Impact of excess and harmful radiation on energy budgets in scleractinian corals

Ecological Modelling 222 (2011) 1315–1322

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Impact of excess and harmful radiation on energy budgets in scleractinian corals Yoan Eynaud a , Roger M. Nisbet b , Erik B. Muller b,∗ a b

Laboratoire de Microbiologie, Géochimie et Ecologie Marines, UMR 6117 CNRS, Centre d’Océanologie de Marseille, Case 901, Campus de Luminy, 13288 Marseille Cedex, France Department of Ecology, Evolution and Marine Biology, University of California, Santa Barbara, CA 93106, United States

a r t i c l e

i n f o

Article history: Received 25 May 2010 Received in revised form 9 January 2011 Accepted 12 January 2011 Available online 14 February 2011 Keywords: Dynamic energy budget (DEB) theory Syntrophy Symbiosis Endosymbiont Scleractinian coral Mutualism Photoinhibition Photodamage Coral bleaching

a b s t r a c t Using dynamic energy budget (DEB) theory, this paper explores the potential of excess and harmful radiation, notably UV, to cause changes in performance and, ultimately, bleaching in scleractinian corals for a range of ambient nitrogen and (beneficial) photosynthetically active radiation levels. Two negative impacts of radiation are considered: a reduction in the capacity of the symbiont to generate energy through photosynthesis (defined in this paper as photoinhibition); an increase in the costs for the symbiont to remain viable due to repair of damage (defined in this paper as photodamage). Model predictions indicate that although both types of impact reduce the growth potential of host and symbiont, photoinhibition predominantly affects host features, except at very low ambient nitrogen levels, under which conditions the severity of nitrogen limitation is so strong that a reduction in photosynthetic rates due to photoinhibition has minimal impact. In steady state, photoinhibition leads to a reduction in host biomass, and an increase in symbiont density, implying that photoinhibition (as defined in this paper) is unlikely to cause bleaching. In contrast, the impact of photodamage is mostly affecting symbiont features, including a decline in symbiont density. Thus, photodamage may contribute to coral bleaching. Furthermore, the model predicts that, with both photoinhibition and photodamage, an increasing ratio of harmful to beneficial radiation accelerates the suppression of growth rates of symbiont and host, implying that coral health deteriorates progressively faster with increasing harmful radiation, such as UVb. Published by Elsevier B.V.

1. Introduction Over the past couple of decades coral reefs have experienced growing pressure from a wide range of stressors, including tourism, destructive fishing practices, run-off of toxicants and nutrients, increasing ocean temperatures, exposure to excess or harmful radiation and acidification due to a changing ocean carbonate chemistry. Some of these factors, either alone or in combination, can bring about massive ‘coral-bleaching’ events (Brown, 1997 and references therein; Douglas, 2003 and references therein). During bleaching, the heterotrophic polyp loses its endosymbiont, a photoautotrophic dinoflagellate of the genus Symbiodinium (without photopigmentation, corals are colorless; hence the term ‘bleaching’). In other words, bleaching is the severing of the symbiotic integrity in corals. Because many species of corals critically depend on the energy generated by their symbionts, bleached corals will die, unless they become quickly recolonized by free-living Symbiodinium sp. or are repopulated by the few viable dinoflagellates that remain after a bleaching event (Douglas, 2003). Given the economic and ecological importance of corals, we need to understand

∗ Corresponding author. E-mail address: [email protected] (E.B. Muller). 0304-3800/$ – see front matter. Published by Elsevier B.V. doi:10.1016/j.ecolmodel.2011.01.004

how environmental stress may affect their symbiotic integrity. In this paper we investigate the negative impact of excess and harmful radiation, notably UVa and UVb, on the stability of coral symbioses using a modified version of a previously published model (Muller et al., 2009) based on dynamic energy budget (DEB) theory. DEB theory describes the rates at which an organism acquires resources from the environment and subsequently utilizes the energy and nutrients therein for production and maintenance (Nisbet et al., 2000; Kooijman, 2010). In line with its grand aim of bringing together, on grounds of shared ancestry, theory describing the acquisition and expenditure of resources of all organisms within a single conceptual framework, DEB theory has been successfully applied to a wide variety of prokaryotic and eukaryotic taxa. Such a unifying framework is of fundamental importance for modeling syntrophic symbiotic relationships for at least two reasons. First, in the course of evolution syntrophic symbiotic partners may merge to become a single organism such as the evolution of the eukaryotic cell from merging prokaryotes; a description of gradual merging requires an energetic basis common to each symbiotic partner (Kooijman and Troost, 2007). Second, within a unified framework, modeling the symbiotic relationship through nutrient and energy exchange is straightforward, given the unambiguous description of mass and energy flows in DEB theory. This unambiguous representation of mass and energy flows has a powerful

