Coral-algae metabolism and diurnal changes in the CO₂-carbonate system of bulk sea water

The relationship between G_net and Ω_arag

The linear regression of G_net plotted as a function of Ω_arag (Fig. 2) has become a widespread method of describing coral and coral reef calcification. A significant statistical relationship is obtained, with substantial variance that is generally assumed to be largely sampling error, or the result of other factors which influence G_net. However, the explanation appears be more complex, as will be discussed in the following sections.

Diel hysteresis, phase lags and night calcification patterns

McMahon et al. (2013) quantified G_net in a healthy coral reef lagoon in the Great Barrier Reef during different times of day. Their observations revealed a diel hysteresis pattern in the G_net versus Ω_arag relationship. This phenomenon can be demonstrated by labeling the points in Fig. 2 with the hour of day as shown in Fig. 3. The diel pattern moves from the lower left quadrant early in the day toward the upper right through mid-day and then back to the lower center during the night before returning to the lower left quadrant at first light. The pattern is nearly identical for the “Corals only” mesocosm (Fig. 3A) and the “Corals plus Algae” (Fig. 3B), which tracked each other closely (Fig. 1). The “Algae only” mesocosm did not show this pattern. The linear regression for the G_net vs. Ω_arag data for the mesocosm with coral (Fig. 2) accounted for part of the variance (R² = 0.40). A linear regression does not adequately describe the variance resulting from the diel pattern.

Cyronak et al. (2013) used chambers to measure in situ benthic solute fluxes at three different advection rates at Heron Island lagoon, Australia and observed a strong diurnal hysteresis pattern similar to that in Fig. 3. They suggested that diel hysteresis is caused by the diurnal interaction between photosynthesis and respiration. The data did not follow a trend consistent with the Ω_arag of the water column being the main driver of carbonate precipitation and dissolution. Instead, carbonate precipitation and dissolution in these sediment communities is linearly correlated to the rates of photosynthesis and respiration (P_net) occurring over the same time period.

Phase shifts

Evaluation of phase relations for the various parameters listed in Table 2 can be facilitated by scaling each variable on a 0 to 1 scale. The normalized value of a_i for variable A in the ith row was calculated using the equation: (13)${\displaystyle \text{Normalized value }\left(a_i\right)=\frac{a_i-A_{\min }}{A_{\max }-A_{\min }}}$ where A_min is the minimum value for variable A and A_max is the maximum value for variable. Figure 4 summarizes the results for the variables most often considered in the literature (pH, Ω_arag, P_net and G_net).

Figure 4 shows that peak pH and Ω_arag lag behind G_net throughout the daily cycle by two or more hours. The figure also shows that peak G_net follows P_net during daylight photosynthetic hours with a reverse during the nighttime hours. Shamberger et al. (2011) reported that Ω_arag lags behind G_net on the reefs of Kaneohe Bay, Hawaii. McMahon et al. (2013) reported that peak G_net rates occurred 2–3 h before the Ω_arag maximum on a healthy coral reef on the Great Barrier Reef. Thus Ω_arag (along with closely correlated [CO₃²⁻], pH and [DIC]:[H⁺] ratio) is not the primary driver of coral calcification over a diurnal cycle. The paradigm that Ω_arag correlates with G_net on a global scale must be tempered with the caveat that other processes have a much greater influence on calcification on smaller spatial and temporal scales. The data presented above show that diurnal irradiance drives P_net, which in turn drives G_net, and which alters pH, which controls [CO₃²⁻] and Ω_arag as well as other variables based on concentration such as the ratio of [DIC] to [H⁺]. A better understanding of this hierarchy will resolve many of the contradictions in the literature on coral reef calcification.

