Exploring the mismatch between the theory and application of photosynthetic quotients in aquatic ecosystems

Abstract

Estimates of primary productivity in aquatic ecosystems are commonly based on variation in ${\mathrm{O}}_2$, rather than ${\mathrm{CO}}_2$. The photosynthetic quotient (PQ) is used to convert primary production estimates from units of ${\mathrm{O}}_2$ to C. However, there is a mismatch between the theory and application of the PQ. Aquatic ecologists use PQ = 1–1.4. Meanwhile, PQ estimates from the literature support PQ = 0.1–4.2. Here, we describe the theory on why PQ may vary in aquatic ecosystems. We synthesize the current understanding of how processes such as ${\mathrm{NO}}_3^{-}$ assimilation and photorespiration can affect the PQ. We test these ideas with a case study of the Clark Fork River, Montana, where theory predicts that PQ could vary in space and time due to variation in environmental conditions. Finally, we highlight research needs to improve our understanding of the PQ. We suggest departing from fixed PQ values and instead use literature-based sensitivity analyses to infer C dynamics from primary production estimated using ${\mathrm{O}}_2$.

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Scientific Significance Statement

Accurate measures of primary production in aquatic ecosystems are necessary to quantify energy availability to higher trophic levels and biological effects on global CO₂ concentrations, among other reasons. However, we commonly measure primary production using O₂ because it is easier than measuring changes in CO₂ and the subsequent modeling of the full carbonate system. Although we measure O₂ we are often more interested in the rate of fixed C, and thus use the photosynthetic quotient (the ratio of O₂ release to CO₂ fixed, photosynthetic quotient [PQ]) to convert O₂-based metabolism to CO₂. This study summarizes the mismatch between our current knowledge and the application of PQ, highlights knowledge gaps, and emphasizes the need to use literature-based sensitivity analyses rather than uninformed fixed PQ values.

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Primary production in aquatic ecosystems fixes dissolved carbon dioxide (${\mathrm{CO}}_2$) and subsequently releases dissolved oxygen (${\mathrm{O}}_2$) via photosynthesis. Primary production can control the carbon (C) cycling in aquatic ecosystems, which has implications for the availability of energy to higher trophic levels, dissolved nutrient availability and cycling, and global climate dynamics due to the effects on atmospheric ${\mathrm{CO}}_2$ concentrations (McKinley et al. 2017). Primary production can be measured either via the rate of gaseous product (${\mathrm{O}}_2$) generation or as the rate of reactant (${\mathrm{CO}}_2$) consumption following the generic photosynthesis reaction (Eq. 1) or by measuring the C assimilated into biota using isotopic approaches measured in microcosms (Nielsen 1951; Peterson 1999) to whole ecosystems (Bower et al. 1987).[Image Omitted. See PDF]

Most studies measure primary production as the change in ${\mathrm{O}}_2$, rather than ${\mathrm{CO}}_2$ assimilated in aquatic ecosystems, because ${\mathrm{O}}_2$ is easier to continuously and accurately measure using sensors. Indeed, much of the early research on aquatic ecosystem metabolic processes is based on models measuring the change of ${\mathrm{O}}_2$ with either diel variation (Odum 1956) or experimental manipulation of light (Nielsen 1951). Furthermore, methods to measure ${\mathrm{CO}}_2$ lagged that of ${\mathrm{O}}_2$, and also require knowing pH or alkalinity along with more difficult computation to account for the overall dissolved inorganic carbon (DIC) pool (Barnes 1983; Gattuso et al. 1999; Stets et al. 2017).

Because we are often more interested in C cycling we convert primary production measured with ${\mathrm{O}}_2$ data to C using the photosynthetic quotient (PQ), that is, the molar ratio of the flux of ${\mathrm{O}}_2$ released to ${\mathrm{CO}}_2$ assimilated during photosynthesis (Eqs. 2, 3; Note that this equation naturally is negative due to the decline of DIC during photosynthesis, although we follow the common convention of referencing PQ as a positive value).[Image Omitted. See PDF] [Image Omitted. See PDF]

Despite its evident importance to translating from one chemical species to another, the PQ term has been dogmatically employed without appreciating the existing degree of uncertainty and its implications. A mismatch between theory and application of the PQ exists within and across aquatic ecosystem subfields. For example, it is common to assume a PQ of 1 or 1.2 for freshwater ecosystems, even though these values are not necessarily backed by measurements or theory. Marine researchers commonly use a value of 1.1–1.4, which is in part based on theory, but under specific assumptions, such as whether production is new or recycled (Williams et al. 1979; Laws 1991; Hedges et al. 2002). Fixed and field-specific PQ values are used despite PQ measurements from the literature ranging from 0.1 to 4.2 (Table 1).

Table 1 Measured PQ using varying methods and ecosystems show a broad range of possible PQ. SI Table 1 in Supporting Information contains a detailed citation and summary table.

Aquatic ecosystem	Method	Number of studies	Range of PQ	Citations
Marine	${}^{14}\mathrm{C}$	6	0.1–4.2	Laws (1991), Williams and Robertson (1991), Raine (1983), Williams et al. (1979), Iriarte (1999), Carvalho (2014)
	DIC	4	0.4–1.6	Burris (1981), Smith et al. (2012), Du et al. (2018), Bolden et al. (2019), Mercado et al. (2003), Iriarte (1999), Rosenberg et al. (1995)
Freshwater	${}^{14}\mathrm{C}$	2	0.3–2.0	Bell and Kuparinen (1984), Sakamoto et al. (1984)
	DIC	3	0.13–1.4	Pokorny et al. (1989), Hanson et al. (2003), Sakamoto et al. (1984), Kliphuis et al. (2011)

Physiological mechanisms that co-occur with oxygenic carbon fixation alter the rate of net ${\mathrm{O}}_2$ production because they occur at rates and scales commensurate with that employed by our methods even as those methods fail to distinguish them. For example, photorespiration and nitrate (${\mathrm{NO}}_3^{-}$) assimilation are net sinks and sources of ${\mathrm{O}}_2$ (respectively) that are rarely accounted for in models that estimate primary production (Fig. 1). These oversights may have extensive and unappreciated consequences for our understanding of C fluxes associated with primary production across ecosystems.

Fig. 1. Summary of processes relative to the primary production of benthic algae and phytoplankton that affect dissolved O2 (A) and CO2 (B). Both O2 and CO2 are affected by photosynthesis and respiration, while O2 is uniquely affected by NO3− assimilation and photorespiration. O2 concentrations are much more likely to be affected by captive bubbles or ebullition since O2 has low solubility above saturation. In contrast, CO2 equilibration with DIC reduces the potential for bubble formation. Note that the magnitude of the effect of any given process on dissolved gas concentrations depends on a variety of environmental conditions specific to that process.

Here, we explore the current status of PQ values in aquatic ecosystems and their historical application, with the goal to enable better estimates of C transformations based on ${\mathrm{O}}_2$ production. Specifically, we will:

1. summarize measurements of PQ within and between marine and freshwater aquatic ecosystems;
2. describe the state of chemical and biological theory addressing how and why PQ varies across species and environmental conditions;
3. provide a case study of a river where theory predicts that PQ should vary in space and time based on environmental conditions and algal succession; and
4. highlight research needs to improve our understanding of how we translate between C and O metabolism.

Overall, we suggest departing from minimally informed fixed PQ values and instead use literature-based sensitivity analyses to inform how PQ choice affects interpreting C dynamics from primary production estimated using ${\mathrm{O}}_2$. Furthermore, we encourage simultaneous measurements of ${\mathrm{O}}_2$ and ${\mathrm{CO}}_2$ when possible, to provide empirical evidence of environmental PQ variation and accurate elemental translation.

