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Emiliania huxleyi population growth rate response to light and temperature: A synthesis


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The relationship between the maximum specific growth rate (μ, d-1) of the coccolithophore Emiliania huxleyi and photon flux density (PFD, μmol photons m-2s-1) was quantified using a combination of quantile regression and culture experiment data from the literature (n = 1387). This relationship, used in ecosystem models incorporating E. huxleyi or coccolithophores as a functional group, is often assumed to follow a Monod function although values for the model parameters vary greatly. In this analysis, a Monod function was compared with other models to determine the model which best fit E. huxleyi growth rate data. Analysis showed that a Monod model of μ = 1.858 [PFD/(23.91 + PFD)] best described E. huxleyi maximum growth rate as a function of PFD. In addition, an expression combining the Monod function (this study) and the power function relating growth rate to temperature (Fielding 2013; Limnol Oceanogr 58:663-666) was calculated: when both temperature (T, °C) and PFD are known, the resulting expression μ = (0.199 × T0.716) × [PFD/(14.2 + PFD)] predicts maximum E. huxleyi specific growth rate. Current literature models either overestimate or underestimate maximum growth rate by up to 3-fold over a wide range of PFDs. The use of the Monod function and the combined expression presented here is therefore recommended for future models incorporating the growth rate of E. huxleyi when either light or both temperature and light are known.
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Aquat Microb Ecol
Vol. 73: 163–170, 2014
doi: 10.3354/ame01707 Published online October 2
Coccolithophore algae are the major calcium car-
bonate producers in the ocean and are therefore fun-
damental for driving the inorganic carbon pump from
the ocean’s surface waters to the deep sea (Rost &
Riebesell 2004). Coccolithophore calcium carbonate
production also influences alkalinity and dissolved
inorganic carbon concentration in the upper ocean
(Zeebe & Wolf-Gladrow 2001). Additionally, cocco-
lithophores, as members of the haptophyte algae,
produce higher levels of intracellular dimethylsulfo-
niopropionate than most other algal groups (Keller
1988). Therefore, modelling and predicting the growth
of marine coccolithophore algae is key to understand-
ing them as a component of biogeochemical cycles
(e.g. organic carbon, calcium carbonate, di methyl -
sulfide) and aquatic food webs.
In the present-day ocean, Emiliania huxleyi is
the most numerically important species of cocco-
lithophore (Paasche 2001). E. huxleyi has a near
ubiquitous distribution, being found in environ-
ments ranging from estuarine to open ocean, and
from ~81°N (Hegseth & Sundfjord 2008, Sukhanova
et al. 2009) to ~61°S (Findlay & Giraudeau 2000,
Bollmann et al. 2009). Additionally, E. huxleyi
forms large blooms at temperate latitudes (Tyrrell &
Merico 2004).
Recent attempts to determine factors controlling
patterns of E. huxleyi (and other coccolithophore)
distribution and ecology in the present-day ocean
calculate growth rate as a function of major external
bottom-up limiting factors, such as temperature, light
and nutrients. This ap proach first relies on determin-
ing the model variables describing the maximum
growth rate response to individual limiting factors.
© Inter-Research 2014 ·*Corresponding author:
Emiliania huxleyi population growth rate response
to light and temperature: a synthesis
Samuel R. Fielding*
School of Environmental Sciences, 4 Brownlow Street, University of Liverpool, Liverpool L69 3GP, UK
ABSTRACT: The relationship between the maximum specific growth rate (μ, d−1) of the coccolitho-
phore Emiliania huxleyi and photon flux density (PFD, µmol photons m−2 s−1) was quantified using a
combination of quantile regression and culture experiment data from the literature (n = 1387). This
relationship, used in ecosystem models incorporating E. huxleyi or coccolithophores as a functional
group, is often assumed to follow a Monod function although values for the model parameters vary
greatly. In this analysis, a Monod function was compared with other models to determine the model
which best fit E. huxleyi growth rate data. Analysis showed that a Monod model of μ= 1.858
[PFD/(23.91 + PFD)] best described E. huxleyi maximum growth rate as a function of PFD. In addi-
tion, an expression combining the Monod function (this study) and the power function relating
growth rate to temperature (Fielding 2013; Limnol Oceanogr 58: 663 666) was calculated: when
both temperature (T, °C) and PFD are known, the resulting expression μ= (0.199 × T0.716) ×
[PFD/(14.2 + PFD)] predicts maximum E. huxleyi specific growth rate. Current literature models ei-
ther overestimate or underestimate maximum growth rate by up to 3-fold over a wide range of
PFDs. The use of the Monod function and the combined expression presented here is therefore rec-
ommended for future models incorporating the growth rate of E. huxleyi when either light or both
temperature and light are known.