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corollary: DEB theory is a framework within which the integrated impact of a multitude of environmental factors can be investigated. Our model describes the syntrophic symbiotic relationship between a heterotrophic host and an internal photoautotrophic symbiont (Muller et al., 2009). It specifies the flows of matter and energy among host, symbiont and environment as a function of multiple limiting factors, in particular inorganic carbon and nitrogen, and irradiance. To maintain minimal complexity, the model has two passive regulation mechanisms: the symbiont shares only photosynthate that it cannot use itself, and the host delivers only excess nutrients to the symbiont. These two regulatory mechanisms suffice to yield a stable symbiotic relationship in scleractinian corals. According to the model, the dinoflagellate density in the polyp tends to increase with light deprivation or nitrogen enrichment, either directly or via food, but these tendencies are relatively modest under steady state conditions. Because the model predicts a biologically stable symbiotic relationship for a wide range of environmental conditions, it is a suitable starting point for an investigation of environmental impacts that may disrupt the integrity of symbiotic relationships. The primary aim of this paper is to assess the potential of excess and harmful radiation, notably UV, to cause bleaching in corals. Two types of negative impact of radiation are considered. First, detrimental radiation may impair the ability of the symbiont to conduct photosynthesis; this type reduces the rate at which the symbiont generates energy. Second, detrimental radiation may cause damage in the symbiont that needs to be repaired to remain functional; this type increases the cost to the symbiont to maintain homeostasis. In addition to assessing the bleaching potential of detrimental radiation, this paper investigates changes in steady state coral characteristics and performance, such as symbiont to host density and growth potential, caused by harmful radiation for a range of ambient nitrogen and (beneficial) PAR levels.

Fig. 1. Two state equations describe the dynamics of the host (white) and symbiont (green) in DEB theory (the process of ageing is ignored here): one for the dynamics of reserves and one for that of structural biomass (Nisbet et al., 2000; Kooijman, 2010). The rates of feeding and assimilation are functions of resource densities. In addition to assimilation, the fluxes of material and energy are maintenance, growth and reproduction (or maturation in juveniles). The assimilation rate as a function of the availability of multiple substrates is smoothly described with the concept of synthesizing units (SU) (Kooijman, 1998; Muller et al., 2001). Broken lines represent fluxes producing inorganic carbon and nitrogen, which can be recycled, notably by the photosynthesizing and assimilation SUs (see Muller et al., 2009 for model description and evaluation). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

2. Model in which * is the H or S for host or symbiont, respectively; jE∗ ,A∗ is the specific assimilation rate; kE∗ is the reserve turn-over rate; * is the fraction of the reserve mobilization flux dedicated to somatic processes; jE∗ ,D∗ is the specific maintenance rate; yV∗ ,E∗ is the yield of structure from reserves. The equation for structure states that the growth rate is proportional to the reserve mobilization flux dedicated to somatic processes less maintenance demands. The rate of change of the reserve density is the difference between the rates of assimilation (defined in DEB theory as the conversion of resources into reserves) and reserve mobilization. Assimilation in the host differs fundamentally from that in the symbiont. In the host, two parallel sources contribute to the assimilation flux, food and photosynthate (in this paper: glyceraldehyde-3-phosphate or glycerol) excreted by the symbiont, whereas assimilation in the symbiont depends on two complementary input fluxes, photosynthate and nutrients (in this paper: nitrogen in the form of ammonia). According to the DEB assumptions, the stoichiometry of reserves (and structure) is invariant, implying that an imbalance in the assimilation input fluxes will result in a partial rejection of the relatively abundant input. In other words, the symbiont can only assimilate photosynthate to the extent it has nitrogen available to form reserves for a given stoichiometry. The remainder of the photosynthate is excreted and made available to the host. Similarly, the host can only assimilate photosynthate insofar as it has nutrients available to produce reserves. Based on the synthesizing unit concept with two substrates (Kooijman, 1998), the symbiont assimilation rate, JES,AS ≡ jES,AS MVS , is:

We use a published model describing the syntrophic symbiosis between a heterotrophic host and a photoautotrophic endosymbiont (Muller et al., 2009). In short, this model, which is based on Kooijman’s dynamic energy budget (DEB) theory (Nisbet et al., 2000; Kooijman, 2010), specifies the acquisition and expenditure of nutrients and energy by each symbiotic partner. It assumes that symbiotic partners only exchange those nutrients and energy they have in excess and is fully constrained by mass and energy balances (see Fig. 1). Because the model and its foundation in DEB theory have been extensively detailed in the aforementioned publications, we will only present its state equations and the expressions that are of immediate relevance for modeling the impact of irradiation, and refer the reader to Table 1 for model assumptions and Muller et al. (2009) for a complete model specification. The state variables in DEB theory of interest here are the amount of structural biomass (MVH and MVS for the host and symbiont, respectively) and the density of reserves (mEH and mES for the host and symbiont, respectively). The dynamic equations for these state variables are: dmE∗ = jE∗ ,A∗ − kE∗ mE∗ dt

