017 John Wiley & Sons Ltd, Global Change Biology,23, 3269–3280
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24 hours for five days, 2 mL of culture was removed from each
flask, and the flasks were immediately returned to their growth
chambers. These 2 mL subsamples were transferred to individ-
ual wells in microwell plates, and we then measured chloro-
phyll a fluorescence (excitation wavelength: 436 nm, emission
wavelength: 680 nm) using a SpectraMax M5 microplate reader
(Molecular Devices, Sunnyvale, CA, USA). Microplates were
agitated by the microplate reader before measurements were
taken to ensure that the culture was homogeneous. As part of
the measurement procedure, each well was divided into a
393 grid, and 20 fluorescence measurements were made at
each point, with the mean of all 180 measurements being used
for subsequent growth rate estimation.
Statistical analyses
Calculation of specific growth rate. For each culture, we per-
formed linear regressions of log-fluorescence against day
number. On visual inspection of the regressions, we found
that log-fluorescence plateaued during the assay, especially in
low-nutrient cultures. This indicates that cultures did not
experience exponential growth for the full assay, and we
therefore calculated growth rates over the period where
growth rate was exponential. The slope of the resulting regres-
sion is the specific population growth rate (day
1
) of the cul-
ture, l. All growth rate measurements from our experiments
are included in the Appendix S1.
Fitting interaction models (IDE and MI) to the population
growth rate data. We used a maximum likelihood approach
to fit the IDE model to the temperaturephosphate and tem-
peraturenitrate growth rate estimates, and the MI model to
the temperaturenitrate estimates. Using the Rpackage BBMLE
(Bolker & R Development Core Team, 2014), we estimated the
values of all parameters while assuming that observational
error was normally distributed with a variance of r
2
.
Describing variation in population growth rate as a function
of temperature, and estimating T
opt
.To demonstrate that
patterns in growth and T
opt
were not driven by constraints
artificially introduced by the IDE model, we also used gen-
eralized additive models (GAMs) to describe variation in
growth rates, as GAMs have no such parametric constraints.
We did this in two ways using the R package mgcv (Wood,
2011). (i) We used GAMs with temperature as a smoother
term to fit the thermal reaction norms at each phosphate
concentration in our experiment. Using these fits, we then
estimated T
opt
by numerical maximization and simulated
from the posterior distribution of the fitted parameters to
quantify uncertainty in T
opt
. Results were similar if we esti-
mated T
opt
by fitting Eqn (1) to the data. (ii) We used
GAMs with both temperature and nutrient concentration as
smoother terms to describe variation in growth rate in both
our experiment and the published growth data. Curvature
in the GAM-interpolated contours highlights changes in T
opt
with nutrient concentration.
All analyses were performed using the Rstatistical environ-
ment v. 3.2.3 (R Core Team, 2015).
Mechanistic species distribution models (MSDMs):
predicting range limits under current and future ocean
conditions using different growth models
Global earth system models provide realistic data on historic,
contemporary and future ocean conditions (the last under dif-
ferent climate change scenarios). We obtained global surface
temperature and nitrate estimates from the output of the
COBALT ecosystem model (Stock et al., 2014 a, b), which runs
within the earth system model of the Geophysical Fluid
Dynamics Laboratory (GFDL) (ESM2M, Dunne et al., 2012,
2013). These estimates are available for both historic periods
(e.g. 19812000) and future projections (e.g. 20812100) using
the RCP 8.5 scenario (IPCC Fifth Assessment Report 2013,
Stock et al., 2014b). Environmental temperature and nutrient
data were available as monthly averages, with 1 91 degree
spatial resolution (dropping to 1/3 degree in the tropics). For
model and simulation details, see Stock et al. (2014a,b).
Using the environmental temperature and nutrient esti-
mates and two growth models (Eqns 3 and 4) parameterized
with our experimental data (see values in Table S1), we gener-
ated MSDMs (Thomas et al., 2012) to predict the species distri-
bution of T. pseudonana. Ranges were estimated by calculating
the average (arithmetic mean) monthly growth rates of T.
pseudonana at each grid location across the world’s oceans
between 1981 and 2000 as well as 2081 and 2100. For a given
model, areas where mean growth rate was positive were
assumed to lie within the species’ fundamental niche or range.