KEY WORDS: Coccolithophore · Photon flux density · PFD · Temperature · Monod function ·
Quantile regression · Calcium carbonate · Literature review
Resale or republication not permitted without written consent of the publisher
Aquat Microb Ecol 73: 163–170, 2014
These responses can then be combined to give an
expression describing growth rate variation in com-
plex environmental scenarios.
Previously, the effect of temperature on marine
phytoplankton maximum growth rate (Eppley 1972)
has been objectively defined using quantile regres-
sion (Koenker & Bassett 1978) on a large hetero -
geneous dataset derived from culture studies
(Bissinger et al. 2008). The effect of temperature on
maximum potential growth rate has also been
quantified for E. huxleyi using the same method
(Fielding 2013). The majority (>90%) of the E. hux-
leyi dataset used by Fielding (2013) was derived
from nutrient-replete cultures, making it unsuitable
for determining the effect of nutrient limitation on
growth rate in a similar way. However, these cul-
ture data were measured under a wide range of
light intensities, allowing the effect of light on max-
imum growth rate to be estimated using quantile
Light intensity in the ocean varies significantly
with depth below the sea-surface. Incident photosyn-
thetically active radiation (λ= 400 to 700 nm) meas-
ured as photon flux density (PFD) at the sea-surface
varies both spatially and temporally but can be at
least 2000 µmol photons m−2 s−1 (Kirk 1994, Frouin &
Murakami 2007). Light is then attenuated with depth
depending on factors such as turbidity. E. huxleyi
grows in ocean environments with highly variable
light intensity, with PFDs ranging from <10 µmol
photons m−2 s−1 (Egge & Heimdal 1994, Cortes et al.
2001) up to surface irradiance values.
Model calculations of E. huxleyi and coccolitho-
phore maximum growth rate as a function of PFD
usually use the rectangular hyperbolic function after
Monod (1949), where the maximum attainable growth
rate (μ) at each PFD is described by
where μopt is the maximum growth rate at PFD and
Kis the light half-saturation constant.
Sometimes a function incorporating inhibition of
growth rate at high light intensities after Steele
(1962) is used, where μis described by
where μopt is the maximum growth rate at the PFD
which is optimal for growth rate and kis the initial
slope of the curve at low light. The parameter values
of these models are largely based on data from indi-
vidual strains or from cultures grown under differing
conditions even though models attempt to predict
responses of natural populations which comprise
diverse strain assemblages (Medlin et al. 1996). How-
ever, there is considerable intraspecific variation of E.
huxleyi growth rate in relation to light intensity
(Paasche 1999). Therefore, the suitability of current
models for describing the maximum potential growth
rate of E. huxleyi as a function of PFD in the ocean is
not certain.
To better estimate parameters for models describ-
ing growth rate as a function of PFD for E. huxleyi,
I applied quantile regression (Koenker & Bassett
1978) to literature growth rate data comprising
numerous individual E. huxleyi strains and experi-
ments. In addition, I applied quantile regression to
the data using the combined best-fit models for
growth rate as a function of PFD and growth rate as a
function of temperature (Fielding 2013).
Data collection
Emiliania huxleyi growth rate data (n = 1387) were
obtained from literature culture experiments where
light intensity data were also recorded. Data that
were only presented graphically were extracted
using Engauge Digitizer v.4.1. All growth rates were
converted to cell-specific growth rate (μ, d−1). Non-
PFD light measurements (e.g. lumen ft−1, Langleys
min−1, W m−2) were converted to lux (lumen m−2) and
then converted to PFD (µmol photons m−2 s−1) using
the conversion factors in Table 1.
Literature-based E. huxleyi culture growth rate
data were derived from 95 publications, detailing 213
strains from 67 different locations (Fig. 1). Literature
culture experiments reported PFDs ranging from 3 to
1160 µmol photons m−2 s−1, day lengths from 10 to
24 h, temperatures from 2 to 30°C, and salinities from
12 to 45. Around 7% of the data were from nutrient-
limited cultures.