We recognize from the outset that PQ is difficult to assess because we cannot directly measure photosynthesis. Measurements of photosynthesis will always co-occur with respiration and parsing the two measurements is problematic; it is common to measure respiration (in the dark), then measure net ecosystem production (in the light), and subtract respiration from net ecosystem production. The light/dark approach assumes that respiration is constant throughout the day and ignores other abiotic processes that are related to diel cycles of light (e.g., photo-oxidation), and it is becoming clear that these assumptions are often not valid (Hotchkiss and Hall 2014; Schindler et al. 2017). Thus, variation in respiration, and in particular, respiration quotients (RQ) will affect our assessment of PQ. In this work, we are not considering the effects of RQ, since a summary of the RQ variation with environmental conditions already exists (Berggren et al. 2012). Even so, RQ and PQ should both be considered when interpreting ${\mathrm{O}}_2$ and ${\mathrm{CO}}_2$ metabolism data.

History of PQ measurements and values used across aquatic ecosystems

Most of our knowledge of the PQ comes from experiments and measurements in marine ecosystems on planktonic algae. Although our purpose is not to exhaustively review the literature, the papers we encountered were mostly marine with few from freshwater, including only one study with measurements of PQ on freshwater benthic algae (Table 1). The bias of PQ measurements towards phytoplankton and marine ecosystems may be due to historic method constraints on the accurate measurement of ${\mathrm{CO}}_2$ (Williams and Robertson 1991). Instead, radioactive ${}^{14}\mathrm{C}$ has been used since at least the 1960s (Strickland 1960) to measure primary productivity (referred to here as ${}^{14}\mathrm{C}$ productivity). Given the complexities of using radioactive materials in the natural environment, this method is much more favorable at small scales (e.g., bottles that capture microscopic primary producers) and in the laboratory, thus the initial bias towards phytoplankton and marine ecosystems. However, the ${}^{14}\mathrm{C}$ approach is not directly comparable to measures of ${\mathrm{O}}_2$ evolution because the incubation results in something between gross primary production and net primary production (Peterson 1980) as a result of the potential respiration of ${}^{14}\mathrm{C}$-labeled photosynthetic products and/or the recycling of ${}^{12}{\mathrm{CO}}_2$ into the photosynthetic pool. These uncertainties in the measurement of C fixation bias estimates of the PQ.

A review by Williams and Robertson (1991) showed PQ ranged between 0.5 and 3.5, with most measurements made based on ${}^{14}\mathrm{C}$ productivity. They attributed the broad range in PQ to the ${}^{14}\mathrm{C}$ productivity problem (Peterson 1980), and suggested that a more realistic range of values for phytoplankton is between 1.1 and 1.4 (Williams and Robertson 1991). This range was confirmed by Laws (1991), who used chemical equations of photosynthetic products, and reported estimates of phytoplankton chemical composition to show that PQ ranged from 1.1 to 1.4. These values of PQ represent broad averages, and more contemporary site-specific studies using more accurate methods to measure primary production (i.e., direct measurement of ${\mathrm{CO}}_2$ or DIC compared to ${}^{14}\mathrm{C}$ productivity) have resulted in PQ values that differ from 1.1 to 1.4 based on specific species and environmental conditions (Table 1). Using a fixed value of 1.35–1.45 is still common in marine ecology (Bolden et al. 2019); however, in general, marine ecologists tend to be more aware of the inherent variability of the PQ.

Freshwater ecologists also commonly use fixed PQs but usually employ values of 1 or 1.2, based more on tradition rather than on theory or data. We know of no direct source suggesting the use of PQ = 1 although it is probably safe to assume that this value reflects only the photosynthetic creation of glucose (${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$), which results in molar equivalence between ${\mathrm{O}}_2$ released and ${\mathrm{CO}}_2$ fixed. The assumption of glucose as the only photosynthetic product oversimplifies organic matter synthesis and ignores other processes that can affect dissolved ${\mathrm{O}}_2$ concentrations. The PQ value of 1.2 similarly does not have a common source, although some attribute this value to Wetzel (2001) or Bott et al. (1978), despite neither source providing convincing evidence for a fixed value. Although the range of reported PQ measurements in fresh waters is between 0.13 and 2.0 (Table 1), we have not found an article that applies a fixed value other than 1 or 1.2 when the PQ is not directly measured. Moreover, none have accounted for the implications associated with the uncertainty of the PQ values employed.

We suggest that aquatic ecologists need to use greater scrutiny when applying PQ values to translate O₂-based metabolism to rates of C fixation. Given the need for an accurate PQ, we summarize knowledge of why the PQ may vary across species and environmental conditions, and use this knowledge to generate hypotheses about the biological and environmental conditions causing the PQ to vary. Although most of this knowledge is based on studies of phytoplankton from marine ecosystems, the same concepts often hold in freshwater ecosystems.

PQ theory

PQ can be separated into multiple components, with each dictated by the characteristics of the species of primary producer and the environmental conditions surrounding the organism (Williams and Robertson 1991). The appropriate PQ value that represents biological effects on ${\mathrm{O}}_2$ and ${\mathrm{CO}}_2$ (${\mathrm{PQ}}_{\mathrm{Bio}}$) can be represented by Eq. 4:[Image Omitted. See PDF]where ${\mathrm{PQ}}_{\mathrm{C}}$ refers to the change in ${\mathrm{O}}_2$ and ${\mathrm{CO}}_2$ associated with photosynthesis, ${\mathrm{PQ}}_{{\mathrm{NO}}_3}$ refers to the release of ${\mathrm{O}}_2$ associated with the reduction of nitrate (${\mathrm{NO}}_3^{-}$) for nitrogen (N) assimilation, and ${\mathrm{PQ}}_{\mathrm{pr}}$ is the reduction of ${\mathrm{O}}_2$ associated with photorespiration. The ellipsis (…) represents the myriad of other biological processes that may affect ${\mathrm{O}}_2$ or ${\mathrm{CO}}_2$ availability (e.g., nitrification, sulfate reduction). We focus on the three described components identified by considerable evidence to measurably affect the PQ in most aquatic ecosystems.

$\mathbf{C}\mathbf{a}\mathbf{r}\mathbf{b}\mathbf{o}\mathbf{n}\mathbf{ }\mathbf{PQ}\mathbf{ }\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{p}\mathbf{o}\mathbf{n}\mathbf{e}\mathbf{n}\mathbf{t}\mathbf{ }\left({\mathbf{PQ}}_{\mathbf{C}}\right)$