Using the IDE model, we also predicted the species’ potential
range (i) assuming that temperature alone limited growth (by
setting nitrate concentration to 884 um) and (ii) assuming that
nutrients were the primary driver (by assuming that a nutrient
curve was measured at 20°C, a common temperature for phy-
toplankton culturing). To generate reasonable estimates of spe-
cies range in the second case, we applied a background,
temperature-independent mortality rate mof 0.1. We also
fixed mat 0.1 for MSDMs based on the MI model (this constant
mortality rate term is analogous to the d
0
parameter in Eqn
(2)). To explore how the choice of minfluences predicted range
size we estimated range limits using different values of m.
Results
Experiments
Growth rate was strongly influenced by both nutrient
concentration and temperature, ranging from 0.78 to
1.55 day
1
in the temperaturephosphate experiments,
and 0.01 to 1.34 day
1
in the temperaturenitrate exper-
iments (Fig. 4). Our primary prediction was strongly
supported: T
opt
is a saturating function of nutrients,
declining by approximately 3.5°C at the lowest phos-
phate concentrations and 6°C at the lowest nitrate con-
centrations (Figs 5, S2, S3). The saturating function was
a better fit than either a linear model or an intercept-
only model (dAICc >2 in both cases). In addition to the
T
opt
prediction being met, the IDE model also explained
©2017 John Wiley & Sons Ltd, Global Change Biology,23, 3269–3280
3274 M. K. THOMAS et al.
variation in growth rate measurements better than the
MI model (dAIC =3.8). It explained 84% of the
variance in the data in the case of the temperature
phosphate experiment, and 69% in the case of tempera-
turenitrate experiment (Figs 4, S4). GAM fits with both
temperature and nutrients as smoother terms also show
broadly similar patterns in growth rate variation, but
point towards a possible decline in growth rate at the
highest nitrate levels that Eqns (2) and (3) cannot repro-
duce (Fig. S5).
Range limits model comparison
We fit Eqns (3) and (4) to the growth rate measure-
ments from our temperaturenitrate experiment and
used the fits to predict fundamental range limits under
current and future ocean conditions. As expected, pre-
dictions of range limits based on temperature alone dif-
fered strongly from those based on nitrate alone. The
fundamental temperature niche (i.e., the geographical
range over which the species can persist when tempera-
ture is considered to be the only limiting factor) extends
from the tropics to subpolar regions. The fundamental
nitrate niche covers the high-nutrient temperate and
polar regions (Fig. 6). Range sizes are dramatically
reduced when interactions between the two variables
are considered, using either the IDE or the MI models
(Fig. 6). Temperature constrains the range of T. pseudo-
nana at high latitudes, while nitrate limits its range in
oligotrophic tropical/subtropical regions. In regions of
high growth rate, both IDE and MI models generate
similar predicted growth rates. However, over realistic
ranges of mortality rates, the MI model predicts an R*
(minimum nutrient requirement) that is considerably
lower at high temperatures but higher at low tempera-
tures than the IDE model (Figs 3, S6). Therefore, the
IDE and MI models differ considerably in predicted
range limits and sizes (Figs 6, S7). The IDE model pre-
dicts that T. pseudonana will be unable to grow in the
tropics and subtropics except for a small region in the
South Pacific, while the MI model allows for growth in
tropical regions throughout the oceans. Both models
predict that T. pseudonana’s range will change over the
next 80 years, driven most strongly by nitrate
decreases in the tropics and warming in the North
Pacific.
12345
Temperature (°C)
Phosphate concentration (µM)
0.6
0.8
1.0
1.2
(a)
Specific growth rate (per day)
246810
Temperature (°C)
Nitrate concentration (µM)
−0.5
0.0
0.5
1.0
(b)
Specific growth rate (per day)
0.8 1.0 1.2 1.4
Predicted growth rate (per day)
Observed growth rate (per day)
Phosphate
(c)
20 22 24 26 28 30 32 10 15 20 25 30
0.8 1.0 1.2 1.4 0.0 0.5 1.0
0.0 0.5 1.0
Predicted growth rate (per day)
Observed growth rate (per day)
Nitrate
(d)
Fig. 4 Results of IDE model fits to T. pseudonana growth rates in the temperature-phosphate and temperature-nitrate experiments. (a)
Predicted growth rates from IDE model fitted (R
2
= 0.84) to growth rates at 5 phosphate concentrations and 5 temperatures. (b) Pre-
dicted growth rates from IDE model fitted (R
2
= 0.69) to growth rates at 4 nitrate concentrations and 7 temperatures. The nutrient axes
in panels 4a & 4b are truncated to highlight variation at the lowest concentrations (Fig. S4 shows the untruncated plots). (c) and (d)
show the corresponding fitted vs. observed growth rates in the two experiments.
