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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
W. K. Kellogg Biological Station, Michigan State University, Hickory Corners, MI 49060, USA,
Department of Integrative
Biology, Michigan State University, East Lansing, MI 48824, USA,
Program in Ecology, Evolutionary Biology & Behavior,
Michigan State University, East Lansing, MI 48824, USA,
Department of Animal Ecology and Biology, University of Vigo, Vigo
36310, Spain,
Department of Ecology and Evolutionary Biology, Yale University, PO Box 208106, New Haven, CT 06520, USA,
Atmospheric and Oceanic Sciences Program, Princeton University, Princeton, NJ, USA,
Department of Ecology and
Evolutionary Biology, University of Connecticut, Storrs, CT 06269, USA,
Department of Biological Sciences, University of
Illinois at Chicago, 845 West Taylor Street (MC 066), Chicago, IL 60607, USA,
Department of Plant Biology, Michigan State
University, East Lansing, MI 48824, USA
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
, is a saturating function of nutrient concentration. We find strong support for this prediction in exper-
iments with a marine diatom, Thalassiosira pseudonana:T
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
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
Switzerland, tel. +41 587655534, fax +41 587655802,
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.,
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
, 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
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~
on et al., 2014), they have
largely focussed on temperatures below T
. 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
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
Most ectotherms experience temperatures exceeding
at least occasionally (Huey & Bennett, 1990; Huey
et al., 2009; Thomas et al., 2012), and in the tropics, T
is exceeded as well; heat avoidance is a major driver of
Temperature (°C)
0 5 10 15 20 25 30
0.0 0.4 0.8 1.2
0.0 0.4 0.8 1.2
Nutrient concentration (µM)
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
. 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
We have developed and empirically tested such a
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:
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
is the birth rate at a tem-
perature of 0°C, and b
is the exponential change in
birth rate with increasing temperature. The second half
of (1) captures mortality rates, where d
is a tempera-
ture-independent mortality term, while d
and d
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
where specific growth rate ldepends on nutrient con-
centration, R, as well as the maximum growth rate,
, 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
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
lT;RðÞ¼b1expðb2TÞ R
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
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
Model predictions. Our IDE model makes an important,
novel prediction: that T
is a saturating function of
nutrient concentration (Fig. 2a). This is also true of T
(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
(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
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
and T
(Fig. 2a).
Model comparison and evaluation. We tested the first pre-
diction of the IDE model (nutrient dependence of T
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
exp BTTopt
Here, sand Adetermine the height and shape of (4),
while Bdetermines the range of temperatures over
Temperature (°C)
Nutrient concentration (µM)
Tmin, R* Tmax, R*
growth rate
(per day) Nutrient concentration (µM)
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
Specific growth rate (per day)
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
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
and T
. 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
is invariant
across nutrient levels in this and other such models
(Sterner & Grover, 1998; Moisan et al., 2002; Huber
et al., 2008). T
and T
are also higher in the MI
model than in the IDE model (Fig. 3).
Materials and methods
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
and T
(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
. 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
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
and T
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
changes with nutrient concentration
in the two model fits. T
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
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
) 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
Describing variation in population growth rate as a function
of temperature, and estimating T
.To demonstrate that
patterns in growth and T
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
by numerical maximization and simulated
from the posterior distribution of the fitted parameters to
quantify uncertainty in T
. Results were similar if we esti-
mated T
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
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
parameter in Eqn
(2)). To explore how the choice of minfluences predicted range
size we estimated range limits using different values of m.
Growth rate was strongly influenced by both nutrient
concentration and temperature, ranging from 0.78 to
1.55 day
in the temperaturephosphate experiments,
and 0.01 to 1.34 day
in the temperaturenitrate exper-
iments (Fig. 4). Our primary prediction was strongly
supported: T
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
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
Temperature (°C)
Phosphate concentration (µM)
Specific growth rate (per day)
Temperature (°C)
Nitrate concentration (µM)
Specific growth rate (per day)
0.8 1.0 1.2 1.4
Predicted growth rate (per day)
Observed growth rate (per day)
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)
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
= 0.84) to growth rates at 5 phosphate concentrations and 5 temperatures. (b) Pre-
dicted growth rates from IDE model fitted (R
= 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
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
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
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
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
and pollutant
concentrations. In the case of nutrient limitation, the 3
6°C decrease in T
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
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
and T
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
increase and T
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
Phosphate concentration (µM)
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)
Fig. 5 T
is a saturating function of nutrient concentration, as predicted by the IDE model. We estimated T
at each nutrient concen-
tration using GAMs with temperature as a smoother term (Fig. S3, S4). (a) T
varies by 3.5°C across the phosphate gradient (b) T
varies by 6°C across the nitrate gradient. Curves show a saturating function fit to the T
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
). A similar pattern of increasing R*
with decreasing temperature below T
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
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
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
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
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
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~
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.