(1)

and ∗ kE∗ mE∗ − jE∗ ,D∗ dMV∗ ≡ JV∗ ,G∗ = MV∗ dt ∗ mE∗ + 1/yV∗ ,E∗

JES,AS =

(2)

1 1 jES,ASm MVS

+

nN,ES yES,G3P J ∗

N,+S

+

1 yES,G3P JG3P,AS

−

yES,G3P (J ∗

nN,ES +nN,ES JG3P,AS )

N,+S

(3)

Y. Eynaud et al. / Ecological Modelling 222 (2011) 1315–1322 Table 1 Assumptions and definitions. Assumptions 1

The state variables are structural biomass and the ratio of reserves to structural biomass; structural biomass and reserves each have an invariant chemical composition Assimilates from resources become part of reserves; reserves are used to form structural biomass and reproductive matter, and to maintain functional integrity Somatic maintenance rate is proportional to structural biomass Symbiont and host acquire resources at a rate proportional to their structural biomass. The symbiont receives all nutrients through the host. Resource handling times are independent of resource densities The rate at which reserves are utilized is independent of the ambient resource density. In steady state, the ratio of reserve and structural biomass is independent of structural biomass

2

3 4

5

Definitions 1

Assimilation is the process of converting resources into reserves Catabolism is the process of using reserves for growth, reproduction and maintenance Photodamage is the impact of detrimental radiation resulting in an increase in symbiont maintenance requirements Photoinhibition is the impact of detrimental radiation resulting in a decrease in photosynthesis Reserves consist of all somatic biomass not requiring maintenance, not just traditional storage compounds. Compounds in the reserves may have a metabolic role

2 3

4 5

is generally accepted that excess or harmful irradiation hampers the functioning of photosystem II and thereby reduces the capacity of the photosynthetic apparatus. The second type, photodamage, includes the breakage of covalent bonds in macromolecules, notably DNA, due to photo absorption and the oxidative damage caused by radicals and peroxides, which are formed, among other places, at the oxygen evolving complex of the photosynthetic apparatus. It is likely that these radicals and peroxides not only impair the photosynthetic apparatus, an impact which would classify as photoinhibition in this paper, but also other components of the biochemical machinery, an impact that would classify as photodamage proper in this paper. Recognizing that the detrimental potential of irradiance depends on wavelength, we separate the spectrum in three parts, UVb, UVa and PAR and use the photoinhibition model of Muller (2011), who used a simplified model for autotrophic assimilation but with similar formalism for photoinhibition The rate at which each of these types of radiation associate with the biochemical machinery is, respectively:



315 i JUVB,F

i  ()b,L (){JL,F }()d

= ˚S 280



400 i JUVA,F

i  ()b,L (){JL,F }()d

= ˚S



700

JPAR,F = ˚S

 ()b,L (){JL,F }()d

(4)

400

in which  is the wavelength; ˚S is the ratio of symbiont crosssectional surface area perpendicular to the direction of irradiance and symbiont structure;  () is a function accounting for selfshading, light attenuation and scattering; {JL,F }() is the (surface specific) irradiance of photons with wavelength ; b,L () is the probability an arriving photon is captured by the photosynthetic apparatus. This wavelength specific binding probability is similar to the biological weighting factor as described in the literature (e.g. Sathyendranath and Platt, 1989; Cullen et al., 1992; Schofield et al., 1996). Using the synthesizing unit concept with two substrates, the rate of photosynthesis is: JG3P,AS =

1 1 jG3P,ASm MVS

+

1

J∗ C,+S

+

1 yG3P,L JPAR,F MVS

−

1

(5)

(6)

315



700 i  ()b,L (){JL,F }()d

i = ˚S JPAR,F

in which jES,ASm is the maximum specific symbiont assimilation rate; nN,ES is the molar N:C ratio of symbiont reserves; yES,G3P is the ∗ is the arrival yield of symbiont reserves from photosynthate; JN,+S rate of ammonia; JG3P,AS is the rate of photosynthesis (i.e. carbon fixation). To model the rate of photosynthesis, we consider a potentially limiting supply of carbon dioxide and light. The rate at which photons are captured by the photosynthetic apparatus, JPAR,F , is (Muller, 2011):

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400 i () is the probability that an arriving photon in which b,L with wavelength  associates detrimentally with the biochemical machinery. Photoinhibition reduces the rate of photosynthesis according to:

 JG3P,AS =

0 JG3P,AS

1+

i JPAR,F

JI,PAR

+

i JUVA,F

JI,UVA

+

i JUVB,F

−1 (7)