opt 1– PFD
Light source Factor
Cool white fluorescent 0.013
Daylight fluorescent 0.014
Unspecified fluorescent 0.0135
Halogen 0.019
Table 1. Light conversion factors used to convert literature
light intensity data expressed in lux (lumen m−2) to µmol
photons m−2 s−1 for different light sources. Units were multi-
plied by their respective conversion factors to obtain values
in µmol photons m−2 s−1
Fielding: Emiliania growth and light
Modelling and statistical analysis
Quantile re gression can be used to determine the
relationship between environmental variables and
growth rate for the upper edge of a scatterplot. This is
especially useful for datasets where variables other
than the one which has been measured are limiting to
growth (Cade & Noon 2003) and has previously been
used to solve similar problems (Bissinger et al. 2008,
Fielding 2013). To reliably define the upper edge of
the dataset a 99th quantile regression must be used,
as calculating the 100th quantile does not generate
parameter confidence intervals (Cade et al. 1999). In
this paper, 99th quantile regression was used to infer
the relationship between light intensity and maximum
growth rate for a highly heterogeneous set of E. hux-
leyi strains and environmental conditions where
growth was often limited by factors other than light. It
should be noted that a 99th quantile re-
gression is calculated using all data
and not just from the points at the ex-
treme upper edge of the dataset.
Quantile regression was used to esti-
mate the upper edge of the dataset (99th
quantile) using Rv.2.15.3 with the
quantreg v.4.96 package for a selection
of models commonly used to relate al-
gal growth or photosynthesis to light
intensity (Table 2). Model deviance can
be corrected to take into account the
number of para meters in the model,
with a higher number of parameters in-
curring a heavier penalty, using Akaike’s
information criterion (AIC; Akaike
1974), AIC = 2p− 2Lm, where pis the
number of parameters in the model
and Lmis the maximised log likelihood (−2Lmis equiv-
alent to the deviance of the model fit). However, all
the models used in this study use the same number of
independently varied parameters (p = 2), making AIC
redundant. Therefore, model fits are subsequently
compared using only their deviances.
Maximum Emiliania huxleyi specific growth rate
for individual measurements was 1.96 d−1 at approx.
600 µmol photons m−2 s−1 (Fig. 2). Maximum growth
rates appear to fall sharply below ~100 µmol photons
m−2 s−1. Above 600 µmol photons m−2 s−1, maximum
growth rates also appeared to be suppressed al -
though this is likely due to a lack of data (n = 13) in
this PFD range.
Fig. 1. Geographical locations of Emiliania huxleyi strains used in the litera-
ture compilation in this study (see Table S1 in the Supplement at www. int-res.
com/ articles/ suppl/ a073p163 _ supp .pdf for literature sources, strains used, and
geographical location of strain origin)
Model Deviance Equation μopt Kor k
Monod (1949) 11.18 1.858 ± 0.032 23.91 ± 5.608
Smith (1936) 12.81 1.795 ± 0.021 0.058 ± 0.016
Webb et al. (1974) 12.86 1.785 ± 0.022 0.069 ± 0.019
tanh (Jassby & Platt 1976) 13.28 1.780 ± 0.016 0.059 ± 0.020
Steele (1962) 24.34 2.939 ± 0.207 0.004 ± 0.000
( PFD)
opt PFD/ opt
tanh PFD
opt 1– PFD
Table 2. Model parameters with 95% confidence intervals and deviances for the models fit to the data in Fig. 2. Lower de-
viances indicate better relative model fits. PFD is photon flux density (µmol photons m−2 s−1), μopt is the modelled maximum
specific growth rate (d−1) across the entire PFD range, Kis the light half-saturation constant and kis the initial slope of the
curve at low light
Aquat Microb Ecol 73: 163–170, 2014
The rectangular hyperbolic Monod model (Eq. 1)
best described the 99th quantile of the specific growth
rate response to PFD (Fig. 2, Table 2). In contrast, the
Steele model (Eq. 2) had a relatively high deviance
and visibly overestimated maximum growth rate by
almost double at intermediate PFDs while marginally
underestimating maximum growth rate at low PFDs.
The other models (Smith 1936, Webb et al. 1974; and
the tanh model from Jassby & Platt 1976) had inter-
mediate deviances. While these models were nearly
identical to the Monod model at PFDs above ~400 µmol
photons m−2 s−1, they visibly overestimated maximum
growth rate at lower PFDs.
As the shapes of the responses of E. huxleyi maxi-
mum growth rate to both PFD (this study) and tem-
perature (Fielding 2013) have been quantified, it is
possible to formulate a combined expression by sub-
stituting μopt (from the Monod model) with the
power function describing the maximum attainable
growth rate as a function of temperature (Fielding
2013), as:
where Kis the light half-saturation constant, Tis the
temperature (°C), and aand bare the slope and the
power component of the growth rate versus tempera-
ture response, respectively. Quantile regression of
this combined PFD plus temperature model through
the 99th quantile of the data results in:
as shown in Fig. 3.