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.
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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
Figure S3. Growth rates as a function of temperature at different nitrate concentrations, with GAM fits using temperature as a
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.
... We focus on experiments investigating the joint effects of changing CO 2 and temperature levels on marine diatoms and coccolithophores as a case study, though our argument applies to all multiple driver studies where laboratory culturing is easy enough to allow ~25 simultaneous populations to be grown under different combinations of driver levels (25 populations corresponds to a 5 × 5 factorial experimental design with two drivers, and five points is the minimum number needed to fit most nonlinear response curves of known shape, such as temperature and nutrient response curves). We stress that such experiments are doable; temperature × nutrient response surfaces have been generated for the diatom Thalassiosira pseudonana [2] and a handful of freshwater phytoplankton [3]. We look at how their design helps us make progress towards projecting how they jointly affect phytoplankton traits underlying ecological or biogeochemical function in aquatic systems. ...
... These purely multiplicative interactions may be appropriate for community/ecosystem responses, but the scant empirical evidence on population-level interaction surfaces indicates that this strong assumption warrants some scrutiny. For example, Thomas et al. [2] measured a population-level interaction surface, and found that the optimum growth temperature (Topt) and maximum growth temperature (Tmax) decreased at low nutrient concentrations for the model diatom Thalassiosira pseudonana. Implementing this interaction into a mechanistic species distribution model predicted shifts in growth rates and ranges relative to the same model that used a multiplicative interaction. ...
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Climate change is an existential threat, and our ability to conduct experiments on how organisms will respond to it is limited by logistics and resources, making it vital that experiments be maximally useful. The majority of experiments on phytoplankton responses to warming and CO2 use only two levels of each driver. However, to project the characters of future populations, we need a mechanistic and generalisable explanation for how phytoplankton respond to concurrent changes in temperature and CO2. This requires experiments with more driver levels, to produce response surfaces that can aid in the development of predictive models. We recommend prioritising experiments or programmes that produce such response surfaces on multiple scales for phytoplankton.
... Thermal performance curves were fitted to the model by Thomas et al. (2017) using the R package rTPC (Padfield et al., 2021). This is a double-exponential model, which combines exponential increase and decrease functions. ...
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We studied the phenotypic response to temperature of the marine copepod Paracartia grani at the organismal and cellular levels. First, the acute (2 days) survival, feeding and reproductive performances at 6-35 • C were determined. Survival was very high up to ca. 30 • C and then dropped, whereas feeding and fecundity peaked at 23-27 • C. An acclimation response developed after longer exposures (7 days), resulting in a decline of the biological rate processes. As a consequence, Q 10 coefficients dropped from 2.6 to 1.6, and from 2.7 to 1.7 for ingestion and egg production, respectively. Due to the similarity in feeding and egg production thermal responses, gross-growth efficiencies did not vary with temperature. Respiration rates were less sensitive (lower Q 10) and showed an opposite pattern, probably influenced by starvation during the incubations. The acclimation response observed in the organismal rate processes was accompanied by changes in body stoichiometry and in the antioxidant defense and cell-repair mechanisms. Predictions of direct effects of temperature on copepod performance should consider the reduction of Q 10 coefficients due to the acclimation response. Copepod population dynamic models often use high Q 10 values and may overestimate thermal effects.
... a) T opt vs. phosphate concentration in the medium, b) T opt vs. nitrate concentration in the medium. FromThomas et al. (2017) ...
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... Indeed, from our conclusive research, WT is a key driver of phytoplankton primary production and succession seasonally (Bouraï et al., 2020). Our study outcome is comparable to past researches focusing on lake surface temperature impacts on phytoplankton in world largest lakes studied by Kraemer et al. (2017), Thomas et al. (2017), Thrane et al. (2017) and Verbeek et al. (2018). In spring, Tang-Pu Reservoir experienced a lot of rainfall runoff hence increasing nutrient load into the reservoir. ...