©2017 John Wiley & Sons Ltd, Global Change Biology,23, 3269–3280
HEAT +STARVATION KILLS FASTER THAN EITHER 3275
Discussion
A mechanistic understanding of how environmental
factors (or stressors) interact to influence population
growth can provide a deeper understanding of how
communities will be affected by anthropogenic change.
Our new model of temperaturenutrient interactions
makes novel predictions that find strong experimental
support. An important consequence of its structure is
that ectothermic taxa are highly sensitive to a combina-
tion of high temperatures and low nutrients. As a
result, they are likely to be more sensitive to environ-
mental warming than existing population, community
and ecosystem models assume.
Nutrient limitation alters the thermal reaction norm
T
opt
is a saturating function of nutrient concentration
(Fig. 4), as is population growth rate. This pattern par-
allels a recent finding showing that population growth
rate and T
opt
are unimodal functions of irradiance in
phytoplankton, with both peaking at similar irradiance
levels (Edwards et al., 2016). Considered together, these
results suggest that T
opt
increases in concert with maxi-
mum growth rate. If true, this has important implica-
tions for how taxa respond to warming while
simultaneously being challenged by environmental
stresses, including changes in pH, CO
2
and pollutant
concentrations. In the case of nutrient limitation, the 3
6°C decrease in T
opt
we found is likely to be biologi-
cally relevant because the ‘thermal safety margin’ of
many ectotherms is of a similar magnitude, and in
many cases even smaller (Deutsch et al., 2008; Huey
et al., 2009; Sunday et al., 2012; Thomas et al., 2012).
Many natural environments experience nutrient con-
centrations even lower than those used in our
experiments (Tyrrell, 1999; Downing et al., 2001),
implying that an even greater decrease in the environ-
mentally relevant T
opt
is possible.
Both the IDE and MI models imply that tolerance of
extreme temperatures (both high and low) decreases at
low nutrient concentrations, i.e. that T
max
decreases
and T
min
increases (Figs 2 and 3). Although we did not
test these predictions in our experiment, this is consis-
tent with prior experimental findings showing large
increases in organismssusceptibility to extreme tem-
peratures when deprived of nutrients. In diazotrophic
cyanobacteria, nitrogen deprivation causes T
min
to
increase and T
max
to decrease (Thomas & Litchman,
2016). Evidence from other taxa suggests that increased
susceptibility to extreme temperatures under nutrient
limitation may be a general physiological limitation.
Kelp that accumulates nitrogen reserves can tolerate
periods of high-temperature stress, while those that
cannot experience negative growth rates (Gerard, 1997).
Corals are more susceptible to heat-induced bleaching
when they are limited by phosphate (Wiedenmann
et al., 2013), and cold tolerance in tree seedlings
decreases when deprived of nitrogen (DeHayes et al.,
1989). Salmon deprived of food experience a reduction
in both high-temperature and low-temperature toler-
ance (Brett, 1971). This high susceptibility to extreme
temperatures when deprived of nutrients has profound
implications for the survival of organisms in environ-
ments that experience periods of low nutrients.
Temperature dependence of nutrient requirements and
competitive abilities
The IDE model predicts that R*is a U-shaped function
of temperature (Figs 2 and 3), and assumes that the
nutrient half-saturation constant for growth Kdoes not
Topt
(°C)
Phosphate concentration (µM)
(a)
0 5 10 15 20 25 30 35
25 26 27 28
0 200 400 600 800
20 22 24 26 28 30 32
Nitrate concentration (µM)
(b)
Fig. 5 T
opt
is a saturating function of nutrient concentration, as predicted by the IDE model. We estimated T
opt
at each nutrient concen-
tration using GAMs with temperature as a smoother term (Fig. S3, S4). (a) T
opt
varies by 3.5°C across the phosphate gradient (b) T
opt
varies by 6°C across the nitrate gradient. Curves show a saturating function fit to the T
opt
estimates (the saturating function was a better
fit than a linear model or intercept only model, dAICc >2). Error bars represent 95% confidence intervals.