Night calcification

Laboratory studies show that coral calcification continues in darkness, but at a lower rate than observed in light enhanced calcification (Schneider & Erez, 2006). Night calcification rates have generally been assumed to be low and constant at night, although this assumption has largely gone untested. Figures 1 and 4 show decreasing dark calcification following sunset, reaching zero near midnight followed by an increasing rate of dark calcification and an increase in respiration (Figs. 5C and 5D) that rises to a peak at 03:00 well before dawn. This pattern has occurred consistently in our mesocosm experiments, with the same pattern observed in 30 separate mesocosm runs with different communities under various conditions as well as in flume studies at our site (Murillo, Jokiel & Atkinson, 2014). Barnes & Crossland (1980) used time-lapse photography to measure diurnal growth in the staghorn coral Acropora acuminata and found that night-time extension rate was similar to or greater than day-time extension. They suggested that, “symbiotic association permits rapid growth because the coral can invest in flimsy scaffolding at night with the certainty that bricks and mortar will be available in the morning”. Wooldridge (2013) has proposed a new model for “dark” coral calcification, whereby O₂-limitation of aerobic respiration during the night initiates a homeostatic host response that forms the skeletal organic matrix. The matrix formed at night subsequently allows rapid growth of the aragonite fibers during the “light-enhanced” period of calcification, when abundant energy derived from photosynthesis is available. Perhaps the mid-night calcification minimum observed in Figs. 1 and 4 at 00:00 reflects this period of organic matrix formation that precedes the 03:00 night calcification peak.

Diurnal changes in concentration of A_T, pH, Ω_arg and DO

The variables of A_T, pH, Ω_arg DIC, and DO are concentrations while P_net and G_net are flux rates. Care must be taken when comparing concentrations to flux rates because flux rate can be high when concentration is high or low. Or flux rate can be low when concentration is high or low. Figure 4 shows patterns that are difficult to interpret because the figure mixes flux rates with concentrations. This issue will be discussed and resolved later in this discussion, but first we will compare differences in concentrations of key variables over the diurnal cycle (Fig. 5).

Figure 5 reveals several important patterns:

1. Alkalinity in the “Algae only” mesocosm remained high during the entire diurnal cycle. In contrast, the mesocosms containing corals showed lower A_T (Fig. 5A) caused by rapid calcification. A_T reduction by the corals was greatest during the daylight hours when G_net was high (Fig. 1) with the difference diminishing during nighttime hours.

2. The two mesocosms with algae maintained a higher Ω_arag throughout the mid-day portion of the diurnal cycle (Fig. 5B) which can be attributed to higher pH resulting from rapid rates of algae photosynthesis and coral photosynthesis (Eqs. (6)–(8)), with a less pronounced difference during the rest of the cycle.

3. The extreme difference in Ω_arag between the “Corals only” and the “Corals plus Algae” mesocosms (Fig. 5B) did not produce a corresponding difference in G_net between the two mesocosms (Fig. 1), which demonstrates that Ω_arag is uncoupled from G_net and explains differences encountered when comparing the Ω_arag versus G_net relationship in different systems with different diurnal P_net regimes.

4. Night-time pH and Ω_arag values (Figs. 5B and 5C) show less variability than G_net (Fig. 1).

5. The high biomass in the “Coral plus Algae” mesocosm (Fig. 5D) resulted in the highest O₂ values during daylight hours (due to photosynthesis) and the lowest O₂ during the night (due to respiration). The “Algae only” treatment had the second highest daytime level O₂ due to algal photosynthesis and relatively high levels of O₂ at night.

6. The 03:00 calcification peak observed in Fig. 1 is shown by both a decrease in O₂ concentration and a drop in pH due to accelerated respiration. DO (Fig. 5D) and the pH (Fig. 5C) are measured independently and both show this effect to corroborate the observation.

Plotting DIC versus A_T (Fig. 6) demonstrates the major influence of P_net on seawater Ω_arag. Calcification and dissolution shift A_T values horizontally along the abscissa in Fig. 6 and influence DIC values vertically along the ordinate. However, photosynthesis and respiration change DIC along the ordinate without changing A_T. The observed hysteresis pattern results from P_net driving G_net and increasing pH. A linear relationship accounting for only half of the variance (R² ≈ 0.5) between DIC and A_T was observed for the two rapidly calcifying mesocosms containing corals. This relationship does not hold for the low-calcification “Algae only” mesocosm.