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Seasonal variation in phytoplankton community structure within Tang-Pu Reservoir (Shaoxing city, Zhejiang province, China) was investigated in relation to variation in physicochemical and hydrological characteristics. Over the three-study seasons (autumn, winter, and spring), phytoplankton abundance and biomass showed a gradual increase with the peak in spring season. During this study period, phytoplankton community comprised of 7 phyla, 80 genera, and 210 species. The dominating phyla were Chlorophyta 80 species, Bacillariophyta 46, and Cyanophyta 44 as well as other phyla of freshwater ecosystems except Xanthophyta. The phytoplankton density and biomass varied in the six sampling sites between a minimum of 257.42 × 10⁴ cells/L to 1054.15 × 10⁴ cells/L and 1.60 mg/L to 4.56 mg/L respectively. Spring season had higher biomass and density values than autumn and winter. Furthermore, the results indicated that the Shannon–Wiener (H′) and Pielou evenness (J′) indices of phytoplankton community were stable although with slightly higher values in spring. Based on the calculated indices, Tang-Pu reservoir could be considered mesosaprobic in all the three seasons. Redundancy analysis (RDA) revealed that pH, total nitrogen (TN), total phosphorus (TP), transparency, chlorophyll a (Chl a), dissolve oxygen (DO), and water temperature (WT) were responsible for most phytoplankton community shift from Bacillariophyta and Cryptophyta to Cyanophyta and Chlorophyta in spring. These environmental parameters play an essential role in the community structure variation of phytoplankton in the downstream and upstream of Tang-Pu Reservoir. A decreasing phytoplankton abundance trend from the river area (inlet) to the lake (outlet) was also observed.
... Our results have implications for phytoplankton dynamics in nature. First, efforts to use physiological data derived from laboratory studies to predict real-world responses of algae to climate warming (Thomas et al. 2017) should be done with caution if the experimental conditions do not match the natural environment. Given that the greatest difference between predicted and observed growth rates occurred in short photoperiod regimes, researchers should be particularly cautious when making predictions for high latitude environments and/or winter months when daily irradiance is low. ...
Light fluctuations are ubiquitous, exist across multiple spatial and temporal scales, and directly affect the physiology and ecology of photoautotrophs. However, the indirect effects of light fluctuations on the sensitivity of organisms to other key environmental factors are unclear. Here, we evaluate how photoperiod regime (period of time each day where organisms receive light), a dynamic element of aquatic ecosystems, can influence the interactive effects of temperature and irradiance (intensity of light) on the growth rate of phytoplankton populations. We first completed a literature review and meta‐analysis that suggests photoperiod alters the individual effects of temperature – but not irradiance – on algal growth rates and that highlights how few studies experimentally manipulate photoperiod, temperature and irradiance. To address this empirical gap, we conducted a set of laboratory experiments on three freshwater phytoplankton species (Chlamydomonas reinhardtii, Chlorella vulgaris and Cryptomonas ovata). We measured performance surfaces relating growth rate to irradiance and temperature gradients for each species in constant (24:0 h of light:dark) environments. We then evaluated whether analogous surfaces measured under different photoperiods (6:18, 12:12 and 16:8 h of light:dark) and scaled by the duration of light availability could be inferred from results under constant light. For a majority of the combinations of species and photoperiods examined, photoperiod meaningfully altered the intercept and shape of performance surfaces. These differences were most pronounced under the shortest photoperiod (6:18 h light:dark), where populations underperformed expectations. Alterations to performance surfaces were non‐linear and mostly structured by temperature with higher temperatures yielding higher than anticipated growth rates. Collectively, these experiments and synthesis reveal the potential for photoperiod regime to influence the effects of temperature, irradiance and their interaction on phytoplankton growth. Beyond the environmental variables and organisms presently considered, this research highlights the capacity for dynamic, abiotic variables to exert direct effects while also influencing relationships among other environmental factors.
... However, the increasing intensity, frequency, and duration of heatwaves occurring as a result of global warming have been negatively affecting the biomass and productivity of ecosystem primary producers, including terrestrial plants and marine macroalgae [4][5][6][7]. At the same time, increasing evidence suggested that the effect of this global stressor on primary producers can be synergized or antagonized by local nutrient environments [8][9][10]. Moreover, physiological studies have shown that heat stress combined with excess light energy causes photoinhibition (i.e., decline of photosystems II efficiency) through an increase in reactive oxygen species production in chloroplast [11,12]. ...