©2017 John Wiley & Sons Ltd, Global Change Biology,23, 3269–3280
3276 M. K. THOMAS et al.
change with temperature. Our experiments were not
designed to test these patterns, but a few prior studies
have examined them. Tilman et al. (1981) found that R*
was lowest at intermediate temperatures in one freshwa-
ter diatom, Asterionella formosa, and that another, Synedra
ulna, exhibited a pattern consistent with this across the
range of temperatures tested (measurements did not
extend above T
opt
). A similar pattern of increasing R*
with decreasing temperature below T
opt
was reported
for heterotrophic bacteria (Reay et al., 1999), suggesting
that higher nutrient demand at temperature extremes
may be a general phenomenon. The dependence of R*
on temperature should have significant consequences for
resource competition under changing temperatures,
including switching competitive outcomes. Regarding
our model assumption that Kis invariant with tempera-
ture, we found no systematic variation but there were
small differences between temperatures (Figs S8, S9).
Previous studies have investigated the temperature
dependence of Kand found mixed results (Ahlgren,
1978; Tilman et al., 1981; Mechling & Kilham, 1982), but
few of these studies measured Kabove T
opt
.Further
studies will therefore be needed to test this assumption.
In the future, this work may be expanded upon to con-
sider how parameters such as nutrient uptake and mini-
mum nutrient quotas change with temperature. A
previous study (Baker et al., 2016) has found that nutri-
ent uptake rates are highest at intermediate tempera-
tures. Taken together with our results, this suggests that
per-cell nutrient requirement is highest and per-cell
uptake rate is lowest at extreme temperatures.
Influence of temperaturenutrient interactions on species
ranges
Temperaturenutrient interactions can limit species
ranges to a much greater degree than either factor alone
(Fig. 6). T. pseudonana’s temperature curve (at saturat-
ing nitrate levels) allows it to grow in all but the coldest
waters, while its nitrate curve (at 20 °C) limits growth
in parts of the tropical and subtropical ocean. In con-
trast, its range is limited to temperate waters in both
interaction models, as well as a narrow band of the
tropical Pacific in the IDE model and portions of all
tropical oceans in the MI model. As the IDE model pre-
dicts T
opt
patterns that are more strongly supported by
our experiments (Figs 3 and 5), our results suggest that
ecosystem models using multiplicative formulations
will overestimate performance at high temperatures
and consequently inflate tropical range boundaries.
Although this approach has rarely been used to predict
individual species ranges, predictions of aggregate
community productivity an important component of
ocean ecosystem models may suffer from similar
biases. If our results hold for other ectotherms, predic-
tions of terrestrial community responses to warming
will also need to account for this interaction.
Our results also suggest that future changes to ocean
temperature will not alter T. pseudonana’s potential
range greatly, but nitrate decreases will limit its ability
to grow in Arctic waters. Within its range, the species
also sees notable decreases in predicted growth rate,
making it likely that its competitive interactions with
Fig. 6 Influence of temperature and nitrate on predicted growth rate and range limits of T. pseudonana, under recently recorded (1981
2000) conditions and those predicted for the future (2081 2100). In the principal 8 panels, dark grey areas fall outside the species
range. A comparison of the IDE and MI models shows that the former predicts worse performance in the tropics and better perfor-
mance at the poles. In the future, both models predict a decrease in range size in the tropics and subtropics, and an increase at tempe-
rate latitudes. Temperature-only and nitrate-only map calculations were generated by using the fitted temperature-nitrate surface (Fig.
4b) and setting nitrate = 884 lM and temperature = 20°C respectively.
©2017 John Wiley & Sons Ltd, Global Change Biology,23, 3269–3280
HEAT +STARVATION KILLS FASTER THAN EITHER 3277
other species will change. More measurements of tem-
peraturenutrient interaction surfaces will be needed to
understand the physiological and evolutionary con-
straints species face, and to model how environmental
change will modify species interactions.
Temperaturenutrient interactions have important
implications for efforts to link physiological measure-
ments with organismal performance in natural environ-
ments. Attempts to identify patterns of adaptation by
linking species traits to environmental gradients may
be confounded if trait measurements are made under
experimental conditions that do not reflect natural envi-
ronments. Studies examining species’ tolerance to cli-
mate change and forecasts of future community
composition will need to account for the influence of
food/nutrient levels. For example, eutrophication may
facilitate the invasion of non-native taxa early in a sea-
son by increasing their ability to tolerate cold tempera-
tures. And although both high- and low-temperature
tolerance decreases under nutrient-poor conditions,
high temperatures are a greater threat due to pervasive
environmental warming (IPCC, 2013). This is especially
true in aquatic environments where warming drives
stratification, leading to a negative correlation between
temperature and nutrients in the environment (Bopp
et al., 2001). If our IDE model is correct, these simulta-
neous changes are a major threat, as species’ T
max
will
decrease as environmental temperatures and stratifica-
tion increase, due to increasing nutrient limitation dri-
ven by stronger water column stratification. This
simultaneous increase in temperature and nutrient
stress may therefore lead to a much greater decline in
primary productivity than would be predicted by con-
sidering temperature and nutrients separately, or by
different formulations of temperaturenutrient interac-
tions. Recent work has shown that light, a third impor-
tant factor limiting growth in phytoplankton, also
interacts with temperature in complex ways to influ-
ence growth (Edwards et al., 2016). Understanding how
light, nutrients and temperature jointly interact to influ-
ence growth therefore represents an important goal for
the accurate forecasting of primary production and
phytoplankton community dynamics.
