Scaling from fluxes to organic matter: interpreting ¹³C isotope ratios of plant material using flux models

Short abstract

This article is a Commentary on Leppä et al. (2022), 236: 2044–2060.

The isotope ratios of ecosystem fluxes and pools inform us about ecological connections that are otherwise invisible to the human eye at scales ranging from microbes to landscapes, and from seconds to millennia (Fry, 2006). We use mechanistic models to link observations of isotope ratios to underlying physiological processes. These models allow us to retrieve environmental and physiological signals and to test our current theoretical understanding of ecosystem functions. The most common models to describe ¹³C and ¹⁸O isotope ratios in plants are those of Farquhar and coworkers (reviewed in Cernusak et al., 2013, 2016; Ubierna et al., 2018; Song et al., 2022). These models describe isotope effects occurring in the leaf during the processes of photosynthesis and transpiration. While photosynthesis and transpiration are instantaneous fluxes, applications often deal with downstream pools, such as leaf or tree‐ring organic matter, that integrate signals over different timeframes and processes. Scientists have tried to account for this temporal and spatial variation using both simplified (Farquhar & Richards, 1984) and more elaborate (Schiestl‐Aalto et al., 2021) models. Nevertheless, 40 years after the initial applications of stable isotopes in ecophysiology, we are still deciphering how environmental signals are recorded by different plant pools. A significant step forward would be understanding the processes that determine the isotope ratios of the leaf sugar pool and how best to model them, as this is ultimately what gets exported to supply dry‐matter production. What integration time does the leaf sugar pool δ¹³C and δ¹⁸O reflect and are there any post‐photosynthetic isotope effects already observed within this pool? In this issue of New Phytologist, Leppä et al. (2022; pp. 2044–2060) addressed this topic by exploring needle sugar C (δ¹³C) and O (δ¹⁸O) isotope composition in boreal Scots pine over two growing seasons.

Leppä et al. created an environmentally driven dynamic model that predicted δ¹³C and δ¹⁸O of leaf sugars from leaf‐level models of isotope exchange implemented as variants with increasing degrees of complexity. The comparison of model variants found that needle sugar δ¹³C and δ¹⁸O was reasonably well predicted with relatively simple models, as most of the variation in those signals was related to the c _i/c _a (the ratio of intercellular to ambient [CO₂]) and relative humidity (RH), respectively. These results encourage the use of tree rings to reconstruct RH and c _i/c _a records. The c _i/c _a values can subsequently be used to estimate intrinsic water‐use efficiency (iWUE or A/g _s), a parameter that describes the relationships between water and carbon fluxes, which is used from crop science to global ecology (Farquhar & Richards, 1984; Cernusak, 2020; Saurer & Voelker, 2022).

‘Nevertheless, 40 years after the initial applications of stable isotopes in ecophysiology, we are still deciphering how environmental signals are recorded by different plant pools.’

Applications that retrieve an integrated c _i/c _a from dry matter often use a simplified version of the ¹³C photosynthetic discrimination model, while a comprehensive model is used to calculate physiological parameters such as mesophyll conductance (g _m). Model simplifications can result in quantitative errors, but comprehensive models can be difficult to parametrize. Choosing an adequate model becomes even more of a challenge when applying the flux models to C pools that have been subjected to metabolism, thereby needing the consideration of post‐photosynthetic isotope fractionation. As we struggle to find a balance between model complexity and usefulness, it is important to understand the assumptions and capabilities of each approach. Here, we explain the different models and measurements of C isotope discrimination and how they record and integrate isotope signals. Leppä et al. also assess processes across scales that influence the oxygen isotope composition, but we limit this Commentary to ¹³C processes and refer readers to a recent comprehensive review of ¹⁸O effects in leaf water (Cernusak et al., 2016).