JI,UVB

0 with JG3P,AS as the rate of photosynthesis in absence of photoini as the inhibition scaling flux for * = PAR, UVA or hibition and JI,∗ UVB. As for photodamage, we consider mildly damaging irradiance levels only. Consistently, we assume that, with those levels, induced damage constitutes a repairable insult to cellular homeostasis and exclude damage induced mortality. Furthermore, considering that short-lived reactive oxygen species are formed especially at the photosynthetic machinery, we assume that the symbiont but not the host is subject to the impact of photo damaging irradiance. Thus, the specific somatic maintenance rate of the symbiont is the target of photodamage. Assuming that somatic maintenance requirements increase proportionally with harmful radiance beyond some threshold value, the specific somatic maintenance rate of the symbiont becomes:



jES,DS =

0 jES,DS

1+

0 i − JPAR,F ) (JPAR,F

JDam,PAR

+

+

0 i − JUVA,F ) (JUVA,F

JDam,UVA

+

+

0 i − JUVB,F ) (JUVB,F

JDam,UVB



+

(8)

J∗ +yG3P,L JPAR,F MVS C,+S

∗ in which jG3P,ASm is the maximum specific photosynthesis rate; JC,+S is the arrival rate of carbon dioxide; yG3P,L is the number of quanta needed to fix one carbon dioxide molecule. We consider two types of detrimental effect of excess and harmful irradiation: a reduction in photosynthetic capacity and damage of cellular components other than the photosynthetic machinery. The first type is commonly called photoinhibition. Although several, mutually nonexclusive mechanisms causing photoinhibition have been proposed (see Tyystjarvi, 2008 for a recent review), it

0 as the specific maintenance rate without photodamwith jES,DS 0 as the threshold flux below which photodamage does not age, J∗,F

i occur, and JDam,∗ as the damage scaling flux for * = PAR, UVA or UVB. To parameterize the model, we use values plausible for scleractinian corals (see Muller et al., 2009 for parameter values and justification) and choose parameter values scaling damaging and inhibitory potential of irradiance such that a full range of dynamic behavior is observed (see Table 2); these values are within the

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Table 2 Symbols and parameter values. Symbol ∗ JC,+S ∗ JN,+S

JES,AS jES,AS jES,ASm JEH,AH jEH,DH 0 jES,DS jES,DS JG3P,AS 0 JG3P,AS jG3P,ASm JVS,GS JVH,GS JL,F JPAR,F i JPAR,F i JUVA,F i JUVB,F 0 JPAR,F 0 JUVA,F 0 JUVB,F JI,PAR JI,UVA JI,UVB JDam,PAR JDam,UVA JDam,UVB kES kEH mEH MVH mES MVS nN,ES yES,G3P yVS,ES yVH,EH yG3P,L H S i () b,L ˚S 

Interpretation Total carbon dioxide assimilation rate symbiont Total ammonia assimilation rate symbiont Assimilation rate symbiont Specific assimilation rate symbiont Maximum specific assimilation rate symbiont Assimilation rate host Specific maintenance rate host Specific maintenance rate symbiont without photodamage Specific maintenance rate symbiont G3P production rate G3P production rate without photoinhibition Maximum specific G3P production rate Symbiont structure growth rate Host structure growth rate Total irradiation Total PAR irradiation Total detrimental PAR irradiation Total UVA irradiation Total UVB irradiation PAR photodamage threshold UVa photodamage threshold UVb photodamage threshold PAR photoinhibition scaling parameter UVa photoinhibition scaling parameter UVb photoinhibition scaling parameter PAR photodamage scaling parameter UVa photodamage scaling parameter UVb photodamage scaling parameter Turn over rate of reserves in symbiont Turn over rate of reserves in host Density of host reserves Structural biomass of host Density of symbiont reserves Structural biomass of symbiont Molar ratio of N and C in symbiont reserves Yield of symbiont reserves from G3P Yield of structure from reserves symbiont Yield of structure from reserves host Yield of G3P from photons Fraction catabolic flux to growth and maintenance host Fraction catabolic flux to growth and maintenance symbiont Probability symbiont photosynthesis SU binds photon Ratio symbiont surface area to structure Function relating irradiance and arrival flux of quanta

range of realistic values (Muller, 2011). As a default value, we consider that the irradiance of UVb and UVa is 1% and 10%, respectively, of that of PAR, which is a realistic value for corals living at a depth of about 10 meters (de Mora et al., 2000). We assume an environment in which ambient resource densities are constant independent variables; then, after some transient dynamics, the system will eventually exhibit exponential growth or decline of all its components, and ratios of model fluxes will remain constant (Muller et al., 2009). 3. Results We investigate the impact of inhibitory and damaging irradiance on several characteristics of the symbiotic assemblage, such as the ratio of symbiont to host structure, specific growth rate of the host (which equals that of the symbiont) and reserve densities of host and symbiont in a constant environment. To clarify the role of environmental conditions other than harmful irradiance on the impacts observed, we consider a range of ambient nitrogen and (beneficial) PAR levels. We only show results about the detrimental impact of UVb, as it has strongest impact, and note that results obtained with UVa and PAR are similar, except that the impacts are weaker than those observed with UVb. In order to maximize transparency, we will only show results for systems in which the