The ${\mathit{PQ}}_C$ represents the change in ${\mathrm{O}}_2$ and ${\mathrm{CO}}_2$ associated with photosynthesis. The ${\mathrm{PQ}}_{\mathrm{C}}$ can be broken down into the various products of photosynthesis dictated by the state of reduction of the products for the general compound $\mathrm{C}{\left(\mathrm{H}\right)}_Y{\left(\mathrm{O}\right)}_Z$ (Eq. 5) (Ryther 1956; Laws 1991):[Image Omitted. See PDF]where $Y$ and $Z$ represent the number of H and O atoms in the photosynthetic product, respectively. Thus, the net change in ${\mathrm{O}}_2$ and ${\mathrm{CO}}_2$ associated with the sum of $\mathrm{C}{\left(\mathrm{H}\right)}_Y{\left(\mathrm{O}\right)}_Z$ products equals ${\mathrm{PQ}}_{\mathrm{C}}$. The most common products intimately coupled with photosynthesis are glucose (${\mathrm{C}}_6{\mathrm{H}}_{12}{\mathrm{O}}_6$), glycolic acid (${\mathrm{C}}_2{\mathrm{H}}_3{\mathrm{O}}_3$), saturated fatty acids (e.g., ${\mathrm{C}}_{20}{\mathrm{H}}_{30}{\mathrm{O}}_2$), nucleic acids (e.g., ${\mathrm{C}}_{38}{\mathrm{H}}_{47}{\mathrm{O}}_{28}{\mathrm{N}}_{15}{\mathrm{P}}_4$), and protein (e.g., ${\mathrm{C}}_{18}{\mathrm{H}}_{24}{\mathrm{O}}_6{\mathrm{N}}_5$). The proportion of C in each of these compounds relative to the total C in the algal cell will dictate the value of the ${\mathrm{PQ}}_{\mathrm{C}}$. The range of plausible ${\mathrm{PQ}}_{\mathrm{C}{\left(\mathrm{H}\right)}_Y{\left(\mathrm{O}\right)}_Z}$ values is 0.625–1.5, with the lowest value assuming the production of glycolic acid only, and the highest value assuming the sole production of saturated fatty acids. In reality, these extremes are not likely, and the ${\mathrm{PQ}}_{\mathrm{C}}$ will fall somewhere in the middle of this range. Laws (1991) estimated the ‘typical’ planktonic cell to contain 40% each of proteins and carbohydrates, 15% lipids, and 5% nucleic acids, which equates to a ${\mathrm{PQ}}_{\mathrm{C}}$ of 1.08. This value is specific to phytoplankton, and there is likely species-specific variation in ${\mathrm{PQ}}_{\mathrm{C}}$ based on algal physiology and life history. Notably, benthic algae may have a different ${\mathrm{PQ}}_{\mathrm{C}}$ than phytoplankton given the need for making structures to anchor to the substratum (among other physiological differences); however, there is little information available to calculate the ${\mathrm{PQ}}_{\mathrm{C}}$ of benthic algae.

Few papers have measured the effect that specific photosynthetic end products have on the PQ, although speculation abounds that environmentally driven changes in lipid production increase the PQ. These changes in the PQ are likely associated with variation in light and energy availability occurring in environments replete with other possible limiting nutrients as the algal cell uses the opportunity to generate lipids that require more energy and C, thus increasing the PQ (Norici et al. 2011; Palmucci et al. 2011). Indeed, many studies have observed increased PQ with diel increases in light (Carvalho 2014), and experimental light manipulation (Du et al. 2018). The mechanistic link (or lack thereof) between environmental variables and lipid production is a knowledge gap relevant to estimates of PQ in freshwater and marine ecosystems.

$\mathbf{N}\mathbf{i}\mathbf{t}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{e}\mathbf{ }\mathbf{P}\mathbf{Q}\mathbf{ }\mathbf{component} \left({\mathrm{PQ}}_{{\mathrm{NO}}_3^{-}}\right)$

The biosynthesis associated with primary production also requires N, and the concurrent reduction of ${\mathrm{NO}}_3^{-}$ by the cell for assimilation will release ${\mathrm{O}}_2$, thus increasing the PQ. Specifically, 2 mol of ${\mathrm{O}}_2$ are released for every mole of ${\mathrm{NO}}_3^{-}$ reduced to ${\mathrm{NH}}_3$.[Image Omitted. See PDF]

Organismal demand for N controls ${\mathrm{PQ}}_{{\mathrm{NO}}_3^{-}}$; C : N ratios in organismal biomass are a good indicator of this demand (Redfield et al. 1963) with lower values reflecting greater demand for N. Finally, it is energetically favorable for organisms of all sizes to assimilate N as ammonium (${\mathrm{NH}}_4^{+}$), which does not produce ${\mathrm{O}}_2$, relative to ${\mathrm{NO}}_3^{-}$. Therefore, the relative amount of ${\mathrm{NO}}_3^{-}$ in the total dissolved inorganic nitrogen pool (${\mathrm{NO}}_3^{-}+{\mathrm{NH}}_4^{+}$; DIN) also controls the amount of ${\mathrm{O}}_2$ released as a part of N assimilation (Smith et al. 2012).[Image Omitted. See PDF]

Lab experiments demonstrate that ${\mathrm{O}}_2$ release due to ${\mathrm{NO}}_3^{-}$ assimilation increases PQ values (Raine 1983; Bell and Kuparinen 1984). Raine (1983) manipulated ${\mathrm{NO}}_3^{-}$ concentrations of salt water containing phytoplankton in the lab, while keeping all other environmental conditions constant. PQ varied from 1.0 to 2.25 and the measured change in PQ was similar to the theoretical change in PQ based on chemical stoichiometry (e.g., Eq. 7; Raine 1983). Field measurements tell the same story; Smith et al. (2012) observed an increase in the PQ from 1.24 to 1.42 over $\sim$ 30-yr in a Rhode Island estuary. The observed increase in the PQ coincided with increased proportion of DIN present as ${\mathrm{NO}}_3^{-}$ associated with a new wastewater treatment plant upstream of the estuary. The change in relative N availability (i.e., Eq. 7) suggests that the PQ should have increased by 0.15–0.23, which includes the observed increase of 0.18 (Smith et al. 2012). Note that we do have some hesitation about the validity of Eq. 7 as it is not immediately clear that the units are balanced and Smith et al. (2012) do not show their derivation; however, the match between expected values derived from chemical stoichiometry and empirical measurements enhances confidence in estimates of ${\mathrm{PQ}}_{{\mathrm{NO}}_3^{-}}$ estimated from Eq. 7. Nonetheless, the lowest confidence is assigned to estimates of ${\mathrm{PQ}}_{\mathrm{pr}}$, which addresses the complicated and poorly addressed influences of photorespiration.

$\mathbf{P}\mathbf{h}\mathbf{o}\mathbf{t}\mathbf{o}\mathbf{r}\mathbf{e}\mathbf{s}\mathbf{p}\mathbf{i}\mathbf{r}\mathbf{a}\mathbf{t}\mathbf{i}\mathbf{o}\mathbf{n} \mathbf{PQ}\mathbf{ }\mathbf{c}\mathbf{o}\mathbf{m}\mathbf{p}\mathbf{o}\mathbf{n}\mathbf{e}\mathbf{n}\mathbf{t} \left({\mathbf{PQ}}_{\mathbf{pr}}\right)$

Photorespiration is the light-dependent ${\mathrm{O}}_2$ reduction and ${\mathrm{CO}}_2$ release by photoautotrophs. Unlike mitochondrial respiration, photorespiration only occurs in light, does not conserve energy in ATP, and does not use substrates from the tricarboxylic acid cycle (Tolbert 1974). Instead, photorespiration reduces ${\mathrm{O}}_2$ via the RuBisCO mediated reaction with ribulose 1,5-bisphosphate (RuBp) that generates C-2 compounds (e.g., 2-phosphoglycolate) further processing of which consumes more ${\mathrm{O}}_2$ and liberates ${\mathrm{CO}}_2$.