As pointed out by McMahon et al. (2013), connecting the points on a graph of A_T vs. DIC reveals a circular hysteresis pattern over the diel cycle as shown for the G_net versus Ω_arag plot (Fig. 6). G_net can account for changes in both the A_T and DIC concentrations. However, P_net can only account for changes DIC concentration. Therefore, Ω_arag is a function of the changes in carbonate chemistry due to both P_net and G_net, and any changes in DIC concentration relative to A_T will result in different influences on Ω_arag. For example, in systems with high organic production relative to calcification (Coral plus Algae mesocosm), Ω_arag will increase during daylight due to high pH caused by high uptake of CO₂ used for photosynthesis (Fig. 5D). Conversely, in systems with low organic production relative to calcification (Coral only mesocosm), Ω_arag will decrease due to the uptake of A_T. Any decrease in G_net associated with an increase in P_net will increase Ω_arag and change the way that G_net responds to OA. Therefore, any prediction of future global changes on coral reef G_net based on oceanic seawater Ω_arag must also take into account the influence of future localized P_net on G_net and Ω_arag as well as changes in carbonate dissolution of reef carbonates as described by Murillo, Jokiel & Atkinson (2014) for each reef location.

Comparisons between the hourly and daily G_net and P_net values (Table 3) show a similar calcification rate for both the “Coral only” mesocosm and the “Coral plus Algae” mesocosm in spite of the differences in DO, pH, A_T (Fig. 5) and P_net. However, daily P_net for the “Coral plus Algae” mesocosm was only one third of the P_net of the “Coral only” mesocosm. Hourly production was much higher in the “Corals plus Algae” mesocosm during the daylight hours, but production was consumed by extremely high respiration during nighttime hours. The “Algae only” mesocosm showed very low daily G_net and extremely high daily P_net.

Anthony, Kleypas & Gattuso (2011) proposed a model that areas dominated by algal beds draw CO₂ down and elevate Ω_arag, potentially offsetting ocean acidification impacts at the local scale. Their model is based on the paradigm that G_net is controlled by Ω_arag. Results suggested that a shift from coral to algal abundance under ocean acidification can lead to improved conditions for calcification (i.g. increased Ω_arag) in downstream habitats and that alga beds can provide a significant mechanism for buffering ocean acidification impacts at the scale of habitat to reef. However, this conclusion is at odds with the measured values shown in Table 3 and Fig. 5. G_net in the “Corals plus Algae” treatment was the same as the “Coral Only” treatment even though the Ω_arag was much higher. In addition, the presence of the algae caused a precipitous drop in P_net. The flaw in their model appears to be the assumption that G_net is controlled by Ω_arag. Algal photosynthesis increases pH which shifts the equilibrium to higher [CO₃²⁻] and thus higher Ω_arag. There is a direct correlation between G_net and Ω_arag for a specific reef community, but not a cause and effect relationship.

Diurnal changes in material flux (P_net, G_net, H⁺ flux and DIC flux)

G_net and P_net are measures of material flux. DO, pH and DIC are measures of concentration. The preceding discussion and numerous publications often compare concentrations of one material to flux rate of another material or vice versa. Much more can be learned by plotting DIC flux and H⁺ flux rather than [DIC], [H⁺] or pH in relation to P_net and G_net. DIC flux and H⁺ flux were calculated using the box model and graphed on a 0 to 1 scale in the same manner as in Fig. 4 with the result presented as Fig. 7. This figure illustrates the dynamic geochemical and physiological relationships involved in coral and coral reef metabolism.