Value – – – – ∞ – 0.2 0.2 – – – 6 – – 0–1000 – 0–900 0–90 0–10 0 0 0 ∞ ∞ 4 ∞ ∞ 2 1.2 0.1 – – – – 0.15 0.8 0.8 0.8 0.05 1 1 1 5 × 10−6 1

Units

Comment −1

mol C day mol N day−1 mol C day−1 mol C mol C−1 day−1 mol C mol C−1 day−1 mol C day−1 mol C mol C−1 day−1 mol C mol C−1 day−1 mol C mol C−1 day−1 mol C day−1 mol C day−1 mol C mol C−1 day−1 mol C day−1 mol C day−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 ␮mol quanta m−2 s−1 day−1 day−1 mol C mol C−1 ␮M C mol C mol C−1 ␮M C mol N mol C−1 mol C mol C−1 mol C mol C−1 mol C mol C−1 mol C mol quanta−1 – – – m2 mol C−1 –

Variable, see Muller et al. (2009) Variable, see Muller et al. (2009) Variable, see text Variable, see text See Muller et al. (2009) Variable, see Muller et al. (2009) See Muller et al. (2009) See text Variable Variable Variable See Muller et al. (2009) Variable Variable See text See Muller (2011) See text See text See text See text See text See text See text See text See text See text See text See text See Muller et al. (2009) See Muller et al. (2009) State variable State variable State variable State variable Redfield ratio See Muller et al. (2009) See Muller et al. (2009) See Muller et al. (2009) See Muller et al. (2009) See Muller et al. (2009) See Muller et al. (2009) See Muller et al. (2009) See Muller et al. (2009) See Muller et al. (2009)

host does not feed, i.e. the symbiont is solely responsible for the acquisition of energy and the host takes up nitrogen in the form of DIN only, but stress that results obtained with host feeding are qualitatively quite similar. With photoinhibition, the specific photosynthetic rate as a function of irradiance resembles that of a standard experimental PI curve with marked negative impact of excess radiation (results not shown, but see Eq. (7)). The specific photosynthetic rate is highest at an intermediate irradiance level. Below this level, PAR is a relatively strongly limiting factor for photosynthesis, implying that an increase in PAR stimulates photosynthesis more than that the concomitant increase in UVb can reduce photosynthesis (recall that UVb is a fixed fraction of total radiation in the simulations). Above this optimum level, the increasingly strong negative effects of photoinhibition outweigh the stimulatory effects of PAR. With photoinhibition, the specific rate of excess photosynthate production is highest at intermediate irradiance levels (see Fig. 2B). This excess, which is delivered to the host, cannot be assimilated by the symbiont due to a lack of sufficient nitrogen to meet the stoichiometric constraints to form symbiont reserves. Accordingly, the specific rate of excess photosynthate production decreases with increasing ambient nitrogen levels, a trend which is most clearly observed with photoinhibition and to a much lesser extent with

Y. Eynaud et al. / Ecological Modelling 222 (2011) 1315–1322

Fig. 2. The specific rate of excess photosynthate production, i.e. the specific rate at which the symbiont excretes photosynthate in the host, in steady state is a function of irradiance and ambient nitrogen levels. Without effects of detrimental radiation (A), the specific rate of excess photosynthate production approaches an asymptotic maximum with increasing irradiance due to saturation of the photosynthetic machinery; it declines with increasing ambient nitrogen levels, as the assimilation of photosynthate by the symbiont requires nitrogen. With photoinhibition (B), the specific rate of excess photosynthate production shows a maximum at intermediate irradiance. At higher irradiance levels, the inhibitory impact of extra irradiance increasingly stronger outweighs its stimulatory impact on photosynthesis. Photodamage (C) has little impact on the specific rate at which the symbiont excretes photosynthate in the host.

photodamage (see Fig. 2C) or without detrimental effect of irradiance (see Fig. 2A). The lack of a relatively strongly pronounced trend in the latter two cases is the result of a compensatory mechanism: an increase in nitrogen availability yields a higher production of symbiont reserves, which in turn results in a higher production of