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Heatwaves under global warming have negative impacts on ecosystem primary producers. This warming effect may be synergized or antagonized by local environments such as light and nutrient availability. However, little is known about the interactive effects of warming, irradiance, and nutrients on physiology of marine macroalgae, which are dominant in coastal ecosystems. The present study examined the combined effects of warming (23 and 26 °C), irradiance (30 and 150 µmol photon m−2 s−1), and nutrients (enriched and non-enriched) on specific growth rate (SGR) and biochemical compositions of the canopy-forming marine macroalga Sargassum fusiforme. The negative effect of warming on SGR and ratio of chlorophyll (Chl) c to Chl a was antagonized by decreased irradiance. Moreover, the negative effect of temperature elevation on carbon content was antagonized by nutrient enrichment. These results suggest that the effect of warming on the growth and carbon accumulation of this species can be mitigated by decreased irradiance and nutrient enrichment.
... Empirical studies have demonstrated that warming alters trophic interaction strengths by enhancing top-down, consumer-driven control, causing increased grazing and thus reduced primary producer biomass O'Connor et al., 2009;Shurin et al., 2012). Moreover, warming may increase nutrient use efficiencies and requirements of some species (Baker et al., 2016;De Senerpont Domis et al., 2014;Thomas et al., 2017), while it may lower trophic transfer efficiencies (Barneche et al., 2021). F I G U R E 1 Hypothesized competition-defense trade-off. ...
Functional trade‐offs among ecologically important traits govern the diversity of communities and changes in species composition along environmental gradients. A trade‐off between predator defense and resource competitive ability has been invoked as a mechanism that may maintain diversity in lake phytoplankton. Trade‐offs may promote diversity in communities where grazing‐ and resource‐limited taxa coexist, which determines the extent to which communities are resource‐ or consumer‐controlled. In addition, changes in temperature may alter nutrient demands and grazing pressure, changing the balance between the two regulating factors. Our study aims to understand whether a trade‐off between grazer vulnerability and nutrient limitation promotes coexistence of phytoplankton functional groups in communities that differ in trophic status, and how this trade‐off may shift with warming. We conducted multifactorial experiments manipulating grazing, nutrients, and temperature in phytoplankton communities from three Dutch lakes varying in trophic status, and used a trait‐based approach to classify functional groups based on grazing susceptibility. We found no associations between susceptibility to grazing and response to nutrient additions in any of the communities or temperature regimes, indicating that a competition–defense trade‐off is unlikely to explain diversity within the tested communities. Instead, we observed a tendency toward both a higher grazing resistance and weaker nutrient limitation along with a shift in the functional composition of phytoplankton in communities across a gradient from low to high productivity.
Our scientific understanding of climate change makes clear the necessity for both emission reduction and carbon dioxide removal (CDR). The ocean with its large surface area, great depths and long coastlines is central to developing CDR approaches commensurate with the scale needed to limit warming to below 2 °C. Many proposed marine CDR approaches rely on spatial upscaling along with enhancement and/or acceleration of the rates of naturally occurring processes. One such approach is ‘ocean afforestation’, which involves offshore transport and concurrent growth of nearshore macroalgae (seaweed), followed by their export into the deep ocean. The purposeful occupation for months of open ocean waters by macroalgae, which do not naturally occur there, will probably affect offshore ecosystems through a range of biological threats, including altered ocean chemistry and changed microbial physiology and ecology. Here, we present model simulations of ocean afforestation and link these to lessons from other examples of offshore dispersal, including rafting plastic debris, and discuss the ramifications for offshore ecosystems. We explore what additional metrics are required to assess the ecological implications of this proposed CDR. In our opinion, these ecological metrics must have equal weight to CDR capacity in the development of initial trials, pilot studies and potential licensing. Ocean afforestation is a proposed method for large-scale carbon dioxide removal, involving exporting rafts of nearshore macroalgae to the open ocean for long-term occupation and then sinking. In this Perspective, the authors caution that this approach has multiple potential ramifications for ocean chemistry and ecology.