Although the end result of this process includes the release of ${\mathrm{CO}}_2$, some or all of this ${\mathrm{CO}}_2$ is “recycled,” or immediately fixed by photosynthesis, rather than being released from the cell (Søndergaard and Wetzel 1980). Photorespiration was initially referred to as a “wasteful process” given that glycolate is not needed and is often excreted when in excess (Tolbert and Zill 1956). Later studies discovered that glycolate is eventually funneled through multiple reactions to contribute to the Calvin–Benson cycle, although at a higher energy cost than via photosynthesis (Moroney et al. 2013). During photorespiration ${\mathrm{O}}_2$ occupies the RuBisCO binding site, limiting ${\mathrm{CO}}_2$ fixation and reducing rates of net photosynthesis. Photosynthesis inhibition at high ${\mathrm{O}}_2$ concentrations is a common phenomenon explained by photorespiration. Most algal species have developed C concentrating mechanisms to build up DIC around the RuBisCO enzyme, limiting photorespiration (Giordano et al. 2005). Aquatic photoautotrophs need C concentrating mechanisms because they commonly face an environment with low ${\mathrm{CO}}_2$ concentrations, and need to build up ${\mathrm{CO}}_2$ near RuBisCO for photosynthesis (Moroney et al. 2013). Despite the evolution of C concentrating mechanisms to limit its effects, photorespiration is still necessary. For example, mutant cyanobacteria missing some photorespiration pathways could not to survive outside of abnormally high ${\mathrm{CO}}_2$ environments (Eisenhut et al. 2008), evidence that photorespiration is necessary despite C concentrating mechanisms.

Although the purpose and potential benefits of photorespiration are not yet fully understood (Osmond and Grace 1995; Shi and Bloom 2021), generally 3 moles of ${\mathrm{O}}_2$ are reduced for every mole of ${\mathrm{CO}}_2$ produced during photorespiration, which ultimately lowers PQ (Stewart 1974). Multiple experiments have shown that photorespiration constitutes 20–40% of net photosynthesis across a variety of aquatic ecosystems and measurement scales (Burris 1981; Parkhill and Gulliver 1998; Kliphuis et al. 2011; Buapet et al. 2013), particularly when ${\mathrm{O}}_2$ is readily available and ${\mathrm{CO}}_2$ is relatively low (Vance and Spalding 2005). Photorespiration rates are often $\sim 0$ below 100% ${\mathrm{O}}_2$ saturation, low at or below 100% ${\mathrm{O}}_2$ saturation, and highest when ${\mathrm{O}}_2$ is super-saturated. Although, low ${\mathrm{CO}}_2$ (and indirectly elevated pH) can often increase photorespiration rates as long as some ${\mathrm{O}}_2$ is present (Kliphuis et al. 2011). Multiple studies have measured PQ < 1, which is often attributed to photorespiration (Hough 1974; Burris 1981; Pokorny et al. 1989). Furthermore, some studies have experimentally manipulated light (Iriarte 1999) or ${\mathrm{O}}_2$ concentrations (Burris 1981) and found PQ < 1 matching the theoretical effect of photorespiration. We note that photorespiration has not been observed (when it otherwise should have been) under some environmental conditions and with some specific algal species (Lloyd et al. 1977; Birmingham et al. 1982).

Toward predicting when and where PQ may vary based on environmental conditions

PQ estimates from the literature and direct experimentation provide a theoretical basis for hypothesizing when and where PQ may vary with environmental conditions. Here, we synthesize the relevant information to aid researchers in addressing variation in the PQ. Literature supports the assertion that ${\mathrm{PQ}}_{{\mathrm{NO}}_3}$ and ${\mathrm{PQ}}_{\mathrm{pr}}$ are likely to have the strongest effect on the PQ, and these effects can be predicted based on the proportion of ${\mathrm{NO}}_3^{-}$ that is DIN, the C:N ratio of the algal biomass, and the % ${\mathrm{O}}_2$ saturation. We used data from the literature to simulate the effect of environmental conditions on the PQ using Eq. 7 (for effects of ${\mathrm{PQ}}_{{\mathrm{NO}}_3}$) and data from Burris (1981) (for effects of the ${\mathrm{PQ}}_{\mathrm{pr}}$; Fig. 2). We conducted the simulations across the plausible range of each variable in the environment, where the environmental conditions ranged for the proportion of DIN that is ${\mathrm{NO}}_3$ from 0 and 1, for ${\mathrm{O}}_2$ saturation from 40% and 180%, and with an algal C : N composition of 5 or 20. This simulation provides a broad hypothetical framework for predicting when and where the PQ may vary. Results from the simulation (Fig. 2) illustrate the potential for ${\mathrm{PQ}}_{\mathrm{pr}}$ to increase the ${\mathrm{PQ}}_{\mathrm{Bio}}$ by as much as 0.8 when dissolved ${\mathrm{O}}_2$ is low, and decrease by as much as 1.2 when ${\mathrm{O}}_2$ is well above saturation. Changes associated with ${\mathrm{PQ}}_{{\mathrm{NO}}_3}$ are less dramatic, with changes in the ${\mathrm{PQ}}_{\mathrm{Bio}}$ of 0.2 when N demand is high (low biomass C : N, Fig. 2A) and less when N demand is low (high biomass C : N, Fig. 2B). We note that the simulated changes in ${\mathrm{PQ}}_{\mathrm{Bio}}$ are relative to an assumed ${\mathrm{PQ}}_{\mathrm{C}}$ of 1.1, an assumption that carries its own degree of uncertainty. While the literature supports the possibility of variation in the ${\mathrm{PQ}}_{\mathrm{C}}$, we do not believe there is enough information to adequately predict anything other than a fixed ${\mathrm{PQ}}_{\mathrm{C}}$.

Fig. 2. The simulated change in PQ associated with the PQNO3− (y-axis) and the PQpr (x-axis) components. The top panel assumes a fixed C : N of 5, while the bottom panel assumes a fixed C : N of 20. Both simulations assume PQC=1.1 and the dashed line shows the combination of environmental conditions where PQ does not vary from 1.1. The PQ will increase (positive change relative to PQC) when NO3− is a high proportion of DIN and the aquatic ecosystem is below 100% O2 saturation. In contrast, the PQ will decline the most when NO3− is a low proportion of DIN and waters are supersaturated with O2. Finally, when the demand for N is low (indicated by high C : N ratio), the effect of PQNO3− on the PQ change is less than when N demand is high.

Primary productivity varies with light intensity, and thus PQ can change with the diel progression of light (Hough 1974; Iriarte 1999; Mercado et al. 2003). Furthermore, the degree to which the PQ will vary during a day will depend on the rate of primary productivity, given that ecosystems with low productivity are unlikely to supersaturate with ${\mathrm{O}}_2$, limiting the potential effect ${\mathrm{PQ}}_{\mathrm{pr}}$ may have on ${\mathrm{PQ}}_{\mathrm{Bio}}$. The proportion of ${\mathrm{NO}}_3^{-}$ that is DIN can vary seasonally or spatially, particularly in lotic ecosystems. Accordingly, we simulated how different fixed rates of gross primary production (GPP), in units of moles ${\mathrm{O}}_2$ released (${\mathrm{GPP}}_{\mathrm{O}}$), interact with environmental conditions to control the ${\mathrm{PQ}}_{\mathrm{Bio}}$. Specifically, we simulated three scenarios: (1) low GPP rates (i.e., ${\mathrm{O}}_2$ saturation never exceeds 100%) and low ${\mathrm{NO}}_3^{-}$ assimilation rates (assuming mineralization of ${\mathrm{NH}}_4^{+}$ as is likely at low productivity rates); (2) high GPP rates (i.e., ${\mathrm{O}}_2$ saturation exceeds 100% during most of the photic period) and low ${\mathrm{NO}}_3^{-}$ assimilation rates (assuming a low proportion of ${\mathrm{NO}}_3^{-}$ that is DIN); and (3) high GPP rates and high ${\mathrm{NO}}_3^{-}$ assimilation rates (assuming a high proportion of ${\mathrm{NO}}_3^{-}$ that is DIN). We again assume that ${\mathrm{PQ}}_{\mathrm{C}}$ is fixed at 1.1. We simulated the diel ${\mathrm{O}}_2$ saturation curves assuming low and high fixed values for GPP (19 and 250 mmol m⁻³ d⁻¹, respectively) and ecosystem respiration scaled with GPP, while gas-exchange, average depth, temperature, and pressure were held constant (SI 1, SI Table 2 in Supporting Information). We used the theory presented above to predict ${\mathrm{PQ}}_{\mathrm{C}}$, ${\mathrm{PQ}}_{{\mathrm{NO}}_3^{-}}$, ${\mathrm{PQ}}_{\mathrm{pr}}$, and ${\mathrm{PQ}}_{\mathrm{Bio}}$ in each scenario. We then used the ${\mathrm{PQ}}_{\mathrm{Bio}}$ derived from each scenario to calculate GPP, in units of fixed C (${\mathrm{GPP}}_{\mathrm{C}}$). Finally, we compared the ${\mathrm{GPP}}_{\mathrm{C}}$ predicted with the ${\mathrm{PQ}}_{\mathrm{Bio}}$ from each scenario with the ${\mathrm{GPP}}_{\mathrm{C}}$ estimated using fixed PQ values commonly used in marine and freshwater ecosystems, and from the range observed in the literature.