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structural biomass, including photosynthetic machinery. The result is a higher production of photosynthate and thus an increase in the relative scarceness of nitrogen for symbiont assimilation. The mechanisms described above also explain the trends observed in the reserve densities of the symbiont and host for model runs without detrimental impact of irradiance or those with the impact of photoinhibition, but not those with photodamage. Without detrimental effects of irradiance, the host and symbiont densities are saturating functions of irradiance and nitrogen availability (see Fig. 3A for the symbiont reserve density; host results not shown). With photoinhibition, these densities reach a maximum at intermediate irradiance levels (see Fig. 3B for the symbiont reserve density; host results not shown). However, the trend in the symbiont reserve density for model runs with the impact of photodamage needs an additional explanation. The impact of photodamage on the reserve density of the host is quite insignificant (results not shown), but the symbiont reserve density increases dramatically with increasing irradiance, i.e. with increasing photodamage (see Fig. 3C). Photodamage increases the maintenance requirements of the symbiont and thereby stunts growth. Thus, an increase in photodamage decreases the amount of symbiont structure, which implies an increase in symbiont reserve density, as this density is the ratio of the amount of reserves and structural biomass. In fact, in steady state, the symbiont reserve density increases linearly with the maintenance rate (see Eq. (2)). The trends in the symbiont to host structure reflect shifts in the balance between light and nitrogen limitation (see Fig. 4). When the specific rate of photosynthesis is relatively low, i.e. at low irradiance and with photoinhibition also at high irradiance levels, photosynthate is in relatively short supply, implying that the symbiont retains a relatively large fraction of the photosynthate it produces. As a result, the ratio of symbiont to host structure is relatively high. Furthermore, the ratio of symbiont to host structure increases with nitrogen availability, as an increase in nitrogen availability implies that the symbiont can use a larger fraction of photosynthate to produce more reserves and thus more structural biomass. This trend is less pronounced with photodamage, because an increase in symbiont reserve production only partially translates into an increase in structure. With photodamage, as irradiance increases, maintenance requirements take an increasing proportion of the flux of reserves mobilized for growth and maintenance. Without the detrimental impacts of UVb, the long-term specific growth rates of host and symbiont increase with irradiance and ambient nitrogen to an asymptotic maximum (see Fig. 5; note that in steady state the long-term specific growth rate of host and symbiont are necessarily equal). With either photoinhibition or photodamage occurring, this trend is still evident with increasing ambient nitrogen levels. However, because photoinhibition slows down the rate of photosynthesis and photodamage decreases the rate at which reserves are committed to symbiont growth, the specific growth rate is highest at intermediate irradiance levels. At higher irradiance levels, the increasingly stronger negative effects of photoinhibition or photodamage outweigh the stimulatory effects of PAR, as these stimulatory effects decelerate with increasing PAR. Furthermore, the negative impact of photoinhibition and photodamage on the specific growth rate can be partly compensated by increasing the availability of nitrogen in the environment. Thus far we have explored the effect of detrimental irradiance, here conveniently identified with UVb, while keeping the ratio of UVb to PAR constant. To illustrate the influence of for instance, water depth, the density of UVb absorbing particles or the filtering capacity of the ozone layer, we have also calculated the specific growth rate as function of the fraction of UVb in irradiance at constant ambient nitrogen (2 ␮M) and irradiance levels (750 ␮mol quanta m−2 s−1 ; see Fig. 6). Not surprisingly, with

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Fig. 3. The reserve density of the symbiont in steady state is a function of irradiance and ambient nitrogen levels. Without effects of detrimental radiation (A), the symbiont reserve density approaches an asymptotic maximum with increasing irradiance and ambient nitrogen levels due to saturation of the photosynthetic and assimilatory machineries. Photoinhibition (B) has a relatively modest impact on the reserve density of the symbiont, as photosynthate is, even at high irradiance levels, produced in excess (see Fig. 2B). Photodamage (C) leads to a strong increase in the symbiont reserve density, as it suppresses growth by increasing symbiont maintenance requirements. Although the amount of reserves declines with photodamage, the amount of structural biomass declines relatively more, with the result that the reserve density increases.

either photoinhibition or photodamage, the specific growth rate declines with the fraction of UVb in the irradiance. However, this decline with either type of impact accelerates with an increasing UVb content in irradiance. This trend is general for all PAR and ambient nitrogen levels considered in this study (results not shown).

Fig. 4. The ratio of the symbiont to host structural biomass in steady state is a function of irradiance and ambient nitrogen levels. Without effects of detrimental radiation (A), this ratio decreases with irradiance, as the host receives more photosynthate at higher irradiance levels (see Fig. 2), and increases with ambient nitrogen levels, as the symbiont assimilates a relatively larger fraction of photosynthate at higher nitrogen levels. Photoinhibition (B) causes the rate at which the host is receiving photosynthate to decline, with the result that the amount host structural biomass decreases and the ratio of the symbiont to host structural biomass increases. Photodamage (C) has the opposite effect, as it suppresses symbiont growth by increasing symbiont maintenance requirements.

4. Discussion Given the numerous environmental insults that scleractinian corals must endure in the present day ocean, it is extremely difficult to assign a cause to a bleaching event. Pollution, ocean acidification, harmful irradiance and a rising ocean temperature, among other

Y. Eynaud et al. / Ecological Modelling 222 (2011) 1315–1322

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Fig. 6. The specific growth rate of host and symbiont in steady state declines with increasing exposure to UVb causing photoinhibition (solid line) or photodamage (broken line). The detrimental impact of UVb accelerates with increasing UVb levels (jL,F = 750 ␮mol quanta m−2 s−1 ; jI,UVB = 4 ␮mol q m−2 s−1 ; jDAM,UVB = 2 ␮mol quanta m−2 s−1 ; DIN = 2 ␮M).