Phytoplankton blooms in natural waters are critical for managing drinking water quality. Thus, estimating and understanding algal systems is important to supply safe drinking water and protect public health. The objectives of this study were to evaluate a modified algal module and calibrate algae-associated parameters annually (i.e., dynamic calibration) with identification of the relationship between parameters and environmental variables. The modified algal module in the Soil and Water Assessment Tool (SWAT) model incorporates temperature rate multipliers to correct the temperature effect on phytoplankton. Three different modules (i.e., original module, modified module, and dynamic calibration) were calibrated using 15-year observations in a watershed that provides drinking water resources. The original module resulted in a Nash-Sutcliffe model efficiency (NSE) of 0.334 and a root mean squared error (RMSE) of 0.578, but the modified module increased up to 0.374 and decreased to 0.561. In addition, the dynamic calibration of the modified module further improved the model performance with an NSE of 0.486 and RMSE of 0.508. The random forest method was used to investigate the relative importance of environmental variables to dynamic parameters. The maximum temperature was a relatively important variable for maximum algal growth, and the nutrient concentration was important for temperature multiplier factors. Dynamic calibration not only improved the simulation accuracy but also provided the relationship between environmental variables and algal parameters. This calibration method will be useful for simulating chlorophyll-a (Chl-a) dynamics and preparing watershed management policies for algal blooms.
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Pronounced projected 21st century trends in regional oceanic net primary production (NPP) raise the prospect of significant redistributions of marine resources. Recent results further suggest that NPP changes may be amplified at higher trophic levels. Here, we elucidate the role of planktonic food web dynamics in driving projected changes in mesozooplankton production (MESOZP) found to be, on average, twice as large as projected changes in NPP by the latter half of the 21st century under a high emissions scenario in the Geophysical Fluid Dynamics Laboratory's ESM2M–COBALT (Carbon, Ocean Biogeochemistry and Lower Trophics) earth system model. Globally, MESOZP was projected to decline by 7.9% but regional MESOZP changes sometimes exceeded 50%. Changes in three planktonic food web properties – zooplankton growth efficiency (ZGE), the trophic level of mesozooplankton (MESOTL), and the fraction of NPP consumed by zooplankton (zooplankton–phytoplankton coupling, ZPC), explain the projected amplification. Zooplankton growth efficiencies (ZGE) changed with NPP, amplifying both NPP increases and decreases. Negative amplification (i.e., exacerbation) of projected subtropical NPP declines via this mechanism was particularly strong since consumers in the subtropics have limited surplus energy above basal metabolic costs. Increased mesozooplankton trophic level (MESOTL) resulted from projected declines in large phytoplankton production. This further amplified negative subtropical NPP declines but was secondary to ZGE and, at higher latitudes, was often offset by increased ZPC. Marked ZPC increases were projected for high-latitude regions experiencing shoaling of deep winter mixing or decreased winter sea ice – both tending to increase winter zooplankton biomass and enhance grazer control of spring blooms. Increased ZPC amplified projected NPP increases in the Arctic and damped projected NPP declines in the northwestern Atlantic and Southern Ocean. Improved understanding of the physical and biological interactions governing ZGE, MESOTL and ZPC is needed to further refine estimates of climate-driven productivity changes across trophic levels.
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How the functional traits (FTs) of phytoplankton change with temperature is important for understanding the impacts of ocean warming on phytoplankton mediated biogeochemical fluxes. This study quantifies the thermal performance curves (TPCs) of FTs in the cosmopolitan model diatom, Thalassiosira pseudonana, to advance understanding of trade-offs between physiological (photoacclimation, carbon fixation, nitrate, phosphate and silicate uptake) and morphological traits (cell volume and frustule silicification). We show that each FT has substantial phenotypic plasticity and exhibits a unique TPC, varying in both shape and thermal optimum, and diverging from the growth response. The TPC for growth was symmetric with a thermal optimum (Topt) of 18 °C. In comparison, the TPC for primary productivity was warm-skewed with a Topt around 21 °C, whereas frustule silicification decreased linearly with increasing temperature. Together, this suggests that the optimal temperature for overall fitness is a balance of trade-offs in the underlying functional traits. Moreover, these results demonstrate that growth is not necessarily an accurate estimate of overall biogeochemical performance and that temperature change will likely influence elemental fluxes such as carbon and silicon. Finally, we show that temperature-driven changes in individual traits e.g. photoacclimation, can mimic responses experienced under other environmental stressors (high light) and so a multi-trait assessment is essential for accurate interpretation of the cellular impact of warming. This study also reveals that multi-trait analysis, in the context of TPCs, provides insight into the cellular physiology regulating the whole cell response and has the potential to provide better estimates of how diatom-mediated biogeochemical fluxes are likely to be impacted in the context of ocean warming. Analyzing the response of multiple traits more comprehensively over other environmental gradients may therefore provide a useful framework to advance understanding of how taxon-specific functional traits will respond to multifaceted ocean change.