Terminology

Discrimination (Δ) indicates the change in isotope ratio between two molecules or compounds induced by a process. That process can be instantaneous (i.e. photosynthesis) or integrative (i.e. synthesis and accumulation of organic compounds). Discrimination can be measured or modelled from theory. We use the following terms: (1) instantaneously observed photosynthetic discrimination against ¹³CO₂ (Δ_obs, see Fig. 1 for equations); (2) modelled photosynthetic discrimination (Δ_3‐com or Δ_3‐sim); and (3) plant discrimination (Δ_p) measured in organic compounds.

Fig. 1.

The C isotope composition (δ¹³C) of photosynthate and plant material are partially decoupled; photosynthesis is an instantaneous flux, but plant materials – leaf sugars, leaf biomass and stem biomass – are integrative pools affected by post‐photosynthetic processes. The change in C isotope ratio induced during photosynthesis is measured with Δ_obs (observed discrimination, Eqn 1, Evans et al., 1986) and modelled with Δ_3‐com (comprehensive model for ¹³C photosynthetic discrimination, Eqn 3, presented in Busch et al., 2020, format ignoring ‘alpha’ terms). The change in isotope ratio induced during photosynthesis + post‐photosynthetic processes is measured with Δ_p (plant discrimination, Eqn 2) but we lack a mechanistic model describing all the processes involved. Instead, a simplified version of Δ_3‐com (Δ_3‐sim, Eqn 4) can be used to interpret Δ_p values. Δ_3‐sim accounts for post‐photosynthetic effects with the parameter $\overline{b}$, empirically determined from regressions ${\mathrm{\Delta }}_{\mathrm{p}}=a_{\mathrm{s}}+\left(\overline{b}-a_{\mathrm{s}}\right)\left(c_{\mathrm{i}}/c_{\mathrm{a}}\right)$ (solid lines in (a–c), the intercepts are fixed at a _s = 4.4‰ and $\overline{b}$ is fitted and equal to 24.5‰, 26.9‰, and 25.5‰ for sucrose, leaf biomass and stem biomass, respectively). Flux‐based applications combine Δ_obs and Δ_3‐com to solve for a parameter, such as mesophyll conductance (g _m), and allow the investigation of rapid dynamics. Plant biomass applications combine Δ_p with Δ_3‐sim to calculate parameters such as intrinsic water‐use efficiency (iWUE) over longer periods of time. Δ_p derived from sugars pools (i.e. leaves or phloem) has also been combined with Δ_3‐com to derive g _m. (a) Closed circles are data from Scots pine needle sucrose in this issue of New Phytologist by Leppä et al. (2022: pp. 2044–2060) and solid line is the regression fitted to those data points with an intercept of 4.4‰ and slope of 24.5‰; dotted line is Δ_p = 4.3 + 21.1 (c _i/c _a), where intercept and slope are the mean values reported in Table 1 and the shaded brown area represents that line ±1 SD. Data and regression lines in (b, c) are from Cernusak & Ubierna (2022) consisting of 33 woody species (available in 10.5061/dryad.jm63xsjct). Symbols used in equations: ζ = c _in/(c _in − c _out) (unitless), c _in, c _out, c _a, c _s, c _i and c _c are the CO₂ mole fractions (μmol mol⁻¹) in the air in and out of a gas‐exchange cuvette, ambient air, leaf surface, leaf intercellular spaces and chloroplast, respectively. δ is the δ¹³C (‰) of the incoming (δ_in) and outgoing (δ_out) air streams, ambient air (δ_a) and plant C (δ_p, sugars, leaf, stem). a _b, a _s, a _m, e and f are the fractionations associated with diffusion through the boundary layer (2.9‰), in air (4.4‰), in water (1.8‰), during respiration (0‰ to −5‰) and photorespiration (8–16‰), respectively. b ₃ is discrimination against ¹³CO₂ by carboxylating enzymes, often taken as rubisco fractionation (b _rub = 30‰). A and ${\mathcal{R}}_d$ are the photosynthetic and day respiration rates (μmol m⁻² s⁻¹), respectively. Γ* is the CO₂ compensation point in the absence of day respiration (μmol mol⁻¹). The ternary effect is t = α_ac E/2g _ac, where E is the transpiration rate (mol m⁻² s⁻¹), and g _ac is the conductance to diffusion of CO₂ in air (mol m⁻² s⁻¹).