DIC flux (uptake) in the highly calcifying mesocosms containing coral (Fig. 7) increases with increasing P_net from 06:00 until mid-day peak P_net and then decreases rapidly as P_net decreases with decreasing irradiance. Furla et al. (2000) demonstrated the presence of a DIC pool within coral tissues. The size of this pool was dependent on the lighting conditions, since it increased 39-fold after 3 h of illumination. If we apply this observation to the data shown in Fig. 7, it appears that the DIC pool had increased by mid-day, so rate of DIC uptake dropped rapidly as irradiance and photosynthesis declined. However, note that the high dissipation rates of H⁺ continued for 2–3 h following the peak rates of P_net and G_net as the corals rid themselves of the backlog of H⁺ generated by rapid calcification. Thus the lag of pH behind the peak flux rates of P_net and G_net (Figs. 4A and 4B) represents a disequilibrium that results from the lag in proton efflux from the corals. The correlation between Ω_arag and G_net is simply the response of the CO₂-carbonate system to pH as [H⁺] shifts the equilibria and redistributes the [CO₃²⁻] relative to the other DIC components of [HCO₃⁻] and [CO₂] (Eqs. (3)–(5)) . Therefore Ω_arag closely tracks pH whereas G_net tracks P_net more closely. Changes in Ω_arag are a consequence of changes in P_net and G_net, rather than a driver of G_net. Hence the Ω_arag peak and the pH peak lag behind the P_net and G_net peaks (Figs. 4A and 4B) due to lag in proton efflux seen in Fig. 7. This observation demonstrates the importance of understanding the difference between H⁺ concentration and H⁺ flux.

During the night the H⁺ flux rate is very responsive to changes in G_net in the “Algae only” and “Coral plus Algae” due to large changes in respiration (Fig. 7). The fluctuations of proton flux at night in the “Coral only” mesocosm are dampened considerably compared to the “Algae only” treatment. The “Coral plus Algae” mesocosm shows an intermediate response. Perhaps the coral skeleton acts as a buffer in a manner similar to that proposed by Suzuki, Nakamori & Kayanne (1995). The macroalgae lack the large skeletal carbonate buffer of reef corals.

Back to the basics

The preceding sections have established the importance of using flux rates rather than concentrations when we are describing a dynamic metabolic system such as a coral or coral reef. Most of the previous research in this area has focused on the relationship between G_net, [CO₃²⁻] (or its surrogate Ω_arag), [HCO₃⁻], and [H⁺] expressed as pH. Plotting these variables in exemplary Fig. 8 is very informative and sheds light on results of previous studies.

A coral must uptake inorganic carbon in order to maintain photosynthesis and calcification. As a result [DIC] will decrease no matter which carbonate species (HCO₃⁻, CO₃²⁻ or CO₂) is taken up by the coral (Eqs. (3)–(5)). Thus we see a decline in [DIC] at high rates of G_net (Fig. 8). [HCO₃⁻], which has been identified as the preferred substrate for photosynthesis and calcification (Weis, Smith & Muscatine, 1989; Furla et al., 2000; Roleda, Boyd & Hurd, 2012) closely tracks [DIC] during daylight hours. In contrast, [CO₃²⁻] lags behind G_net and closely tracks pH during the day as shown for Ω_arag in Fig. 4. If [CO₃²⁻] (or its surrogate Ω_arag) drives calcification, then how do we explain the lag behind G_net? And if [CO₃²⁻] is limiting, how do we explain the fact that [CO₃²⁻] is increasing rather than decreasing as the coral calcifies rapidly and takes up inorganic carbon? [CO₃²⁻] increases because of the increase in pH caused by rapid photosynthesis, which shifts the equilibrium between [HCO₃⁻] and [CO₃²⁻]. Thus, P_net is the driver of changes in G_net and [CO₃²⁻] (Eqs. (2)–(5)). A basic physiological interpretation of the patterns shown in Fig. 8 is that daytime coral metabolism rapidly removes DIC (primarily in the form of HCO₃⁻) while photosynthesis provides the energy that drives G_net (Fig. 4). Higher pH resulting from rapid photosynthesis pushes the equilibria toward higher [CO₃²⁻]. This scenario results in a correlation between G_net and Ω_arag, with Ω_arag as the dependent variable.