Growth rate response to light
This study represents the first syn-
thesis of literature-based Emiliania
hux leyi growth rate data as a function
of light intensity. Previous studies have
quantified models describing growth
rate response only from individual strains
or from a small number of strains, de-
spite there being considerable intra -
specific variation of E. huxleyi growth
rate in relation to light intensity (Paasche
2001). As a result, the use of these mod-
els incorporating coccolithophores such as E. huxleyi
(e.g. Merico et al. 2004) may not be straightforward.
However, this study provides an estimate of maximum
growth rate as a function of light intensity from a
multi-strain dataset which may be reasonably as-
sumed to more accurately represent a natural, geneti-
cally diverse global E. huxleyi population.
Potential biases
The dataset used in this study is larger (n = 1387)
than the minimum of n = 500 recommended by
Rogers (1992) for calculating the 99th quantile. How-
0.199 PFD
14.2 PFD
aT K
μ × +
1.858 PFD
23.91 PFD
Fig. 2. Emiliania huxleyi specific growth rate versus photon flux density. Models
(see Table 2) are fitted to the 99th quantile of the data
Fig. 3. 99th quantile regression of Emiliania huxleyi growth
rate response to both photon flux density and temperature.
Note reduced axes compared with Fig. 2. Colour scale: specific
growth rates (bluered: low– high)
Fielding: Emiliania growth and light
ever, determining the best-fit model for the upper
edge of the dataset may be complicated by sampling
bias. Quantile regression is based on least absolute
deviations and is therefore less sensitive to extreme
values and outliers than ordinary least squares re -
gression (Bissinger et al. 2008). Nevertheless, the
lack of data (<1 %) and lower measured maximum
growth rates above 600 µmol photons m−2 s−1 may
affect model parameter estimates.
To test the effect of data above 600 µmol photons
m−2 s−1 on the model, these data were removed and
the models were re-run. Removal of these data did
not alter the order of model goodness of fit but did
slightly alter parameters for some of the models by
<0.7%, although these differences were not notice-
able when plotted. Nevertheless, the use of the Monod
model to describe E. huxleyi growth rate response to
light intensity above 600 µmol photons m−2 s−1 should
be made with this caveat until further data from
these high PFDs can be included in the dataset. How-
ever, E. huxleyi photosynthesis is notable for not dis-
playing inhibition at high light intensities of up to
2500 µmol photons m−2 s−1 (Paasche 2001). Therefore,
it is possible that maximum growth rates at high light
intensities are similarly uninhibited.
As was highlighted by Fielding (2013), only a small
proportion of the data are from strains isolated from
the Southern Hemisphere and far from continental
land masses (Fig. 1). Although it is not anticipated
that strains from different regions will have different
light-dependent growth rate responses, the applica-
tion of the recommended growth rate−PFD model
should be made with this caveat in mind.
Ideally, the growth rate response to both light and
temperature would be modelled for each individual
geographic or climatic region. This would serve both
to elicit any differences between regional-level pop-
ulations of E. huxleyi and to test whether the global
growth rate response models for light and tempera-
ture were universally applicable. However, dividing
the current dataset into regional subsets would de -
tract from the power of the combined global growth
rate response curve. A regional subset of the current
dataset would not be derived from as large a range of
culture variables due to the smaller number of exper-
iments carried out on that subset —for example, only
temperatures between 15 and 20°C or only PFDs
below 50 µmol photons m−2 s−1.
A further problem with dividing the current dataset
into regional subsets is that many regions (e.g. South
Africa, N Pacific) only have data derived from a small
number of strains or in some cases from a single
strain. There appears to be almost as much intraspe-
cific diversity within discrete geographic populations
of E. huxleyi than there is between populations from
different regions (Iglesias-Rodríguez et al. 2006).
Therefore, any differences observed in growth rate
response curves between subsets may not reflect a
true regional difference but may simply be a result of
under-sampling of the genetic diversity in each spe-
cific region.
The division of the current dataset into regional
subsets at the present stage may therefore be a little
premature, and more comprehensive data coverage
of individual regions is likely necessary before any
such analysis is made. The responses presented here
and in Fielding (2013) are, as such, still only rela-
tively blunt tools with which to parameterise E. hux-
leyi growth rate models.
Further bias may be introduced into the dataset by
the use of varying light sources in different literature
studies. Photosynthetically active radiation as meas-
ured by PFD includes all wavelengths between 400
and 700 nm. However, although 2 data points with the
same PFD would have the same quantity of photons
passing through this broad spectral band every sec-
ond, the spectral quality of the 2 data may be different.