Photosynthetic discrimination (both observed Δ_obs and modelled Δ_3‐com) describes the change in C isotope composition occurring during photosynthesis, which is a flux with a starting point of ambient CO₂ and an end point of recent assimilates. On the other hand, plant discrimination (Δ_p) determines the change in isotope abundance between ambient CO₂ and organic matter (e.g. sugars and structural carbohydrates). Recent assimilates and plant matter are partially decoupled in time (instantaneous vs integrative) and space (initial photosynthate vs derived carbohydrates). Accordingly, interpreting δ¹³C signatures of plant matter requires understanding both the turnover time of the pool and the processes downstream of photosynthesis modifying the isotope composition of recent assimilates. The isotope effects occurring after photosynthesis are referred to as post‐photosynthetic fractionations (Badeck et al., 2005). They are numerous, complex to integrate and hinder the physiological interpretation of isotope signals (Gessler & Ferrio, 2022; Kagawa & Battipaglia, 2022). Leppä et al. simplified these complexities by assessing leaf sugars (a step closer to assimilates than sugars in sink tissue or the final dry matter).

Despite these complexities, the comparison between measured (Δ_obs or Δ_p) and modelled (Δ_3‐com or Δ_3‐sim) discrimination permits the retrieval of environmental and physiological signals. The comprehensive model for C₃ photosynthetic discrimination (Δ_3‐com) includes all the steps in the CO₂ journey during photosynthesis (Farquhar et al., 1982; Farquhar & Cernusak, 2012; Ubierna et al., 2019; Busch et al., 2020). This model can be simplified to a version (Δ_3‐sim, Ubierna & Farquhar, 2014) that relates isotope ratios and plant function through a unique variable, the gas exchange parameter c _i/c _a. Neither Δ_3‐com nor Δ_3‐sim explicitly account for post‐photosynthetic fractionations as they are flux models. Nevertheless, as discussed subsequently, Δ_3‐sim can indirectly account for post‐photosynthetic effects providing a framework to interpret Δ_p values.

Using the simplest discrimination model Δ_3‐sim

Leaf biomass

The simplest model Δ_3‐sim lumps the combined effects of model simplifications and post‐photosynthetic fractionations not considered by the flux model into an empirically determined parameter $\overline{b}$ (Fig. 1). The parameter $\overline{b}$ should not be interpreted as a modified value for b ₃, which is discrimination against ¹³CO₂ by carboxylating enzymes (i.e. mostly rubisco in C₃ plants, but some can also occur by phosphoenolpyruvate). Instead, $\overline{b}$ combines several fractionations that occur during and after photosynthesis. Because post‐photosynthetic effects are different across plant tissues, one should not expect a universal $\overline{b}$ value. However, most applications to date have used $\overline{b}$ = 27‰, which was derived from empirical relationships between gas exchange c _i/c _a and Δ_p calculated from leaf bulk material (Farquhar et al., 1982; Cernusak et al., 2013; Cernusak & Ubierna, 2022).

Using a parameter derived from leaf biomass to interpret the isotope ratios of other plant tissues has resulted in suboptimal performance of the Δ_3‐sim model, thereby discouraging its use in favor of more complex formulations (Seibt et al., 2008; Gentsch et al., 2014). However, as discussed here, a simplified model Δ_3‐sim can be an acceptable compromise as long as an appropriate $\overline{b}$ is used, which we suggest could have values of c. 27‰, 25.5‰ and 24.5‰ for leaf bulk material, wood and leaf sugars, respectively.