During the night [HCO₃⁻], [DIC], [CO₃²⁻] and pH mirror changes in G_net. However, note that [HCO₃⁻] diverges from [DIC] and [CO₃²⁻] diverges from pH in darkness. The night divergence can be attributed to respiration causing a decrease in pH. The decreasing pH shifts the equilibria so that [CO₃²⁻] is converted to [HCO₃⁻], thereby changing the offset between the points. This phenomenon is also reflected in the pattern of diurnal hysteresis show in Fig. 3.

Correlations do not establish cause and effect

Linear regression using Ω_arag as the independent variable may be useful as a first approximation, but is a poor descriptor of calcification dynamics on coral reefs. Much of the existing data on coral calcification was developed in static or low turnover incubation experiments under typical laboratory low irradiance artificial light sources on a 12 h light, 12 h dark cycle (Jokiel, Bahr & Rodgers, in press). This regime results in an unrealistic simulation of the actual diurnal cycle that occurs on coral reefs. The standard protocol has been to compare linear regressions between or among treatments. Linear regression provides a very limited description of the actual relationship between the key factors controlling organic and inorganic processes on coral reefs, which are more adequately described by data presentations such as that in Table 3 or Fig. 7. The linear regression approach does not fully embrace natural diurnal calcification patterns and phase lags because these processes are non-linear. The linear regression approach can lead to the assumption that Ω_arag is the independent variable driving the calcification reaction. Nevertheless, correlations at a single location or in a single experiment can result where all other factors are held constant because the two quantities are related to some extent. Use of Ω_arag as an independent variable to compare spatial and temporal variation in G_net is known to create difficulties (Shamberger et al., 2011; Falter et al., 2012).

Numerous field and laboratory studies have demonstrated a positive correlation between G_net and Ω_arag for corals and coral reefs Erez et al. (2011). Well-developed reefs occur within a narrow geographic range characterized by open ocean Ω_arag > 3.3 (Kleypas et al., 1999), which could mean that coral communities have limited capacity to adapt to future levels of anthropomorphic ocean acidification (OA) projected for the 21st century. Recent reports suggest that healthy coral reefs could cease to exist within this time frame as OA continues and oceanic Ω_arag decreases (Hoegh-Guldberg et al., 2007; Silverman et al., 2009). However, there are inconsistencies in the relationship (slope and x-intercept) between G_net as a function of Ω_arag on various reefs throughout the world (Shamberger et al., 2011). For example, Kaneohe Bay, Oahu, Hawaii contains rich coral reefs that show extremely high rates of G_net while living at low Ω_arag levels (mean Ω_arag = 2.85) (Shamberger et al., 2011). Shamberger et al. (2014) report the existence of highly diverse, coral-dominated reef communities at the Rock Islands of Palau that are living at low saturation states (Ω_arag = 1.9–2.5). These values approach those projected for the tropical western Pacific open ocean by 2100 under future OA modeling scenarios. Identification of biological and environmental factors that enable these communities to persist at low Ω_arag could provide important insights into the future of coral reefs under increasing OA. So how do we account for the paradox of rich coral reefs growing at low Ω_arag? Previous work has been based on the assumption that G_net is controlled by or related directly to Ω_arag. The present investigation indicates that P_net rather than Ω_arag drives G_net and that calcification rate is further limited by proton flux, with pH and A_T playing the major role in controlling calcification. Ω_arag on coral reefs is simply a dependent variable being controlled largely by changes in pH due to photosynthesis. A correlation will exist at a given site, but will not be consistent between different coral reef communities.

The [DIC]:[H⁺] ratio correlates with Ω_arag in describing G_net and is useful from a physiological point of view because it involves pH and all of the inorganic carbon species (Jokiel, 2011a; Jokiel, 2013). However, the [DIC]:[H⁺] ratio is simply another variable based on concentration (along with pH, Ω_arag, CO₃²⁻, etc.) that shows a correlation with G_net. Nevertheless, the [DIC]:[H⁺] ratio can be important in describing G_net in situations where Ω_arag is decoupled from [H⁺] as occurs in the paleo-ocean over time scales greater than 10,000 years (Hönisch et al., 2012). A calcifying organism must uptake DIC in order to continue the calcification reaction and must rid itself of the waste protons. So G_net correlates directly to [DIC] and inversely to [H⁺].