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Temperature strongly affects phytoplankton growth rates, but its effect on communities and ecosystem processes is debated. Because phytoplankton are often limited by light, temperature should change community structure if it affects the traits that determine competition for light. Furthermore, the aggregate response of phytoplankton communities to temperature will depend on how changes in community structure scale up to bulk rates. Here, we synthesize experiments on 57 phytoplankton species to analyze how the growth-irradiance relationship changes with temperature. We find that light-limited growth, light-saturated growth, and the optimal irradiance for growth are all highly sensitive to temperature. Within a species, these traits are co-adapted to similar temperature optima, but light-limitation reduces a species' temperature optimum by ∼5°C, which may be an adaptation to how light and temperature covary with depth or reflect underlying physiological correlations. Importantly, the maximum achievable growth rate increases with temperature under light saturation, but not under strong light limitation. This implies that light limitation diminishes the temperature sensitivity of bulk phytoplankton growth, even though community structure will be temperature-sensitive. Using a database of primary production incubations, we show that this prediction is consistent with estimates of bulk phytoplankton growth across gradients of temperature and irradiance in the ocean. These results indicate that interactions between temperature and resource limitation will be fundamental for explaining how phytoplankton communities and biogeochemical processes vary across temperature gradients and respond to global change.
Temperature provides a powerful theme for exploring environmental adaptation at all levels of biological organization, from molecular kinetics to organismal fitness to global biogeography. First, the thermodynamic properties that underlie biochemical kinetics and protein stability determine the overall thermal sensitivity of rate processes. Consequently, a single quantitative framework can assess variation in thermal sensitivity of ectotherms in terms of single amino acid substitutions, quantitative genetics, and interspecific differences. Thermodynamic considerations predict that higher optimal temperatures will result in greater maximal fitness at the optimum, a pattern seen both in interspecific comparisons and in within‐population genotypic variation. Second, the temperature‐size rule (increased developmental temperature causes decreased adult body size) is a common pattern of phenotypic plasticity in ectotherms. Mechanistic models can correctly predict the rule in some taxa, but lab and field studies show that rapid evolution can weaken or even break the rule. Third, phenotypic and evolutionary models for thermal sensitivity can be combined to explore potential fitness consequences of climate warming for terrestrial ectotherms. Recent analyses suggest that climate change will have greater negative fitness consequences for tropical than for temperate ectotherms, because many tropical species have relatively narrow thermal breadths and smaller thermal safety margins.
Summary. Recent work by Reiss and Ogden provides a theoretical basis for sometimes preferring restricted maximum likelihood (REML) to generalized cross-validation (GCV) for smoothing parameter selection in semiparametric regression. However, existing REML or marginal likelihood (ML) based methods for semiparametric generalized linear models (GLMs) use iterative REML or ML estimation of the smoothing parameters of working linear approximations to the GLM. Such indirect schemes need not converge and fail to do so in a non-negligible proportion of practical analyses. By contrast, very reliable prediction error criteria smoothing parameter selection methods are available, based on direct optimization of GCV, or related criteria, for the GLM itself. Since such methods directly optimize properly defined functions of the smoothing parameters, they have much more reliable convergence properties. The paper develops the first such method for REML or ML estimation of smoothing parameters. A Laplace approximation is used to obtain an approximate REML or ML for any GLM, which is suitable for efficient direct optimization. This REML or ML criterion requires that Newton–Raphson iteration, rather than Fisher scoring, be used for GLM fitting, and a computationally stable approach to this is proposed. The REML or ML criterion itself is optimized by a Newton method, with the derivatives required obtained by a mixture of implicit differentiation and direct methods. The method will cope with numerical rank deficiency in the fitted model and in fact provides a slight improvement in numerical robustness on the earlier method of Wood for prediction error criteria based smoothness selection. Simulation results suggest that the new REML and ML methods offer some improvement in mean-square error performance relative to GCV or Akaike's information criterion in most cases, without the small number of severe undersmoothing failures to which Akaike's information criterion and GCV are prone. This is achieved at the same computational cost as GCV or Akaike's information criterion. The new approach also eliminates the convergence failures of previous REML- or ML-based approaches for penalized GLMs and usually has lower computational cost than these alternatives. Example applications are presented in adaptive smoothing, scalar on function regression and generalized additive model selection.