Fractionations occurring during photosynthesis, but neglected in the simplified model, are associated with mesophyll diffusion, respiration and photorespiration. The largest of these, mesophyll diffusion, amounts to a reduction from b ₃ to $\overline{b}\cong b_3\left(c_{\mathrm{c}}/c_{\mathrm{i}}\right)$ (Ubierna & Farquhar, 2014). The value for rubisco fractionation determined in vitro is 30‰ (Roeske & O'Leary, 1984), but it could be lower in vivo if some C fixation occurs through phosphoenolpyruvate carboxylation (Farquhar & Richards, 1984; Brugnoli et al., 1988). Using c _c/c _i = 0.85 (Ubierna & Farquhar, 2014) and b ₃ = 30‰ results in $\overline{b}$ = 25.5‰. Under current ambient conditions (21% O₂, 400 ppm of CO₂) and at 25°C, photorespiration would further reduce $\overline{b}$ by 1.1‰ (Ubierna & Farquhar, 2014) and respiration is a minor contributor in most situations. Therefore, the combined effects of model simplifications can be balanced out using $\overline{b}$ ≅ 24.5‰. This is consistent with the findings of Bickford et al. (2009), who determined that Δ_obs could be approximated with Δ_3‐sim using $\overline{b}$ = 25‰ in Juniperus monosperma.

Leaves are 2–3‰ more depleted than nonphotosynthetic tissues (Craig, 1953). Several processes have been suggested to explain this depletion (Cernusak et al., 2009), ranging from variation in biochemical composition (Park & Epstein, 1961; Badeck et al., 2005) to the legacy of depleted structural C added through photosynthesis during leaf expansion, a period when leaves operate at higher c _i/c _a ratios than those typical of mature foliage (Evans, 1983; Vogado et al., 2020). Adjusting the 24.5‰ obtained from model simplifications by the 2–3‰ developmental depletion (larger discrimination with respect to atmospheric CO₂) results in the empirically determined value of $\overline{b}$ = 27‰ for leaf biomass.

Sugar pool

When using a sugar pool, one might expect a value for $\overline{b}$ near 24.5‰ because in this case, the partial decoupling between the measured pool (sugars) and model (instantaneous photosynthate) might only be temporal and will be accounted for by using an integrated c _i/c _a in the model of Δ_3‐sim. Nevertheless, there could also exist post‐photosynthetic fractionations affecting leaf sugar δ¹³C values. For example, sucrose exported from the leaf has been shown to be more ¹³C depleted during the day than at night (Gessler et al., 2008). We used Leppä et al.'s measured leaf sugar δ¹³C values to produce a relationship Δ_p vs weighted c _i/c _a, which had a slope of 20.1 ± 0.2‰ when the intercept was fixed at 4.4‰, and resulted in $\overline{b}$ = 24.5‰ (Δ_p = 4.4 + (24.5 − 4.4) c _i/c _a, P < 0.0001, R ² = 0.7, Fig. 1). This $\overline{b}$ is the same as the value we estimated from theory for recent assimilates, suggesting that in Scots pine, the leaf sugar pool was not significantly affected by post‐photosynthetic fractionations, but rather it was an integration of the photosynthetic flux (2–5 d).

A value of $\overline{b}$ = 24.5‰ translates to c _c/c _i ≅ 0.82 (because $\overline{b}\cong b_3\left(c_{\mathrm{c}}/c_{\mathrm{i}}\right)$), which is consistent with Leppä et al.'s modelling assumption for including g _m in the comprehensive model of ¹³C discrimination of c _c/c _i = 0.8. A similar c _c/c _i ratio has been observed for other C₃ species (Ubierna & Farquhar, 2014). Other approaches have also been used to account for g _m in models of discrimination, such as using a constant g _m (Wingate et al., 2007), a constant ratio of stomata to mesophyll conductance g _s : g _m c. 0.78 (Ma et al., 2021) or equations that calculate g _m from different combinations of parameters such as photosynthetic rate, light, temperature and water stress (Schiestl‐Aalto et al., 2021). Here we show that Leppä et al.'s data could be predicted with a much simpler model Δ_3‐sim parametrized with $\overline{b}$ = 24.5‰.