Results of this investigation (Fig. 7) demonstrate the difficulty that corals encounter in shedding waste protons generated during calcification. High rates of H⁺flux continued for several hours following peak G_net. An important conclusion of this work is that measurements of DIC flux and H⁺ flux are far more useful in describing coral metabolism dynamics than [DIC] and [H⁺] (Fig. 8). Likewise, Ω_arag is not a very useful variable in that it simply tracks pH (Fig. 4). This pattern becomes clear when one considers that [CO₃²⁻] (and hence Ω_arag) shifts with changing [H⁺] as described in Eqs. (2)–(5). DIC flux follows P_net and G_net and decreases rapidly following peak P_net and peak G_net indicating that corals can cope more effectively with the problem of DIC supply compared to the problem of eliminating H⁺.

Future research directions

The time lag between G_net and Ω_arag reported previously in field studies (Shamberger et al., 2011; Cyronak et al., 2013; McMahon et al., 2013) provides evidence that diffusion and advection of materials between the coral and the water column involves time delays. One reason is that corals convert inorganic carbon to organic carbon, translocate the organic carbon to distal calcification sites, store organic carbon as lipid, and can eventually convert stored organic carbon back to inorganic carbon (Jokiel, 2011b), creating numerous possible phase lags for metabolic materials. The second reason for the time lag is that rapidly calcifying systems have difficulty dissipating waste protons as shown by continued rapid proton efflux for hours after peak calcification (Fig. 7). What other mechanisms can account for the phase lag? Boundary layers (BL) can slow the exchange of metabolic materials between the coral and the water column. The results of Cyronak et al. (2013) revealed that stirring had a net stimulatory effect on A_T flux and on the diurnal cycle of hysteresis. Boundary layers slow exchange of metabolic materials, so this is an area of investigation that can provide an explanation.

Three hydrodynamic boundary layers have previously been defined and measured (Shashar, Cohen & Loya, 1993; Shashar et al., 1996). The Diffusion Boundary Layer (DBL) is only a few mm thick and in contact with the coral epidermis. The Momentum Boundary Layer (MBL) controls water movement in the proximity of the sessile organisms and is thicker by an order of magnitude than the DBL. The Benthic Boundary Layer (BBL), which controls the interactions of the reef with the surrounding sea water, was typically found to be more than 1 m thick and characterized by a roughness height of 31 cm and a shear velocity of 0.42 cm s⁻¹ in the studies.

The DBL is a thin layer of stagnant seawater adjacent to the coral produced by frictional drag. This quiescent layer influences the flux of material between the benthic surface and the water column. The transport of Ca²⁺, CO₂, CO₃²⁻, HCO₃⁻, O₂, nutrients and H⁺ through the DBL is limited by the physical processes of diffusion and advection (Jokiel, 1978; Lesser et al., 1994; Kaandorp et al., 2005; Kaandorp, Filatov & Chindapol, 2011). Kühl et al. (1995) found that zooxanthellae photosynthesis resulted in a build-up of O₂ in the photosynthetic tissue of up to 250% saturation and a tissue pH of up to 8.6 (i.e., 0.7 pH units above the pH value of the overlying seawater). In darkness the O₂ within the coral tissue was depleted by respiration to near anoxic (<2% air saturation) conditions, with tissue pH of 7.3–7.4. O₂ and pH profiles demonstrated the presence of a 200–300 µm thick DBL that separated the coral tissue from the overlying flowing seawater. Various models invoke boundary layer controls on coral metabolism. Kaandorp et al. (2005) and Kaandorp, Filatov & Chindapol (2011) addressed DBL limitation of DIC influx while Jokiel (2011a), Jokiel (2011b) and Jokiel (2013) challenged the paradigm that calcification is limited by CO₃²⁻ supply on the reactant side of the calcification equation. Rather, he argued that rate of dissipation of H⁺ on the product side due to boundary layer conditions can be the actual limiting factor.

