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AQUATIC MICROBIAL ECOLOGY

Aquat Microb Ecol

Vol. 73: 163–170, 2014

doi: 10.3354/ame01707 Published online October 2

INTRODUCTION

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 · www.int-res.com*Corresponding author: s.r.fielding@outlook.com

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

regression.

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

(1)

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

(2)

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).

MATERIALS AND METHODS

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.

K

PFD

PFD

opt

μ=μ×+

μ=×μ××

×

PFD e

opt 1– PFD

k

k

164

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.

RESULTS

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.

165

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

K

PFD

PFD

opt

μ=μ×+

μ×+

μ+×

PFD

( PFD)

opt

22

k

k

opt

()

μ×−×μ

1e

opt – PFD/ opt

k

μ××

μ

⎛

⎝

⎜⎞

⎠

⎟

tanh PFD

opt

opt

k

×μ××

×

PFD e

opt 1– PFD

kk

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)

(3)

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:

(4)

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:

(5)

as shown in Fig. 3.

DISCUSSION

Growth rate response to light

intensity

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-

()

()

μ=××

+

0.199 PFD

14.2 PFD

0.716

T

aT K

bPFD

PFD

()

()

μ=× × +

μ=×+

1.858 PFD

23.91 PFD

166

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 (blue–red: 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

167

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

intensity.

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

future.

In addition to modelling the coccolithophore E.

huxleyi as a discrete ecosystem component, there are

some studies which model all coccolithophore spe-

168

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

Coccolithophores

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

T

T

()

()

×+

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.

CONCLUSION

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.

169

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

Aquat Microb Ecol 73: 163–170, 2014

LITERATURE CITED

Akaike H (1974) A new look at statistical-model identifica-

tion. IEEE Trans Automat Contr 19: 716−723

Balch WM, Holligan PM, Kilpatrick KA (1992) Calcification,

photosynthesis and growth of the bloom-forming cocco-

lithophore Emiliania huxleyi. Cont Shelf Res 12: 1353−1374

Bissinger JE, Montagnes DJS, Sharples J, Atkinson D (2008)

Predicting marine phytoplankton maximum growth rates

from temperature: improving on the Eppley curve using

quantile regression. Limnol Oceanogr 53: 487−493

Bollmann J, Herrle JO, Cortes MY, Fielding SR (2009) The

effect of sea water salinity on the morphology of Emilia-

nia huxleyi in plankton and sediment samples. Earth

Planet Sci Lett 284: 320−328

Brown JH, Gillooly JF, Allen AP, Savage VM, West GB

(2004) Toward a metabolic theory of ecology. Ecology 85:

1771−1789

Buitenhuis ET, Pangerc T, Franklin DJ, Le Quere C, Malin G

(2008) Growth rates of six coccolithophorid strains as a

function of temperature. Limnol Oceanogr 53: 1181−1185

Cade BS, Noon BR (2003) A gentle introduction to quantile

regression for ecologists. Front Ecol Environ 1: 412−420

Cade BS, Terrell JW, Schroeder RL (1999) Estimating effects

of limiting factors with regression quantiles. Ecology 80:

311−323

Cortes MY, Bollmann J, Thierstein HR (2001) Coccolithophore

ecology at the HOT station ALOHA, Hawaii. Deep-Sea

Res II 48: 1957−1981

Egge JK, Heimdal BR (1994) Blooms of phytoplankton

including Emiliania huxleyi (Haptophyta). Effects of

nutrient supply in different N: P ratios. Sarsia 79: 333−348

Eppley R (1972) Temperature and phytoplankton growth in

the sea. Fish Bull 70: 1063−1085

Fielding SR (2013) Emiliania huxleyi specific growth rate de -

pendence on temperature. Limnol Oceanogr 58: 663−666

Findlay CS, Giraudeau J (2000) Extant calcareous nanno-

plankton in the Australian Sector of the Southern Ocean

(austral summers 1994 and 1995). Mar Micropaleontol

40: 417−439

Findlay HS, Tyrrell T, Bellerby RGJ, Merico A, Skjelvan I

(2008) Carbon and nutrient mixed layer dynamics in the

Norwegian Sea. Biogeosciences 5: 1395−1410

Frouin R, Murakami H (2007) Estimating photosynthetically

available radiation at the ocean surface from ADEOS-II

global imager data. J Oceanogr 63: 493−503

Gregg WW, Casey NW (2007) Modeling coccolithophores in

the global oceans. Deep-Sea Res II 54: 447−477

Gregg WW, Ginoux P, Schopf PS, Casey NW (2003) Phyto-

plankton and iron: validation of a global three-dimen-

sional ocean biogeochemical model. Deep-Sea Res II 50:

3143−3169

Hegseth EN, Sundfjord A (2008) Intrusion and blooming of

Atlantic phytoplankton species in the high Arctic. J Mar

Syst 74: 108−119

Iglesias-Rodríguez MD, Schofield OM, Batley J, Medlin LK,

Hayes PK (2006) Intraspecific genetic diversity in the

marine coccolithophore Emiliania huxleyi (Prymnesio-

phyceae): the use of microsatellite analysis in marine

phytoplankton population studies. J Phycol 42: 526−536

Jassby AD, Platt T (1976) Mathematical formulation of the

relationship between photosynthesis and light for phyto-

plankton. Limnol Oceanogr 21: 540−547

Joassin P, Delille B, Soetaert K, Harlay J and others (2011)

Carbon and nitrogen flows during a bloom of the cocco-

lithophore Emiliania huxleyi: modelling a mesocosm

experiment. J Mar Syst 85: 71−85

Keller MD (1988) Dimethyl sulfide production and marine

phytoplankton: the importance of species composition

and cell size. Biol Oceanogr 6: 375−382

Kirk J (1994) Light and photosynthesis in aquatic ecosys-

tems. Cambridge University Press, Cambridge

Koenker R, Bassett G (1978) Regression quantiles. Econo-

metrica 46: 33−50

Le Quere C, Harrison SP, Prentice IC, Buitenhuis ET and

others (2005) Ecosystem dynamics based on plankton

functional types for global ocean biogeochemistry mod-

els. Glob Change Biol 11: 2016−2040

Medlin LK, Barker GLA, Campbell L, Green JC and others

(1996) Genetic characterisation of Emiliania huxleyi

(Haptophyta). J Mar Syst 9: 13−31

Merico A, Tyrrell T, Lessard EJ, Oguz T, Stabeno PJ, Zee-

man SI, Whitledge TE (2004) Modelling phytoplankton

succession on the Bering Sea shelf: role of climate influ-

ences and trophic interactions in generating Emiliania

huxleyi blooms 1997–2000. Deep-Sea Res I 51: 1803−1826

Merico A, Tyrrell T, Cokacar T (2006) Is there any relation-

ship between phytoplankton seasonal dynamics and the

carbonate system? J Mar Syst 59: 120−142

Monod J (1949) The growth of bacterial cultures. Annu Rev

Microbiol 3: 371−394

Oguz T, Merico A (2006) Factors controlling the summer

Emiliania huxleyi bloom in the Black Sea: a modeling

study. J Mar Syst 59: 173−188

Paasche E (1967) Marine plankton algae grown with light-dark

cycles. I. Coccolithus huxleyi. Physiol Plant 20: 946−956

Paasche E (1999) Reduced coccolith calcite production

under light-limited growth: a comparative study of three

clones of Emiliania huxleyi (Prymnesiophyceae). Phyco -

logia 38: 508−516

Paasche E (2001) A review of the coccolithophorid Emiliania

huxleyi (Prymnesiophyceae), with particular reference to

growth, coccolith formation, and calcification-photosyn-

thesis interactions. Phycologia 40: 503−529

Rogers WH (1992) Quantile regression standard errors.

Stata Tech Bull 9: 16−19

Rost B, Riebesell U (2004) Coccolithophores and the biologi-

cal pump: responses to environmental changes. In: Thier-

stein HR, Young JR (eds) Coccolithophores: from molec-

ular processes to global impact. Springer, Berlin, p 99– 125

Smith EL (1936) Photosynthesis in relation to light and car-

bon dioxide. Proc Natl Acad Sci USA 22: 504−511

Steele JH (1962) Environmental control of photosynthesis in

the sea. Limnol Oceanogr 7: 137−150

Sukhanova IN, Flint MV, Pautova LA, Stockwell DA, Greb-

meier JM, Sergeeva VM (2009) Phytoplankton of the

western Arctic in the spring and summer of 2002: structure

and seasonal changes. Deep-Sea Res II 56: 1223−1236

Tyrrell T, Merico A (2004) Emiliania huxleyi: bloom observa-

tions and the conditions that induce them. In: Thierstein

HR, Young JR (eds) Coccolithophores: from molecular

processes to global impact. Springer, Berlin, p 75– 97

Tyrrell T, Taylor AH (1996) A modelling study of Emiliania

huxleyi in the NE Atlantic. J Mar Syst 9: 83−112

van’t Hoff MJH (1884) Etudes de dynamique chimique. Recl

Trav Chim Pays-Bas 3: 333−336

Webb WL, Newton M, Starr D (1974) Carbon dioxide ex -

change of Alnus rubra. A mathematical model. Oecolo-

gia 17: 281−291

Zeebe RE, Wolf-Gladrow DA (2001) CO2in seawater: equi-

librium, kinetics, isotopes. Elsevier Oceanography Series,

Vol 65. Elsevier, Amsterdam

170

Editorial responsibility: Hugh MacIntyre,

Halifax, Nova Scotia, Canada

Submitted: April 4, 2013; Accepted: June 6, 2014

Proofs received from author(s): August 28, 2014

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