For the collated literature studies presented here, the
light source was specified for 78% (n = 1082) of the
data. Around 75% of the entire dataset are from cul-
tures grown using fluorescent tubes, of which 52 %
were cool white, 26% were daylight and 22 % were
unspecified. Around 3% of the dataset were from cul-
tures grown using halogen lamps, of which one datum
was from a study published in 1992 (Balch et al. 1992)
and the remainder were from a study published in
1967 (Paasche 1967). These data all fell well below the
upper edge of the scatterplot and any resultant differ-
ences in spectral quality are not likely to influence the
results of this study. The 22% of the dataset where the
light source was unspecified were all from studies
published in 1995 or after, of which 82% were pub-
lished in 2000 or after. As the last recorded usage of
halogen lamps in this dataset was from 1992, it is
likely that data from cultures with unspecified light
sources were also grown using fluorescent tubes.
Combined growth rate response to light
and temperature
In addition to determining its response to PFD, this
study represents the first attempt at simultaneously
quantifying the response of E. huxleyi maximum spe-
cific growth rate to both light and temperature. This
combined model (see Results) can now be compared
Aquat Microb Ecol 73: 163–170, 2014
to other models used to estimate maximum specific
growth rate for E. huxleyi and for coccolithophores
as a functional group from temperature and light
Four of the literature models for E. huxleyi use a
rectangular hyperbola (Monod 1949), while one uses
a hyperbolic tangent (tanh; Jassby & Platt 1976) func-
tion to describe growth rate versus PFD. In addition,
2 of the models use an exponential function after
Eppley (1972) to describe growth rate response to
temperature, while 3 use an exponential Q10 function
(van’t Hoff 1884). The combined expressions used in
these studies to calculate specific growth rate from
both temperature and PFD are detailed in Table 3.
In comparison with the combined model presented
in this study, all 5 literature models (Fig. 4A–E) over-
estimate E. huxleyi maximum growth rate by > 300%
across a wide range of PFDs at low temperatures,
while all 5 models overestimate E. huxleyi maximum
growth rate to a lesser extent across a wide range of
PFDs and temperatures, with the exception of Find-
lay et al. (2008), where growth rate is underestimated
over the majority of the PFD and temperature range
(Fig. 4A). The model used by Joassin et al. (2011)
overestimated maximum growth rate across the
entire PFD and temperature range (Fig. 4B).
The widespread overestimation of maximum E.
huxleyi growth rate by literature models is largely
due to the use of overly high values for μopt (i.e. the
maximum growth rate across all temperatures and
light intensities). For example, Merico et al. (2006)
give a maximum specific growth rate of 1.15 d−1 at
0°C. However, extrapolation using the specified tem-
perature−growth rate function results in high maxi-
mum specific growth rates of 4.05 d−1 at 20°C and an
even higher 7.61 d−1 at 30°C, much higher than that
observed in E. huxleyi culture experiments.
In addition to overly high μopt in literature models,
the literature values for the initial slope of the growth
rate response to PFD, with the exception of those
used by Oguz & Merico (2006) and Joassin et al.
(2011), are also higher than that presented in this
study. This results in generally shallower PFD−
growth rate slopes up to the growth optima in litera-
ture models, and therefore in the underestimation of
growth rate at low PFD values across all or the major-
ity of the temperature range for these studies
(Fig. 4A,C,E). Hence, previously used parameters for
both PFD and temperature components of growth
rate models appear to be inappropriate for E. huxleyi
and it is recommended that the combined model
parameters presented in this study should be used in
In addition to modelling the coccolithophore E.
huxleyi as a discrete ecosystem component, there are
some studies which model all coccolithophore spe-
Literature model Tmodel PFD model Equation
E. huxleyi
Findlay et al. (2008) Eppley Monod
Joassin et al. (2011) Q10 Monod
Merico et al. (2004, 2006)a Eppley Monod
Oguz & Merico (2006) Q10 tanh
Tyrrell & Taylor (1996) Q10 Monod
Gregg et al. (2003) Eppley Monod
Gregg & Casey (2007) Eppley Monod
aSensitivity analysis run
0.5 e PFD
205 PFD
0.063 T
2.64 / 1.5 PFD
20 PFD
(20– )/10T
1.5 e PFD
205 PFD
0.063 T
2.2 / 1.5 tanh 0.026 PFD
2.2 / 1.5
(20– )/10
(20– )/10
1.8 / 2 PFD
100 PFD
(16 – )/ 10T
0.228 e PFD
71.2 PFD
0.063 T
0.321 e PFD
71.2 PFD
0.063 T
Table 3. Models used in literature studies to predict maximum specific growth rate (μ) from temperature (T, °C) and photon
flux density (PFD, µmol photons m−2 s−1). The differences between these models and the combined temperature photon flux
density model calculated in this study are shown in Fig. 4
Fielding: Emiliania growth and light
cies as a combined functional group (Gregg et al.
2003, Le Quere et al. 2005, Gregg & Casey 2007).