Our study highlights how underappreciated interac-
tions between environmental factors can alter growth
and patterns of occurrence in natural systems. Mecha-
nistic models, grounded in physiology, have the poten-
tial to resolve important disagreements about how the
environment influences communities, such as the rela-
tive importance of temperature and nutrients in influ-
encing phytoplankton growth globally (Regaudie-de-
Gioux & Duarte, 2012; Mara~
n
on et al., 2014). These
models can form a vital bridge between theoretical and
empirical efforts to understand how dynamic
environments affect species and provide us with a com-
mon conceptual framework, aiding the integration of
disparate efforts to understand ecological systems.
Acknowledgements
This work was supported by NSF grants DEB-0845932 to EL,
OCE-0928819 and DEB 11-36710 to EL and CAK, NSF PRFB Fel-
lowship 1402074 to CTK, a postdoctoral fellowship from Xunta
de Galicia (Spain) to MAG, and REU grants from the US
National Science Foundation that supported MRG and KA.
Also, we are grateful to C. A. Stock for data from the COBALT
ecosystem model. This is W. K. Kellogg Biological Station con-
tribution number 1977.
Author contribution
MKT and EL conceived the study. MKT, EL and MAG
designed the experiments. MKT, MAG, MRG and KA
performed the experiments. CAK and CTK designed
the model. MKT analysed the experimental data. CTK
generated the MSDM predictions. MKT wrote the
manuscript with substantial input from EL, CAK, MAG
and CTK.
References
Ahlgren G (1978) Growth of Oscillatoria agardhii in chemostat culture. 2. Depen-
dence of growth constants on temperature. In: Symposium: Experimental Use of
Algal Cultures in Limnology, Sandefjord, Norway, October 2628, 1976, pp. 88
102. Schweizerbart Science Publishers, Stuttgart, Germany.
Baker KG, Robinson CM, Radford DT, McInnes AS, Evenhuis C, Doblin MA (2016)
Thermal performance curves of functional traits aid understanding of thermally
induced changes in diatom-mediated biogeochemical fluxes. Frontiers in Marine
Science,3, 44.
Barnett TP, Pierce DW, AchutaRao KM, Gleckler PJ, Santer BD, Gregory JM, Wash-
ington WM (2005) Penetration of human-induced warming into the world’s
oceans. Science,309, 284287.
Behrenfeld MJ, Boss ES, Siegel DA, Shea DM (2005) Carbon-based ocean produc-
tivity and phytoplankton physiology from space. Global Biogeochemical Cycles,
19,114.
Berges JA, Franklin DJ, Harrison PJ (2001) Evolution of an artificial seawater medium:
improvements in enriched seawater, artificial water over the last two decades.
Journal of Phycology,37, 11381145.
Bolker B, R Development Core Team (2012) bbmle: Tools for general maximum likeli-
hood estimation. R package version 1.0.4.
Bopp L, Monfray P, Aumont O et al. (2001) Potential impact of climate change on
marine export production. Global Biogeochemical Cycles,15,8199.
Boyd PW, Rynearson TA, Armstrong EA et al. (2013) Marine phytoplankton tempera-
ture versus growth responses from polar to tropical waters - Outcome of a scien-
tific community-wide study (ed Browman H). PLoS ONE,8, e63091.
Bren A, Hart Y, Dekel E, Koster D, Alon U (2013) The last generation of bacterial
growth in limiting nutrient. BMC Systems Biology,7, 27.
Brett JR (1971) Energetic responses of salmon to temperature. A study of some ther-
mal relations in the physiology and freshwater ecology of Sockeye Salmon Oncor-
hynchus nerka.American Zoologist,11,99113.
Corkrey R, Olley J, Ratkowsky D, McMeekin T, Ross T (2012) Universality of thermo-
dynamic constants governing biological growth rates. PLoS ONE,7, e32003.