In low productivity ecosystems, N assimilation and photorespiration are likely low, thus the ${\mathrm{PQ}}_{\mathrm{Bio}}\approx {\mathrm{PQ}}_{\mathrm{C}}$ (Fig. 3). Based on our current understanding of ${\mathrm{PQ}}_{\mathrm{C}}$, when ${\mathrm{PQ}}_{\mathrm{Bio}}$ $\approx$ ${\mathrm{PQ}}_{\mathrm{C}}$ the choice of traditional fixed PQ values will minimally bias estimates of ${\mathrm{GPP}}_{\mathrm{C}}$ from measured ${\mathrm{GPP}}_{\mathrm{O}}$. However, if future research found evidence that the ${\mathrm{PQ}}_{\mathrm{C}}$ varies with environmental variables or by species-specific characteristics, then ${\mathrm{PQ}}_{\mathrm{Bio}}$ may diverge from canonical values. In contrast, highly productive ecosystems with low ${\mathrm{NO}}_3^{-}$ will have a ${\mathrm{PQ}}_{\mathrm{Bio}}$ that is < 1. This scenario causes the largest bias of ${\mathrm{GPP}}_{\mathrm{C}}$ estimates from ${\mathrm{GPP}}_{\mathrm{O}}$. PQ values $<$ 1 will have a higher bias than values $>$ 1 of the same magnitude (i.e., 0.8 compared to 1.2) (Fig. SI 1 Supporting Information). In the final scenario, the ${\mathrm{O}}_2$ consumed through photorespiration is negated by the addition of ${\mathrm{O}}_2$ from ${\mathrm{NO}}_3^{-}$ assimilation, resulting in a ${\mathrm{PQ}}_{\mathrm{Bio}}$ $>$ ${\mathrm{PQ}}_{\mathrm{C}}$. In this scenario, the ${\mathrm{PQ}}_{\mathrm{Bio}}$ is similar in magnitude with the traditional fixed values, with minimal bias based on the choice of ${\mathrm{PQ}}_{\mathrm{Bio}}$.

Fig. 3. The simulated effect of each PQx component on the PQBio given different GPPO rates and NO3− availability. Each column represents a different scenario: left column—low GPP and low NO3−, middle column—high GPP and low NO3−, right column—high GPP and high NO3−. The O2 saturation data are simulated based on fixed values of GPP (A = 19 mmol O2 m−3 h−1 and B, C = 250 mmol O2 m−3 h−1). SI 1 in Supporting Information contains full methods on O2 saturation simulation. The middle row shows the simulated effects of each PQx component on the PQBio (Eq. 4). The mean PQx for each scenario was fixed based on our current knowledge of the effect of environmental conditions on each compartment. In the low GPP scenario (D), PQBio≈PQC since the effects of PQPr and PQNO3− are negligible when O2 saturation is [less than] 100% and NO3− concentration is low. For the high productivity and low NO3− scenario (E), the PQBio is [less than] PQC due to photorespiration occurring when O2 saturation is ≥ 100%. For the high productivity and high NO3− scenario (F), PQBio > PQC primarily controlled by the large effect of PQNO3−. The final row shows how the fixed GPP value in units of O2 would be transformed to C units using: the mean PQBio from (D) to (F), the two most common fixed freshwater (FW) values (1, 1.2), the most common marine value (1.4), and a conservative range of PQ values observed in the literature (0.5 and 3.5, respectively). The error associated with using the conventional fixed PQ values is low when GPP rates are low, and vice versa when rates are high. The highest error when converting GPP from units of O2 to C occurs when GPP rates are high, NO3− is low, and photorespiration is occurring.

Considerations of observation error and measurement bias

The above theory provides testable hypotheses that can be confronted with measurements of the PQ (${\mathrm{PQ}}_{\text{Meas}}$) across environmental conditions. In an ideal world, ${\mathrm{PQ}}_{\text{Meas}}$ would match ${\mathrm{PQ}}_{\mathrm{Bio}}$; however, this scenario is unlikely ever true. It is necessary to consider the observation error $\left({\mathrm{PQ}}_{\mathrm{Obs}\text{error}}\right)$ and measurement bias (${\mathrm{PQ}}_{\text{Meas bias}}$).[Image Omitted. See PDF]

${\mathrm{PQ}}_{\mathrm{Obs}\text{error}}$ is the error imposed by imperfectly measuring ${\mathrm{O}}_2$ or DIC. For example, an improperly calibrated or drifting sensor may add observation error to the PQ. In general, it is possible to limit ${\mathrm{PQ}}_{\mathrm{Obs}\text{error}}$ with careful calibration and lab work. Even so, there are statistical approaches to account for measurement error (e.g., state-space models, Pedersen et al. 2011; Appling et al. 2018). We define ${\mathrm{PQ}}_{\text{Meas bias}}$ as the error imposed when a model for dissolved ${\mathrm{O}}_2$ or DIC does not reflect the process of interest. ${\mathrm{PQ}}_{\text{Meas bias}}$ is process error and can occur for a variety of reasons. For example, abiotic processes other than the biological processes associated with primary production can bias estimates of GPP (e.g., bubble formation in chambers). ${\mathrm{PQ}}_{\text{Meas bias}}$ will be most prevalent when comparing photosynthesis based on ${\mathrm{O}}_2$ or ${\mathrm{CO}}_2$ at the ecosystem level and provides a substantial challenge for discerning the biological signal within ${\mathrm{PQ}}_{\text{Meas}}$. Although ${\mathrm{PQ}}_{\text{Meas bias}}$ can take many forms, we highlight a few sources of ${\mathrm{PQ}}_{\text{Meas bias}}$ that deserve further consideration and research.