When compared to the combined PFD and tempera-
ture model presented in this study (Fig. 4F I), cocco-
lithophore functional group models described by
Gregg et al. (2003) and Gregg & Casey (2007) have a
lower maximum growth rate over almost the entire
PFD range due to lower μopt values.
A multi-species coccolithophore population is
indeed likely to have a lower combined maximum
growth rate than a monospecific E. huxleyi popula-
tion due to the inclusion of larger, slower growing
species such as Coccolithus spp. and Calcidiscus spp.
Existing functional group models likely somewhat
reflect this lower multi-species coccolithophore com-
munity growth rate. However, E. huxleyi is one of the
smallest (if not the smallest) species of coccolitho-
phore (Buitenhuis et al. 2008) and is therefore likely
to be the fastest growing as predicted by the meta-
bolic theory of ecology (Brown et al. 2004). As such
the 99th quantile E. huxleyi growth rate envelope
presented in this study likely represents the maxi-
mum potential growth rate for all coccolithophore
species as a functional group, and will become
increasingly more appropriate as E. huxleyi starts to
dominate the coccolithophore assemblage, for exam-
ple in an E. huxleyi bloom scenario.
The Monod model presented in this study repre-
sents a first step towards quantifying the maximum
specific growth rate response of E. huxleyi to light. It
is recommended that the function μ= 1.858[PFD/
(23.91 + PFD)], and not a Steele equation, be used in
future models incorporating E. huxleyi growth rate.
However, data from PFDs above 600 µmol photons
m−2 s−1 and from a more geographically diverse set of
culture strains than make up the current dataset will
allow for a future reappraisal of this relationship.
Where both temperature and PFD are known, maxi-
mum E. huxleyi growth rate should be calculated
from the combined expression μ= (0.199 × T0.716) ×
[PFD/(14.2 + PFD)].
Acknowledgements. Thanks to 3 anonymous reviewers for
advice and comments on the manuscript.
Fig. 4. The percentage which literature
models (Table 3) underestimate (negative
values) or overestimate (positive values)
maximum specific growth rate compared to
the combined temperature–photon flux den-
sity model presented in this study (Fig. 3).
0% equals no difference between the litera-
ture model and the model presented in this
study. Contours are at 50% intervals al-
though no data are shown above 300%.
Colour scale: specific growth rates (blue
red: low– high). Models for Emiliania hux-
leyi: (A) Findlay et al. (2008), (B) Joassin et
al. (2011), (C) Merico et al. (2004, 2006) (D)
Oguz & Merico (2006) and (E) Tyrrell & Tay-
lor (1996); and for coccolithophores as a
functional group: (F) Gregg et al. (2003) low
light model, (G) Gregg et al. (2003) high
light model, (H) Gregg & Casey (2007) low
light model and (I) Gregg & Casey (2007)
high light model
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Editorial responsibility: Hugh MacIntyre,
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Submitted: April 4, 2013; Accepted: June 6, 2014
Proofs received from author(s): August 28, 2014

Supplementary resource (1)

... The evolutionary effect of temperature on phytoplankton should now be investigated concomitantly to other factors (which has been partially done by [Sauterey et al., 2014]), such as irradiance, nutrient [Irwin et al., 2015] or pH and CO 2 concentrations [Coello-Camba et al., 2014]. The phytoplankton species Emiliana huxleyi is known to be acidsensitive, but its adaptation capability to co-variation of temperature and pH are not clearly understood [Fielding, 2014, Gibbs et al., 2016, Schlüter et al., 2014. ...
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Unicellular photosynthetic organisms forming the phytoplankton are the basis of primary production. Because these organisms cannot regulate their inner temperature, the medium temperature strongly constrains their growth. Understanding the impact of this factor is topical in a global change context. In this PhD thesis we have investigated how phytoplankton adapts to temperature. By analyzing the growth rate as a function of temperature for hundreds of species we highlighted the characteristics that can be accurately described by a mathematical model. We have identied the links between the cardinal temperatures as well as their thermodynamical fundament using the mechanistic Hinshelwood model. We then challenged the Eppley hypothesis `hotter is faster' for 5 phylogenetic phytoplankton groups and determined the evolutionary limits for each of them. We have also studied the adaptation mechanisms associated to long term temperature variations by developing an evolutionary model using the adaptive dynamics theory allowing to predict the evolutionary outcome of species adaptation to a simple temperature cycle. Our results have been compared to a selection experiment carried out in a controlled device on Tisochrysis lutea. Our method has been extended to predict the adaptation of a strain to periodic temperature profiles and study phytoplankton adaptation at the global ocean scale. In situ data of sea surface temperature have been used as a forcing variable and have permitted to show that the elevation of temperature will be critical for several species in particular for those living in areas where the annual temperature fluctuation is high such as the Mediterranean sea.