DeHayes DH, Ingle MA, Waite CE (1989) Nitrogen fertilization enhances cold toler-
ance of red spruce seedlings. Canadian Journal of Forest Research,19, 10371043.
Dell AI, Pawar S, Savage VM (2011) Systematic variation in the temperature depen-
dence of physiological and ecological traits. PNAS,108, 1059110596.
Deutsch CA, Tewksbury JJ, Huey RB, Sheldon KS, Ghalambor CK, Haak DC, Martin
PR (2008) Impacts of climate warming on terrestrial ectotherms across latitude.
PNAS,105, 66686672.
©2017 John Wiley & Sons Ltd, Global Change Biology,23, 3269–3280
3278 M. K. THOMAS et al.
Downing JA, Watson SB, McCauley E (2001) Predicting Cyanobacteria dominance in
lakes. Canadian Journal of Fisheries and Aquatic Sciences,58, 19051908.
Dunne JP, John JG, Adcroft AJ et al. (2012) GFDL’s ESM2 global coupled climate-car-
bon earth system models. Part I: physical formulation and baseline simulation
characteristics. Journal of Climate,25, 66466665.
Dunne JP, John JG, Shevliakova E et al. (2013) GFDL’s ESM2 global coupled climate-
carbon earth system models. Part II: carbon system formulation and baseline simu-
lation characteristics. Journal of Climate,26, 22472267.
Dutkiewicz S, Scott JR, Follows MJ (2013) Winners and losers: ecological and biogeo-
chemical changes in a warming ocean. Global Biogeochemical Cycles,27, 463477.
Edwards KF, Thomas MK, Klausmeier CA, Litchman E (2016) Phytoplankton growth
and the interaction of light and temperature: a synthesis at the species and com-
munity level. Limnology and Oceanography,61, 12321244.
Elser JJ, Bracken MES, Cleland EE et al. (2007) Global analysis of nitrogen and phos-
phorus limitation of primary producers in freshwater, marine and terrestrial
ecosystems. Ecology Letters,10, 11351142.
Enquist BJ, West GB, Charnov EL, Brown JH (1999) Allometric scaling of production
and life-history variation in vascular plants. Nature,401, 907912.
Eppley RW (1972) Temperature and phytoplankton growth in the sea. Fishery Bulletin,
70, 10631085.
Eppley RW, Rogers JN, McCarthy JJ (1969) Half-saturation constants for uptake of
nitrate and ammonium by marine phytoplankton. Limnology and Oceanography,14,
912920.
Falkowski PG, Barber RT, Smetacek V (1998) Biogeochemical controls and feedbacks
on ocean primary production. Science,281, 200206.
Follows MJ, Dutkiewicz S, Grant S, Chisholm SW (2007) Emergent biogeography of
microbial communities in a model ocean. Science,315, 18431846.
Geider RJ, MacIntyre HL, Kana TM (1997) Dynamic model of phytoplankton growth
and acclimation: responses of the balanced growth rate and the chlorophyll a : car-
bon ratio to light, nutrient-limitation and temperature. Marine Ecology Progress Ser-
ies,148, 187200.
Geider RJ, MacIntyre HL, Kana TM (1998) A dynamic regulatory model of phyto-
planktonic acclimation to light, nutrients, and temperature. Limnology and Oceanog-
raphy,43, 679694.
Gerard VA (1997) The role of nitrogen nutrition in high-temperature tolerance of the
kelp Laminaria saccarina (Chromophyta). Journal of Phycology,33, 800810.
Gillooly JF, Brown JH, West GB, Savage VM, Charnov EL (2001) Effects of size and
temperature on metabolic rate. Science,293, 22482251.
Gillooly JF, Charnov EL, West GB, Savage VM, Brown JH (2002) Effects of size and
temperature on developmental time. Nature,417,7073.
Guillard RRL, Hargraves PE (1993) Stichochrysis immobilis is a diatom, not a chryso-
phyte. Phycologia,32, 234236.
Holling CS (1959) The components of predation as revealed by a study of small-mam-
mal predation of the European Pine Sawfly. The Canadian Entomologist,91, 293320.
Huber V, Adrian R, Gerten D (2008) Phytoplankton response to climate warming
modified by trophic state. Limnology and Oceanography,53,113.
Huey RB, Bennett AF (1990) Physiological adjustments to fluctuating thermal envi-
ronments: an ecological and evolutionary perspective. In: Stress Proteins in Biology
and Medicine (eds Morimoto RI, Tissi
eres A, Georgopoulos C), pp. 3759. Labora-
tory Press. Cold Spring Harbor, New York, USA.