For ecosystems with attached benthic primary producers (Fig. 1A), captive bubbles (i.e., bubbles from primary production trapped in biofilms) are common, but understudied in productive ecosystems and are more likely to affect ${\mathrm{O}}_2$ than ${\mathrm{CO}}_2$. Dissolved ${\mathrm{CO}}_2$ readily equilibrates with the DIC pool in many circumneutral pH environments, while the ${\mathrm{CO}}_2$ remaining as dissolved gas has a much higher solubility than ${\mathrm{O}}_2$. Bolden et al. (2019) attribute observed captive bubbles on marine coral reefs to abnormally low PQ measurements after ruling out the contribution of ${\mathrm{PQ}}_{\mathrm{pr}}$ and ${\mathrm{PQ}}_{{\mathrm{NO}}_3^{-}}$. The bias in measured ${\mathrm{O}}_2$ was large enough that the authors suggested that O₂-based estimates of metabolism are unreliable in highly productive benthic environments (Bolden et al. 2019). Ebullition occurs when captive bubbles are released into the water column, and eventually traverse the air–water divide. The effect of ebullition on primary production estimates has been documented in many lakes, where emissions of bubbles can be similar in magnitude to diffusive ${\mathrm{O}}_2$ exchange (Koschorreck et al. 2017), and contain up to 20% of daily net oxygen production (Howard et al. 2018). Ultimately, captive and ebullated bubbles can affect estimates of ${\mathrm{PQ}}_{\mathrm{Bio}}$ in variable ways depending on the degree to which gases in bubbles equilibrate with the water around them (Hall and Ulseth 2020).

Groundwater inputs can affect ${\mathrm{O}}_2$ and ${\mathrm{CO}}_2$ concentrations in receiving freshwater ecosystems (Sear et al. 1999; Duvert et al. 2018). Generally groundwater in local flow is replete with ${\mathrm{CO}}_2$ and low in ${\mathrm{O}}_2$ due to soil respiration (Tank et al. 2018); low ${\mathrm{O}}_2$ groundwater can bias estimates of GPP (Hall and Tank 2005). The contribution of groundwater ${\mathrm{CO}}_2$ can generally be predicted by stream hydrology, with higher groundwater ${\mathrm{CO}}_2$ contributions in small headwater streams compared to larger rivers (Hotchkiss et al. 2015; Horgby et al. 2019b); however, knowledge of local land use and geology, among other factors, are needed to adequately predict groundwater ${\mathrm{O}}_2$ and ${\mathrm{CO}}_2$ contributions (Tank et al. 2018; Horgby et al. 2019a; Hutchins et al. 2021). Furthermore, groundwater contributions are not static and will likely vary with environmental conditions (Ulseth et al. 2018). Overall, groundwater inputs of ${\mathrm{CO}}_2$ are likely to be high in many freshwater ecosystems, which may lead to an underestimation of ${\mathrm{PQ}}_{\mathrm{Bio}}$.

Case study: The Upper Clark Fork River, Montana

The literature clearly supports that the ${\mathrm{PQ}}_{\mathrm{Bio}}$ can vary from the canonical fixed values based on environmental conditions with measures further complicated by a mismatch between ${\mathrm{PQ}}_{\mathrm{Bio}}$ and ${\mathrm{PQ}}_{\text{Meas}}$. Next, we provide a case study of a river where changing environmental conditions predict that the ${\mathrm{PQ}}_{\mathrm{Bio}}$ varies in space and time, and differs from ${\mathrm{PQ}}_{\text{Meas}}$. This case study reveals the inability to reconcile the application of canonical PQs, PQ theory, and measurements of PQ.

The Upper Clark Fork River in western Montana is a mid-order river that is highly productive during the summer growing season due to ample light, warm water, and plenty of nutrients (both N and P). The ${\mathrm{NO}}_3^{-}$ concentration is high near the headwaters of the river, due to a combination of natural and anthropogenic inputs, and generally declines moving downstream. Phosphorus (as soluble reactive phosphorus) is high in the middle section of the Clark Fork due to weathering of P-rich rocks in this region (Carey 1991). Variability in nutrients and productivity make the Clark Fork a useful location to explore how environmental conditions may translate to variation of the ${\mathrm{PQ}}_{\mathrm{Bio}}$ in space and time. Specifically, we explore how variation in ${\mathrm{NO}}_3^{-}$, and the maximum daily ${\mathrm{O}}_2$ saturation might control spatial and temporal variation in the ${\mathrm{PQ}}_{\mathrm{Bio}}$ during the summer growing season. Data, metadata, and code are publicly available (Trentman et al. 2023).

We present data collected in the Clark Fork from summer 2020 (1 August–30 October) at two sites, an upstream site near Warm Springs, Montana (Site 1) and a downstream site near Clinton, Montana (Site 2). Data presented are: ${\mathrm{O}}_2$ concentrations collected using continuous sensors (PME) at 10-min. intervals, and DIN concentrations (as ${\mathrm{NO}}_3^{-}+{\mathrm{NH}}_4$) collected as bi-weekly filtered grab samples and analyzed using standard methods. The ${\mathrm{O}}_2$ data were used to calculate maximum ${\mathrm{O}}_2$ saturation for each day, and estimate ${\mathrm{GPP}}_{\mathrm{O}}$ using a single-station approach. More details on data collection and analyses are provided in SI 3 in Supporting Information. We use these data and the theory presented above to predict ${\mathrm{PQ}}_{\mathrm{Bio}}$ at each site over the algal growing season. Data presented here are unpublished and associated with long-term efforts to characterize the relationship between nutrients, algal biomass, and metabolism in the Clark Fork (H.M. Valett unpubl. data).

Diel ${\mathrm{O}}_2$ reflected a highly productive river with large daily excursions. Maximum daily ${\mathrm{O}}_2$ saturation exceeded 100% at both sites for most of the time series (Fig. 4). Maximum daily ${\mathrm{O}}_2$ saturation dipped below 100% at the downstream site for the final 2 weeks, and at the upstream site for the final 3 d of data. Our current understanding of the link between ${\mathrm{O}}_2$ saturation above 100% and photorespiration suggests that photorespiration was likely affecting ${\mathrm{PQ}}_{\mathrm{Bio}}$. The effect of photorespiration likely declined in the later portion of the sampling period as max ${\mathrm{O}}_2$ saturation dipped below 100%, with a longer dip at the downstream site. The proportion of DIN that was ${\mathrm{NO}}_3^{-}$ was generally higher (between 0.6 and 0.95) at the upstream site, compared to the downstream site (between 0.2 and 0.9; Fig. 4). At both sites, the proportion declined by 0.4 during the growing season and then rebounded toward the end of the growing season. The predicted effect of ${\mathrm{O}}_2$ release from ${\mathrm{NO}}_3^{-}$ assimilation on the PQ was greater at the upstream site compared to the downstream site, with similar amounts of within-site variation over the growing season (Fig. 4).

Fig. 4. The measured environmental conditions that may affect PQBio from two sites on the Upper Clark Fork River, MT during summer 2020: The maximum O2 saturation from continuous (10 min) diel measurements (A,B), and the proportion of DIN present as NO3− from bi-weekly linearly interpolated grab samples (line), and the grab samples used in the interpolation (points; C,D). Measured environmental conditions predicted PQBio [less than] 1 through time at each site (E,F).