Fig. 5. The specific growth rates of host and symbiont in steady state are functions of irradiance and ambient nitrogen levels (in steady state these growth rates are similar). Without effects of detrimental radiation (A), the specific growth rates approach an asymptotic maximum with increasing irradiance and ambient nitrogen levels. With photoinhibition (B) and photodamage (C), the specific growth rates are highest at an intermediate irradiance level; beyond this level the detrimental impacts of extra radiation outweigh its stimulatory impacts.

stress factors, may all impact in some way or another the integrity of the symbiotic relationship between polyp and dinoflagellates. Models are a powerful tool for identifying the symptoms of a particular insult and for projecting the potential of this insult to destroy the integrity of a symbiotic relationship. An appropriate model can help us extract information from existing data and design targeted, cost efficient experiments. Here, we use an established modeling framework to investigate the bleaching potential of relatively mild exposure to excess and harmful radiation, i.e. levels of radiation

causing the rate of photosynthesis to slow down (defined in this paper as photoinhibition) or causing the rate of repair costs due to sublethal damage to increase (defined here as photodamage). There are striking differences between the projected impact of photoinhibition and photodamage. The consequences of photoinhibition are expressed more strongly in the host than in the symbiont, whereas the opposite is the case with photodamage. Photoinhibition reduces the energy supply to the host (see Fig. 2) more than that to the symbiont, since the symbiont takes priority in assimilating photosynthate in the model. As a result, the ratio of symbiont to host structural biomass increases (see Fig. 4), implying that the symbiont density in the host increases. Thus, photoinhibition cannot explain coral bleaching. Although it may appear that corals look healthy with photoinhibition, it does affect coral growth rates (see Fig. 6). In fact, it is quite worrisome that the suppression of coral growth rates accelerates with increasing UVb radiation without a clear sign of a decline in coral health (i.e. a decline in symbiont density). Photodamage yields symbionts with a higher content of energy reserves (see Fig. 3), but a lower ratio of symbiont to host structural biomass (see Fig. 4). Thus, in contrast to photoinhibition, photodamage causes a reduction in the symbiont density in the host, and, therefore, can lead to coral bleaching. The model observations discussed above are the result of shifting energy and nutrient flows within and between host and symbiont due to detrimental radiation. In the model, host and symbiont endure excess and harmful radiation passively, as the model does not include active control and response mechanisms. However, real coral symbioses respond actively to detrimental radiation. For instance, the host can produce mycosporine-like amino acids compounds that absorb radiation, notably high energy photons in the UV and blue range of the spectrum (Dunlap and Chalker, 1986). These compounds are likely to give at least partial protection up to some threshold level. In the context of the model, they would change parameter values and thereby cause the inhibitory or damaging impact of radiation to become apparent at higher irradiance levels, but they would not change model behavior qualitatively. In other words, the trends projected by the model would not change. Another potentially important active control mechanism not included in the model is the ability of the host to stimulate symbionts to increase photosynthate excretion through host release factors (Gates et al., 1995; Davy and Cook, 2001). Although it

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seems unlikely the host needs to manage the flow of energy it receives from the symbiont, as photosynthate is generally produced in excess to meet the requirements of both symbiont and host (see Muller et al., 2009), it may use this control mechanism to acquire high quality compounds, i.e. nitrogen rich compounds, from the symbiont. Such a control mechanism would mitigate the impacts of detrimental radiation as presented in this paper, especially impacts due to photoinhibition as these impacts start with a reduction of the flow of photosynthate to the host, but it would not change observed trends qualitatively. Furthermore, the model does not include symbiont succession. Symbiodinium sp. in scleractinian corals form a genetically diverse group of dinoflagellates from different clades and with different sensitivities to temperature and radiation, among other environmental factors (Baker, 2003). Thus, a change in environmental conditions may bring about a change in (dominant) symbiont type in a coral. Consequently, corals may be more resilient in their response to detrimental radiation than suggested by the results in this paper. However, although a succeeding symbiont type may be more tolerant to detrimental radiation, it will also be affected, albeit at higher exposure levels. Therefore, we do not expect model trends to change qualitatively as a result of symbiont succession. In sum, our model analysis shows that photoinhibition and photodamage can reduce the health of corals, but in different ways. The impact of photoinhibition on host and symbiont is, in effect, similar to that of low irradiance. It affects the host more strongly than the symbiont and has relatively little impact when ambient nitrogen levels are very low, as under those conditions nitrogen rather than energy availability is the most important factor determining the budgeting of nutrients and energy in host and symbiont. This conclusion illustrates a powerful feature of DEB theory: it naturally integrates the effects of multiple environmental factors – here: nitrogen availability, and beneficial and detrimental radiation – on the performance of organisms; the impact of other factors, such as toxicants and temperature, can be seamlessly incorporated in the modeling framework (see Kooijman, 2010, for several examples). Photodamage predominantly affects the symbiont and may, either alone or in combination with other environmental stressors, lead to coral bleaching. Acknowledgements We thank Bharath Ananthanthasubramaniam, Charlie Boch, Frank Doyle, Peter Edmunds, Ruth Gates, Tin Klanjscek, Dan Morse, Laure Pecquerie, Mathias Gauduchon, David Nérini, Marc Tedetti, Jean-Francois Rontani and Jean-Christophe Poggiale for the many valuable discussions that helped shape the manuscript. The authors are also grateful to two anonymous reviewers for useful comments.