Boundary layer limitation of photosynthesis provides an analog to boundary layer limitation of calcification. Photosynthetic rate can be limited by rate of waste O₂ dissipation through the boundary layer rather than being limited by supply of reactant CO₂. By analogy, calcification can be limited by rate of removal of waste protons rather than by availability of inorganic carbon. The importance of water motion in reducing boundary layer thickness and thereby increasing oxygen flux between the photosynthetic organisms and the water column has been demonstrated (Mass et al., 2010). By analogy, increased water motion can decrease boundary layer thickness and thereby increase removal of protons from the coral.

Studies of reef metabolism beginning with the classic work of Odum & Odum (1955) at Enewetak Reef flat and followed by others (Shamberger et al., 2011; Falter et al., 2012) were conducted in shallow water reef flats within the BBL in situations where unidirectional currents allowed calculation of flux rates. Substantial boundary layers occur over all reefs. For example, Price et al. (2012) investigated a range of sites from exposed coastal situations to lagoons and found that ambient variability in pH was substantial and oscillated over a diurnal cycle with diel fluctuations in pH exceeding 0.2. Daily pH maxima were identified as an important control on calcification. Net accretion among sites was positively related to the magnitude and duration of pH above the climatological seasonal low, despite myriad other ecological (e.g., local supply, species interactions, etc.) and physical oceanographic (e.g., temperature, current magnitude and direction, wave strength, latitudinal gradients, etc.) drivers. In general, accretion rates were higher at sites that experienced a greater number of hours at high pH values each day. Where daily pH within the BBL failed to exceed pelagic climatological seasonal lows, net accretion was slower and fleshy, non-calcifying benthic organisms dominated space. Thus, key aspects of coral reef ecosystem structure and function are clearly related to natural diurnal variability in pH, which is driven primarily by photosynthesis and respiration as P_net.

The master variables

The practice of calculating and comparing linear regressions of G_net vs. Ω_arag to obtain a first approximation of calcification rates under different conditions is fraught with problems but probably will continue because it is ingrained in science and is convenient to use. The correlation of a primary biological response (G_net) to a primary physical chemistry measurement (Ω_arag) is attractive, especially in modeling the possible future changes on coral reefs. Unfortunately, the physical chemistry concept of Ω_arag has no basic physiological meaning in describing G_net other than a correlation with the [DIC]: [H⁺] ratio (Jokiel, 2013) as well as with other factors such as pH. There is no consistent relationship between Ω_arag and G_net when comparing reefs throughout the world (Shamberger et al., 2011). Coral reefs are systems in constant disequilibrium with the water column. So we must take care not to be led astray in our thinking about the variables that actually drive and control coral and coral reef metabolism and bulk water chemistry. The correlation between G_net and other factors is a result of P_net driving both G_net and Ω_arag (McMahon et al., 2013). The observed phenomenon of diurnal hysteresis and diurnal phase lag show the importance of measuring flux rates and emphasizes the challenge in predicting the future effects of OA on coral reefs. The method of using linear extrapolations of Ω_arag to determine threshold levels that will shift coral reefs from net calcifying systems to a net dissolving state has been questioned (McMahon et al., 2013). Perhaps predicted changes in Ω_arag in the open ocean can be used to calculate changes on reefs if we assume that the baseline on the reefs will change in concert with ocean values and that all other processes such as P_net and carbonate dissolution will not be influenced by OA. An explanation for the many paradoxes of coral calcification discussed herein has been presented as the “Two Compartment Proton Flux Model of Coral Metabolism” (Jokiel, 2011b). This model is focused on localized gradients that influence coral metabolism with a focus on proton flux, carbon pools and translocation of fixed carbon. A major feature of the model is the presence of boundary layers which control local pH gradients and inorganic carbon speciation in addition to proton flux. Results of the present investigation support this model.