We applied the predicted ${\mathrm{PQ}}_{\mathrm{Bio}}$ reflecting the influences of the components addressed herein to the ${\mathrm{GPP}}_{\mathrm{O}}$ measurements derived at the upstream and downstream sites to estimate ${\mathrm{GPP}}_{\mathrm{C}}$ (Fig. 5). We then compared ${\mathrm{GPP}}_{\mathrm{C}}$ rates estimated with the predicted ${\mathrm{PQ}}_{\mathrm{Bio}}$ to the ${\mathrm{GPP}}_{\mathrm{C}}$ estimated with the canonical PQ value of 1.2, as well as a conservative range of PQ values from the literature (0.4–3.5). At both sites, ${\mathrm{GPP}}_{\mathrm{O}}$ rates declined by 50–60% during the measurement period. During the early part of the measurement period, ${\mathrm{GPP}}_{\mathrm{C}}$ using the predicted ${\mathrm{PQ}}_{\mathrm{Bio}}$ was $\sim$ 30% greater than the ${\mathrm{GPP}}_{\mathrm{C}}$ estimated using the traditional fixed PQ of 1.2. The difference between estimates declined as the growing season progressed. At Site 1, the two estimates converged for the final 2 weeks of measurements as max ${\mathrm{O}}_2$ saturation declined to less than 100% saturation and ${\mathrm{PQ}}_{\mathrm{Bio}}$ increased to near 1. At Site 2, the two estimates of ${\mathrm{GPP}}_{\mathrm{C}}$ nearly converged for the final few days of measurements, again matching patterns in maximum ${\mathrm{O}}_2$ saturation. Assuming our predicted ${\mathrm{PQ}}_{\mathrm{Bio}}$ is accurate, using a fixed value of 1.2 may lead to an error in ${\mathrm{GPP}}_{\mathrm{C}}$ estimates of 0–33% based on the site and time of the year.

Fig. 5. The measured GPPO (in units of O2; A,C) and estimated GPPC (in units of C); B,D) from two sites in the UCFR in the summer of 2020 (Site 1, top; Site 2, bottom). We used multiple PQs to estimate the GPPC, including the PQBio from Fig. 4, PQ = 1.2 (traditionally used in freshwater ecosystems), and the range of PQ values from the literature (0.4–3.5). The GPPC estimates using PQBio are 0–33% higher than GPPC estimates based on the fixed value of 1.2.

To capture the potential uncertainty imposed by the various PQs used here, we also compared the ${\mathrm{GPP}}_{\mathrm{C}}$ estimated from the canonical value with the range of PQs found in the literature. The ${\mathrm{GPP}}_{\mathrm{C}}$ using the range of literature PQ values was $\pm$ 63% different than the ${\mathrm{GPP}}_{\mathrm{C}}$ estimates using PQ = 1.2 (Fig. 5), which is a wide range that has implications for how we interpret and analyze ${\mathrm{GPP}}_{\mathrm{C}}$ estimates.

Finally, to employ a more controlled assessment of ${\mathrm{PQ}}_{\mathrm{Bio}}$, we compared the ${\mathrm{PQ}}_{\mathrm{Bio}}$ predicted from environmental conditions with a set of measured PQ values using instruments to directly quantify ${\mathrm{CO}}_2$ and ${\mathrm{O}}_2$. We used sealed recirculating acrylic chambers (Dodds and Brock 1998) to measure the PQ from substrate collected from the Clark Fork River in summer 2021. The PQ was estimated using the change in ${\mathrm{O}}_2$ (measured from continuous sensors) and DIC (estimated from ${\mathrm{CO}}_2$ measured using in situ sensors, DeGrandpre 1993, and ex situ measurements of alkalinity). Six PQ measurements were made based on independent substrata and at varying levels of productivity, provided by altering the available light using a shade cloth. SI 3 in Supporting Information contains a detailed description of the methods. Based on the linear regression of molar rates among the six experiments, the ${\mathrm{PQ}}_{\text{Meas}}$ from the sealed chambers was 1.6 ($\pm$ 0.5 SE of the regression slope; Fig. 6).

Fig. 6. The relationship between O2 and DIC-based gross primary production measured simultaneously in a chamber using substrate from the Clark Fork River. The slope of the blue line was calculated using a reduced major axis approach since the axes are symmetrical and represents PQMeas=1.6 (± 0.5 SE of the slope), which is higher than the predicted PQBio from the same river.

The difference between the mean predicted ${\mathrm{PQ}}_{\mathrm{Bio}}$ (0.7) and the mean ${\mathrm{PQ}}_{\text{Meas}}$ (1.6) in the Clark Fork River shows that there were either substantial bias and error in our measures of C and ${\mathrm{O}}_2$ metabolism (i.e., ${\mathrm{PQ}}_{\text{Meas}}$) or poor predictions based on gaps in the current theory (i.e., ${\mathrm{PQ}}_{\mathrm{Bio}}$). These data cannot adjudicate the true value of the PQ and rather exposes our extensive knowledge gaps in theory and measurement of PQ. It is necessary to resolve these problems in PQ theory and measurements in order to generate accurate assessments of ${\mathrm{GPP}}_{\mathrm{C}}$.

Knowledge gaps Photorespiration

Photorespiration may be more prevalent when estimating aquatic primary production than we know. Studies that estimate photorespiration at the ecosystem level are uncommon (but see Parkhill and Gulliver 1998), despite ample evidence that photorespiration is occurring in highly productive and pH-neutral waters. Thus, more ecosystem-level estimates of the prevalence and magnitude of photorespiration are necessary. Although some evidence shows a relationship between photorespiration and ${\mathrm{O}}_2$ saturation or the ratio of ${\mathrm{O}}_2$ to ${\mathrm{CO}}_2$, the data representing these empirical relationships are lacking. Furthermore, it is not clear if empirical relationships are species-specific. For example, some species of red and brown algae suppress photorespiration more than many green algae species (Reiskind et al. 1989). In general, it is not clear how strongly species differ in the magnitude and prevalence of photorespiration, and if the potential variation is relevant to ecosystem-level estimates of primary production.

${\mathbf{NO}}_{\mathbf{3}}^{-}$ assimilation

Although multiple field and lab studies have characterized the effect of ${\mathrm{O}}_2$ release during ${\mathrm{NO}}_3^{-}$ assimilation on the PQ, our ability to predict this effect is more complicated than our current knowledge (i.e., Eq. 7). Equation 7 does not account for the scenario where ${\mathrm{NH}}_4^{+}$ and ${\mathrm{NO}}_3^{-}$ are both saturated in respect to nutrient demand (Dodds et al. 2002; e.g., algae are limited by their maximum nutrient uptake rate rather than nutrient availability). For example, a realistic scenario in many agricultural streams is that both ${\mathrm{NH}}_4^{+}$ and ${\mathrm{NO}}_3^{-}$ are present in high concentrations (e.g., 10 and 110 μmol ${\mathrm{L}}^{-1}$, respectively; M. T. Trentman pers. observ.). In this scenario, using Eq. 7 would lead to an overestimate of the effect of ${\mathrm{NO}}_3^{-}$ assimilation on the PQ because the form of N uptake is dominated by ${\mathrm{NH}}_4^{+}$, which is preferentially assimilated by organisms. Furthermore, in marine environments, urea can be a substantial proportion of DIN (Ignatiades 1986; Antia et al. 1991) and is more readily assimilated than ${\mathrm{NH}}_4^{+}$. In short, Eq. 7 should account for the abundance of ${\mathrm{NH}}_4^{+}$ and urea in relation to demand as well as the relative availability of ${\mathrm{NO}}_3$.