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A revised estimate of the relationship between the maximum growth rate (mu(max), d(-1)) of Emiliania huxleyi and temperature (T, degrees C) was made using quantile regression and literature data from culture experiments (n = 1415). For modeling E. huxleyi bloom formation and coccolithophore functional group growth rate, this relationship is commonly assumed to follow an exponential relationship, as is the case for photosynthetic algal species in general. However, data specific to E. huxleyi show that this relationship is better described by a power function. Direct comparison with growth rate-temperature relationships used to model E. huxleyi from the literature shows that they overestimate growth rate by up to 250% over a wide range of temperatures. It is recommended that the revised relationship of mu(max) = 0.1419T(0.8151) be used in future models incorporating temperature-dependent maximum growth rate estimates of E. huxleyi and of coccolithophores as a functional group.
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The Eppley curve describes an exponential function that defines the maximum attainable daily growth rate of marine phytoplankton as a function of temperature. The curve was originally fitted by eye as the upper envelope of a data set, and despite its wide use, the reliability of this function has not been statistically tested. Our analysis of the data using quantile regression indicates that while the curve appears to be a good estimate of the edge of the data, it may not be reliable because the data set is small (n = 162). We construct a contemporary, comprehensive data set (n = 1,501) and apply an objective approach, quantile regression, to estimate its upper edge ${\rm{(99}}^{{\rm{th}}} {\rm{quantile)}.}$ This analysis yields a new predictive equation, $\mu _{{\rm{max}}} {\rm{ = 0}}.{\rm{81}}e^{0.0631T},$ that describes the maximum specific growth rates $(\mu _{\max },$ d⁻¹ of marine phytoplankton as a function of temperature (T, °C). The Liverpool phytoplankton database (LPD) curve is higher than the Eppley curve across all temperatures, and at temperatures below 19°C, the Eppley curve falls below the lower 95% confidence interval of the LPD curve. However, the LPD $Q_{10}$ value (1.88) is identical to that of the Eppley curve and thus supports the use of models that incorporate this as an estimate of phytoplankton growth-rate response to temperature change. To assess the potential effect of the LPD curve on primary production, we embedded the LPD function into a one-dimensional numerical model of a temperate, pelagic ecosystem. This analysis suggests that models using the Eppley function will underestimate primary production by as much as 30%.
Enclosures containing natural phytoplankton communities were fertilized with nitrate and phosphate in duplicates in three different ratios (16 : 5, 16 : 1, 16 : 0.2) in order to initiate blooms of the coccolithophorid Emiliania huxleyi (Lohmann) Hay et Mohler under controlled environmental conditions. The development of the phytoplankton community was in addition followed in two unfertilized enclosures and in the surrounding sea water. The phytoplankton succession during the experiment (22 April - 29 May 1992) was mainly dinoflagellates-diatoms-E. huxleyil Phaeocystis sp. in all fertilized enclosures, but the importance of the different species/groups were different in enclosures with different N : P ratio. Diatom numbers decreased when the N : P ratio increased in the nutrient supply. From an initial concentration of 0.09 109 cells m−3 E. huxleyi increased to concentrations between 20 109 cells m−3 and 37 109 cells m−3 in the enclosures supplied with nitrate and phosphate in aN: P ratio of 16 : 1 and 16 : 0.2. The growth of E. huxleyi in the four enclosures was remarkably synchronous with a specific growth rate µ ≈ 0.3 day−1. The peak of the blooms differed only by a few days in time, and the blooms decayed immediately after maximum in cell numbers (decay rate µ ≈ -0.2 day−1). Control factors of growth and decay of the blooms are discussed. The growth was apparently controlled by temperature and in periods also by low irradiance, while estimated viral mortality could explain the decay. In enclosures supplied with nitrate and phos~hate in aN: P ratio of 16 : 5 E. huxleyi only reached concentrations of 5 109 cells m−3. The highest cell numbers of Phaeocystis sp. were observed in enclosures with low and balanced N : P ratios. An analysis of blooms of E. huxleyi and Phaeocystis sp. from enclosure experiments carried out every year between 1988 and 1992 illustrated that E. huxleyi grow well at low concentrations of phosphate, and was a better competitor than Phaeocystis sp. as long as the sea water temperature was about 10° C or higher and the surface irradiance was 20 mol m−2 day−1 or higher. Phaeocystis sp. had a higher phosphate demand, but was a better competitor than E. huxleyi at sea water temperatures lower than 1° C and at surface irradiance lower than 20 mol m−2 day−1, if nutrients were available.