Huey RB, Slatkin M (1976) Costs and benefits of lizard thermoregulation. The Quar-
terly Review of Biology,51, 363384.
Huey RB, Deutsch CA, Tewksbury JJ, Vitt LJ, Hertz PE,
Alvarez P
erez HJ, Garland T
(2009) Why tropical forest lizards are vulnerable to climate warming. Proceedings of
the Royal Society B: Biological Sciences,276, 19391948.
IPCC (2013) Climate Change 2013: The Physical Science Basis. Contribution of Working
Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change
(eds Stocker TF, Qin D, Plattner G-K, Tignor M, Allen SK, Boschung J, Nauels A,
Xia Y, Bex V, Midgley PM). Cambridge University Press, Cambridge, UK and
New York, NY, USA.
Kingsolver JG (2009) The well-temperatured biologist. The American Naturalist,174,
755768.
Lutz MJ, Caldeira K, Dunbar RB, Behrenfeld MJ (2007) Seasonal rhythms of net pri-
mary production and particulate organic carbon flux to depth describe the effi-
ciency of biological pump in the global ocean. Journal of Geophysical Research,112,
C10011.
Lyman JM, Good SA, Gouretski VV et al. (2010) Robust warming of the global upper
ocean. Nature,465, 334337.
Mara~
n
on E, Cerme~
no P, Huete-Ortega M, L
opez-Sandoval DC, Mouri~
no-Carballido
B, Rodr
ıguez-Ramos T (2014) Resource supply overrides temperature as a control-
ling factor of marine phytoplankton growth. PLoS ONE,9, e99312.
Martin TL, Huey RB (2008) Why “suboptimal” is optimal: Jensen’s inequality and
ectotherm thermal preferences. The American Naturalist,171, E102E118.
McCoy MW, Gillooly JF (2008) Predicting natural mortality rates of plants and ani-
mals. Ecology Letters,11, 710716.
Mechling JA, Kilham SS (1982) Temperature effects on silicon limited growth of the
Lake Michigan diatom Stephanodiscus minutus (Bacillariophyceae). Journal of Phy-
cology,18, 199205.
Moisan JR, Moisan TA, Abbott MR (2002) Modelling the effect of temperature on the
maximum growth rates of phytoplankton populations. Ecological Modelling,153,
197215.
Monod J (1949) The growth of bacterial cultures. Annual Review of Microbiology,3,
371394.
Norberg J (2004) Biodiversity and ecosystem functioning: a complex adaptive systems
approach. Limnology and Oceanography,49, 12691277.
R Core Team (2015) R: A language and environment for statistical computing. R
Foundation for Statistical Computing, Vienna, Austria.
Raven JA, Geider RJ (1988) Temperature and algal growth. New Phytologist,110, 441
461.
Reay DS, Nedwell DB, Priddle J, Ellis-Evans JC (1999) Temperature dependence of
inorganic nitrogen uptake: reduced affinity for nitrate at suboptimal tempera-
tures in both algae and bacteria. Applied and Environmental Microbiology,65,
25772584.
Regaudie-de-Gioux A, Duarte CM (2012) Temperature dependence of planktonic
metabolism in the ocean. Global Biogeochemical Cycles,26,110.
Rhee G-Y, Gotham IJ (1981) The effect of environmental factors on phytoplankton
growth: temperature and the interactions of temperature with nutrient limitation.
Limnology and Oceanography,26, 635648.
Savage VM, Gilloly JF, Brown JH, Charnov EL (2004) Effects of body size and temper-
ature on population growth. The American Naturalist,163, 429441.
Schoolfield RM, Sharpe PJH, Magnuson CE (1981) Non-linear regression of biological
temperature-dependent rate models based on absolute reaction-rate theory. Journal
of Theoretical Biology,88, 719731.
Sterner RW, Elser JJ (2002) Ecological Stoichiometry: The Biology of Elements from Mole-
cules to the Biosphere, vol. 38. Princeton University Press, Princeton, NJ.
Sterner RW, Grover JP (1998) Algal growth in warm temperate reservoirs: kinetic
examination of nitrogen, temperature, light, and other nutrients. Water Research,
32, 35393548.
Stock CA, Dunne JP, John JG (2014a) Global-scale carbon and energy flows through
the marine planktonic food web: an analysis with a coupled physical-biological
model. Progress in Oceanography,120,128.