Photosynthetic products

Information on the production of different C products during photosynthesis are uncommon, specifically for freshwater algae and species that have no commercial interest, making it difficult to calculate the theoretical ${\mathrm{PQ}}_{\mathrm{C}{\left(\mathrm{H}\right)}_Y{\left(\mathrm{O}\right)}_Z}$. Thus, our understanding of how ${\mathrm{PQ}}_{\mathrm{C}}$ may vary by species and with environmental conditions (e.g., light) is limited. However, most photosynthetic products, including proteins, nucleic acids, and glucose, have a ${\mathrm{PQ}}_{\mathrm{C}{\left(\mathrm{H}\right)}_Y{\left(\mathrm{O}\right)}_Z}$ of approximately 1. That leaves glycolic acid and saturated fatty acids as two possible sources of variation, which could decrease and increase the ${\mathrm{PQ}}_{\mathrm{C}{\left(\mathrm{H}\right)}_Y{\left(\mathrm{O}\right)}_Z}$, respectively, based on their content in an algal cell. It is unlikely that the production of glycolic acid is substantial enough to shift the PQ given the relatively low production rate (Cheng et al. 1972). It is more likely that the species-specific variability in saturated fatty acid production (Harwood 2019) would change the ${\mathrm{PQ}}_{\mathrm{C}{\left(\mathrm{H}\right)}_Y{\left(\mathrm{O}\right)}_Z}$. For example, the lipid content of benthic algae can range in complexity (i.e., O and H contents; Guschina and Harwood 2006; Li-Beisson et al. 2019), but there are little data on how this variation in lipid chemistry affects the proportion of the total C of algal biomass. Research is needed that quantifies the rate of saturated fatty acid production across algae species, and how this production varies with environmental variability.

PQ measurements across scales and species

More measurements of PQ, particularly on freshwater benthic algae and using methods other than ${}^{14}\mathrm{C}$, would improve our understanding of how the ${\mathrm{PQ}}_{\mathrm{Bio}}$ varies among species and with environmental variables. The PQ can be measured through a variety of approaches that can be generally separated by the location of the measurements, whether controlled (e.g., in bottles or chambers) or in the natural environment. Measuring the PQ requires simultaneous monitoring of the C that is fixed and the ${\mathrm{O}}_2$ that is released during the process of primary production (Although, see the above text that describes the measurement challenges imposed by respiration). The measurement of ${\mathrm{O}}_2$ can be accurately obtained with low-cost optical sensors (assuming no captive bubbles). Estimating the change in DIC is more involved and includes either direct measurements of DIC or is accomplished by estimating the DIC pool via measures of dissolved ${\mathrm{CO}}_2$ concentrations and either pH or alkalinity (Dickson et al. 2007). In highly buffered waters, the relative decline in DIC will be small, and this decline is difficult to accurately quantify, but the decline in ${\mathrm{CO}}_2$ will be large. Given this fact, we briefly highlight the pros, cons, and limitations of the best-known approaches that use accurate measures of ${\mathrm{O}}_2$ and ${\mathrm{CO}}_2$.

Using sealed containers to measure algal productivity allows for control of environmental conditions. Controlled measurements of PQ will promote equivalence between ${\mathrm{PQ}}_{\text{Meas}}$ and ${\mathrm{PQ}}_{\mathrm{Bio}}$, since it will be easier to limit ${\mathrm{PQ}}_{\text{Meas bias}}$. The bottle approach is useful for phytoplankton, while more complex chambers should be used for benthic algae, especially from rivers. Unidirectional flow in rivers is one of many controls on primary productivity, thus chambers with continuous, circulating flow are needed to measure the PQ for riverine benthic algae (Dodds and Brock 1998; Rüegg et al. 2015). PQ measurements sealed from the atmosphere are best because, if used properly, the chambers allow the researcher to rule out gas-exchange between the water and the atmosphere, which can be challenging to measure in low productivity and turbulent ecosystems (among other conditions; Hall and Ulseth 2020). The benefits of bottles or chambers should be balanced with the potential bias of measuring ex situ processes. When working with chambers, it is common to not let ${\mathrm{O}}_2$ exceed 100% saturation in order to limit bubble formation in the chamber. Thus, chamber experiments may be biased in that the effects of ${\mathrm{PQ}}_{\mathrm{Pr}}$ are limited. Finally, large chambers can be expensive and cumbersome to use (M.T. Trentman pers. observ.).

Measuring diel variation in ${\mathrm{O}}_2$ and DIC to estimate metabolic processes is another approach to estimate the PQ, although in most scenarios ${\mathrm{PQ}}_{\text{Meas}}\ne {\mathrm{PQ}}_{\mathrm{Bio}}$ due to ${\mathrm{PQ}}_{\text{Meas bias}}$. The bias of PQ measured with diel sensors will be particularly problematic given that there is a range of environmental controls on reach scale or whole lake ${\mathrm{O}}_2$ and DIC budgets. Bubbles, groundwater inputs, and the complexities of DIC chemistry (e.g., calcite precipitation), among many other factors, may impose higher variation on ${\mathrm{PQ}}_{\text{Meas}}$ than the biological signal. That said, simultaneous monitoring of diel ${\mathrm{O}}_2$ and ${\mathrm{CO}}_2$ concentrations is a relatively new approach made possible by the increased availability of accurate ${\mathrm{CO}}_2$ sensors (Vachon et al. 2020). However, at the time of writing this article, the models used to estimate metabolism from DIC are still in development despite their prior use (Wright and Mills 1967). A degree of caution is necessary to interpret reach-level estimates of PQ given that measurements will likely not reflect ${\mathrm{PQ}}_{\mathrm{Bio}}$. Future methods and models should be developed with the specific goal of parsing ${\mathrm{PQ}}_{\mathrm{Bio}}$ from ${\mathrm{PQ}}_{\text{Meas}}$ at all levels of measurement. Isotopic approaches at either scale (Ferrón et al. 2016, e.g., with labeled ${}^{18}\mathrm{O}$ water or ${}^{13}\mathrm{C}$) may be useful in parsing ${\mathrm{PQ}}_{\mathrm{Bio}}$ from ${\mathrm{PQ}}_{\text{Meas}}$ or specific process (e.g., photorespiration); however, to our knowledge, specific methods and approaches do not yet exist.

Conclusions

An accurate ${\mathrm{PQ}}_{\mathrm{Bio}}$ is needed for understanding C metabolism derived from ${\mathrm{O}}_2$ data. The current evidence suggests that the ${\mathrm{PQ}}_{\mathrm{Bio}}$ can vary with environmental conditions. Thus, the use of fixed canonical ${\mathrm{PQ}}_{\mathrm{Bio}}$ values is likely causing inaccurate estimates of C-based metabolism from ${\mathrm{O}}_2$ data. Although the current theory provides a basic understanding of the processes that may control the ${\mathrm{PQ}}_{\mathrm{Bio}}$, much research will be necessary to use environmental conditions to predict ${\mathrm{PQ}}_{\mathrm{Bio}}$ values more accurately and precisely. Furthermore, consideration needs to be given to observation error and measurement bias that will be common when measuring the PQ in the natural environment. Until we improve PQ theory and our ability to reconcile error and bias from ${\mathrm{PQ}}_{\text{Meas}}$, we suggest we should employ more scrutiny when applying PQ values to convert O₂-based metabolism to C. Specifically, researchers should move beyond fixed values of the PQ. Instead, we suggest matching our current knowledge of how the PQ varies with the environmental conditions at any given measurement site to generate a range of plausible PQ values (e.g., Fig. 5) from the literature. Such an approach will better account for the uncertainty of the PQ when estimating C-based metabolism from ${\mathrm{O}}_2$ data.

Acknowledgments

National Science Foundation EPSCoR Cooperative Agreement OIA-175735, National Science Foundation grants EF-1834679 and LTREB DEB 1655197 supported our research. We thank the Associate Editor, Gerard Rocher-Ros, and an anonymous reviewer for feedback on the manuscript. Venice Bayrd and Robert Payne were essential in compiling metadata, code, and data for submission to EDI. Amanda Spencer and Sam Bosio assisted with chamber PQ measurements.