In a recent Concepts paper in Ecology, Thomson et al. emphasized that assumptions of conventional correlation and regression analyses fundamentally conflict with the ecological concept of limiting factors, and they called for new statistical procedures to address this problem. The analytical issue is that unmeasured factors may be the active limiting constraint and may induce a pattern of unequal variation in the biological response variable through an interaction with the measured factors. Consequently, changes near the maxima, rather than at the center of response distributions, are better estimates of the effects expected when the observed factor is the active limiting constraint. Regression quantiles provide estimates for linear models fit to any part of a response distribution, including near the upper bounds, and require minimal assumptions about the form of the error distribution. Regression quantiles extend the concept of one-sample quantiles to the linear model by solving an optimization problem of minimizing an asymmetric function of absolute errors. Rank-score tests for regression quantiles provide tests of hypotheses and confidence intervals for parameters in linear models with heteroscedastic errors, conditions likely to occur in models of limiting ecological relations. We used selected regression quantiles (e.g., 5th, 10th, ..., 95th) and confidence intervals to test hypotheses that parameters equal zero for estimated changes in average annual acorn biomass due to forest canopy cover of oak (Quercus spp.) and oak species diversity. Regression quantiles also were used to estimate changes in glacier lily (Erythronium grandiflorum) seedling numbers as a function of lily flower numbers, rockiness, and pocket gopher (Thomomys talpoides fossor) activity, data that motivated the query by Thomson et al. for new statistical procedures. Both example applications showed that effects of limiting factors estimated by changes in some upper regression quantile (e.g., 90-95th) were greater than if effects were estimated by changes in the means from standard linear model procedures. Estimating a range of regression quantiles (e.g., 5-95th) provides a comprehensive description of biological response patterns for exploratory and inferential analyses in observational studies of limiting factors, especially when sampling large spatial and temporal scales.
The oceans are the largest natural source of organic sulfur compounds, primarily dimethyl sulfide (DMS), a potentially important factor in the global climate. Significant production of dimethylsulfoniopropionate (DMSP), the precursor of DMS, is confined to a few classes of phytoplankton, primarily the Dinophyceae (dinoflagellates) and Prymnesiophyceae (which includes coccolithophores). Because of this taxonomic relationship and the spatial and temporal heterogenity of these forms of algae, DMS emissions will vary according to their presence. Current values of DMS production may be considerably underestimated due to sampling inadequacies and a lack of information about biological parameters that affected rate of production.
Three clonal isolates of Emiliania huxleyi (Lohmann) Hay et Mohler of different geographical origins were grown in semicontinuous culture under irradiances ranging from 8 to 330 mu mol quanta m(-2) s(-1), resulting in growth rates between < 5% and 100% of the maximum rate. Coccolith calcium and cell carbon were determined by chemical analysis. Counts of cells and of attached plus detached coccoliths were obtained by microscopy. The molar ratio of calcium in coccoliths to organic carbon in cells (the Ca : org.C ratio) declined by 30-40% when irradiance was reduced from 100 to 18 mu mol m(-2) s(-1). This decline was due to two separate effects: in two of the clones, fewer coccoliths were produced by each cell; and in all three clones, less calcium carbonate was deposited in each coccolith. Electron microscopy showed that the latter effect was associated with a debilitation of the distal shield elements. No naked cells appeared in these cultures. Calcification in a coccolith-forming culture and in nature is probably regulated in such a way that a complete layer of 12-15 coccoliths on the cell surface is secured even under adverse light conditions. Significant interclonal differences appear to exist in the Ca:org.C ratio. possibly also in the mean calcium content of individual coccoliths.
Measurements were made of photosynthesis and calcification in a bloom of coccolithophores in the Gulf of Maine as well as in laboratory batch cultures of the Emiliania huxleyi strain 88E. The14C technique for measuring calcification was evaluated with calcifying and noncalcifying coccolithophore strains. Shipboard bloom observations showed physiological evidence of stratification between surface and deep populations within the surface mixed layer. Photosynthesis and calcification rates were enhanced within hours of addition of KNO3 or nitrate-rich deep water (to the same final concentration). Such rates were strongly temperature dependent in laboratory cultures, decreasing over a factor of two from 15 to 20°C. Calcification was considerably less light-dependent than photosynthesis and consistently had a measurable dark rate. In culture, maximum calcification rates and degree of cell plating were limited to logarithmic growth phase. This was followed by rapid increase in the coccolith shedding rate 1 day prior to the onset of stationary phase which continued several days after cell division stopped. The regional significance of these features to total organic and inorganic carbon production as well as calcite burial is discussed.