This is a contribution of the Moorea Coral Reef (MCR) Long Term Ecological Research (LTER) site. The research was supported in part by grant EF-0742521 from the U.S National Science Foundation, and by the Institute for Collaborative Biotechnologies through contract no. W911NF-09-D-0001 from the U.S. Army Research Office. The content of the information herein does not necessarily reflect the position or policy of the Government and no official endorsement should be inferred. References Baker, A.C., 2003. Flexibility and specificity in coral–algal symbiosis: diversity, ecology, and biogeography of symbiodinium. Annu. Rev. Ecol. Evol. Syst. 34, 661–689. Brown, B.E., 1997. Coral bleaching: causes and consequences. Coral Reefs 16, S129–S138. Cullen, J.J., Neale, P.J., Lesser, M.P., 1992. Biological weighting function for the inhibition of phytoplankton photosynthesis by ultraviolet-radiation. Science 258, 646–650. Davy, S.K., Cook, C.B., 2001. The influence of ‘host release factor’ on carbon release by zooxanthellae isolated from fed and starved Aiptasia pallida (Verrill). Comp. Biochem. Physiol. A: Mol. Integr. Physiol. 129, 487–494. de Mora, S., Demers, S., Vernet, M., 2000. The Effects of UV Radiation in the Marine Environment. The Press Syndicate of the University of Cambridge, Cambridge, p. 324. Douglas, A.E., 2003. Coral bleaching – how and why? Mar. Pollut. Bull. 46, 385–392. Dunlap, W.C., Chalker, B.E., 1986. Identification and quantitation of near-UV absorbing compounds (S-320) in a hermatypic scleractinian. Coral Reefs 5, 155–159. Gates, R.D., Hoeghguldberg, O., Mcfallngai, M.J., Bil, K.Y., Muscatine, L., 1995. Free amino-acids exhibit anthozoan host factor activity – they induce the release of photosynthate from symbiotic dinoflagellates in-vitro. Proc. Natl. Acad. Sci. U. S. A. 92, 7430–7434. Kooijman, S.A.L.M., 1998. The synthesizing unit as model for the stoichiometric fusion and branching of metabolic fluxes. Biophys. Chem. 73, 179–188. Kooijman, S.A.L.M., 2010. Dynamic Energy and Mass Budgets in Biological Systems. Cambridge University Press, Cambridge. Kooijman, S.A.L.M., Troost, T.A., 2007. Quantitative steps in the evolution of metabolic organisation as specified by the dynamic energy budget theory. Biol. Rev. 82, 113–142. Muller, E.B., 2011. Synthesizing units as modeling tool for photosynthesizing organisms with photoinhibition and nutrient limitation. Ecol. Model. 222, 637–644. Muller, E.B., Kooijman, S.A.L.M., Edmunds, P.J., Doyle, F.J., Nisbet, R.M., 2009. Dynamic energy budgets in syntrophic symbiotic relationships between heterotrophic hosts and photoautotrophic symbionts. J. Theor. Biol. 259, 44–57. Muller, E.B., Nisbet, R.M., Kooijman, S., Elser, J.J., McCauley, E., 2001. Stoichiometric food quality and herbivore dynamics. Ecol. Lett. 4, 519–529. Nisbet, R.M., Muller, E.B., Lika, K., Kooijman, S.A.L.M., 2000. From molecules to ecosystems through dynamic energy budget models. J. Anim. Ecol. 69, 913–926. Sathyendranath, S., Platt, T., 1989. Computation of aquatic primary production – extended formalism to include effect of angular and spectral distribution of light. Limnol. Oceanogr. 34, 188–198. Schofield, O., Prezelin, B., Johnsen, G., 1996. Wavelength dependency of the maximum quantum yield of carbon fixation for two red tide dinoflagellates, Heterocapsa pygmaea and Prorocentrum minimum (pyrrophyta): implications for measuring photosynthetic rates. J. Phycol. 32, 574–583. Tyystjarvi, E., 2008. Photoinhibition of photosystem II and photodamage of the oxygen evolving manganese cluster. Coordin. Chem. Rev. 252, 361–376.