Stock CA, Dunne JP, John JG (2014b) Drivers of trophic amplification of ocean pro-
ductivity trends in a changing climate. Biogeosciences,11, 71257135.
Sunday JM, Bates AE, Dulvy NK (2012) Thermal tolerance and the global redistribu-
tion of animals. Nature Climate Change,2, 686690.
Thomas MK, Litchman E (2016) Effects of temperature and nitrogen availability
on the growth of invasive and native cyanobacteria. Hydrobiologia,763,
357369.
Thomas MK, Kremer CT, Klausmeier CA, Litchman E (2012) A global pattern of ther-
mal adaptation in marine phytoplankton. Science,338, 10851088.
Thomas MK, Kremer CT, Litchman E (2016) Environment and evolutionary history
determine the global biogeography of phytoplankton temperature traits. Global
Ecology and Biogeography,25,7586.
Tilman D (1982) Resource Competition and Community Structure, vol. 17. Princeton
University Press, Princeton, NJ.
Tilman D, Cowan ML (1989) Growth of old field herbs on a nitrogen gradient. Func-
tional Ecology,3, 425438.
Tilman D, Mattson M, Langer S (1981) Competition and nutrient kinetics along a tem-
perature gradient: an experimental test of a mechanistic approach to niche theory.
Limnology and Oceanography,26, 10201033.
Toseland A, Daines SJ, Clark JR et al. (2013) The impact of temperature on marine
phytoplankton resource allocation and metabolism. Nature Climate Change,3,16.
Tyrrell T (1999) The relative influences of nitrogen and phosphorus on oceanic pri-
mary production. Nature,400, 525531.
Vasseur DA, DeLong JP, Gilbert B et al. (2014) Increased temperature variation poses
a greater risk to species than climate warming. Proceedings of the Royal Society B:
Biological Sciences,281, 20132612.
Vitousek PM, Aber JD, Howarth RW et al. (1997) Human alteration of the
global Nitrogen cycle: sources and consequences. Ecological Applications,7,
737750.
West GB, Brown JH, Enquist BJ (1997) A general model for the origin of allometric
scaling laws in biology. Science,276, 122126.
©2017 John Wiley & Sons Ltd, Global Change Biology,23, 3269–3280
HEAT +STARVATION KILLS FASTER THAN EITHER 3279
Wiedenmann J, D’Angelo C, Smith EG, Hunt AN, Legiret F-E, Postle AD, Achterberg
EP (2013) Nutrient enrichment can increase the susceptibility of reef corals to
bleaching. Nature Climate Change,3, 160164.
Wood SN (2011) Fast stable restricted maximum likelihood and marginal likelihood
estimation of semiparametric generalized linear models. Journal of the Royal Statis-
tical Society,73,336.
Yvon-Durocher G, Dossena M, Trimmer M, Woodward G, Allen AP (2015) Tempera-
ture and the biogeography of algal stoichiometry. Global Ecology and Biogeography,
24, 562570.
Supporting Information
Additional Supporting Information may be found in the online version of this article:
Table S1. Parameter values used in Fig. 6 model results.
Table S2. Parameters describing Monod model fits to the growth rates across a range of phosphorus concentrations, at each of the
five temperatures measured.
Figure S1. The predicted effect of temperature and nutrient interactions on growth rate, based on Eqn (3).
Figure S2. Growth rates as a function of temperature at different phosphate concentrations, with GAM fits using temperature as a
smoother.
Figure S3. Growth rates as a function of temperature at different nitrate concentrations, with GAM fits using temperature as a
smoother.
Figure S4. Results of model fits to T. pseudonana growth rates in temperature x phosphate and temperature x nitrate experiments,
untruncated at high nutrient concentrations to show the entire range of the data.
Figure S5. GAM fits to growth rate data, with both temperature and nutrient concentration as smoother terms.
Figure S6. The effect of assumed mortality rate (in the Darwin model) on the zero net growth isocline (R*curve).
Figure S7. The effect of assumed mortality rate (in the Darwin model) on the estimated range size.
Figure S8 Growth rates as a function of phosphate at different temperatures, with Monod fits to the data (parameters values for the
fits may be found in Table S2).
Figure S9 Phosphate half-saturation constants for growth (K) from Monod fits to the growth curves shown in Fig. S8 (precise values
may be found in Table S2).
Appendix S1. Growth rate measurements from our experiments.
©2017 John Wiley & Sons Ltd, Global Change Biology,23, 3269–3280
3280 M. K. THOMAS et al.
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