To assess the variability associated with $\overline{b}$, we compiled studies reporting the linear relationship between Δ_p from leaf sugars and c _i/c _a (Table 1). These studies used a variety of species (poplar, cotton, bean, sugar beet and rice) and treatments (drought, irradiance, different vegetative states, and age). On average, the slope and intercepts reported in these studies (mean and SD, n = 8) were 21.1‰ (2.6) and 4.3‰ (2.5), respectively. A slope of 21.1‰ translates into $\overline{b}$ = 25.4‰ (if a is the average intercept of 4.3‰, Table 1). The 1‰ offset between this mean $\overline{b}$ and the value we calculated with Leppä et al.'s data could be related to the fact that studies in Table 1 analysed water‐soluble sugars (sucrose, glucose, fructose and pinitol) while Leppä et al.'s study analysed sucrose. Bulk leaf sugars are ¹³C depleted compared to sucrose, mostly due to the contribution of ¹³C depleted pinitol (Rinne et al., 2015). The δ¹³C of pinitol has been shown to be almost invariant during a growing season (Rinne et al., 2015), diluting out the signal of the sugar pool δ¹³C (Leppä et al., 2022). Therefore, applications would benefit from calculating Δ_p from sucrose, or empirically removing the contribution of pinitol.

Table 1.

Studies reporting Δ_p = Intercept + slope (c _i/c _a) where Δ_p is calculated with Eqn 2 (see Fig. 1) using leaf sugar δ¹³C.

Reference	Species	Slope (‰)	Intercept (‰)	Driver of c i/c a variation
Brugnoli et al. (1988)	Populus nigra L. × Populus deltoides Marsh Gossypium hirsutum L. Phaseolus vulgaris L.	21.3	3.9	VPD, light intensity and CO2
Scartazza et al. (1998)	Oryza sativa L. vegetative state	20.1	6.2	Drought and developmental state
	O. sativa L. flowering	26.6	−0.5
	O. sativa L. grain filling	22.0	2.1
Monti et al. (2006)	Beta vulgaris L. 5 DAS	21.3	6.3	Drought and crop ageing
	B. vulgaris L. 38 DAS	19.8	4.9
	B. vulgaris L. 53 DAS	20.1	5.2
	B. vulgaris L. 71 DAS	17.7	6.6
Average (SD)		21.1 (2.6)	4.3 (2.5)

The simplest model for ¹³C is ${\mathrm{\Delta }}_{3‐\mathrm{sim}}=a_{\mathrm{s}}+\left(\overline{b}-a_{\mathrm{s}}\right)\left(c_{\mathrm{i}}/c_{\mathrm{a}}\right)$ (Farquhar et al., 1982). VPD, vapor pressure deficit. In the Monti et al. (2006) data, DAS stands for days after stress imposition, which was drought. Re‐watering occurred at DAS 37.

While variation exists and more studies are needed to quantify the impact of using different sugar fractions, on average, $\overline{b}$ for leaf sugars is likely to be 24.5 ± 1‰ (Fig. 1). If this value for $\overline{b}$, expected from theory and supported by data from Leppä et al. and others (Brugnoli et al., 1988; Scartazza et al., 1998; Monti et al., 2006), is demonstrated to apply to other species and conditions, then it would provide an easy means of deriving integrated c _i/c _a from sugar‐derived Δ_p. An integrated c _i/c _a can be preferred over instantaneous gas exchange c _i/c _a to capture plant function, particularly in field settings where collecting sufficient gas exchange records to grasp photosynthetic dynamics is unfeasible. Values of δ¹³C for stem phloem have been demonstrated to integrate the activity of the entire canopy (Ubierna & Marshall, 2011). Therefore, sugar pools can serve to derive integrative physiological parameters that combine with records from eddy flux or remote sensing.

Wood

Tree‐ring wood has been found to be 1–2‰ more depleted in ¹³C than in phloem sugars (Wei et al., 2014) but 1–3‰ enriched compared to leaves (Cernusak et al., 2009). That would suggest a $\overline{b}$ for wood in between those derived for sugars (24.5‰) and leaves (27‰). Indeed this expectation has been confirmed via a regression analysis between Δ_p derived from wood δ¹³C and gas exchange c _i/c _a revealing a value for $\overline{b}$ = 25.5‰ (Cernusak & Ubierna, 2022; Fig. 1). Though much debate still exists regarding post‐photosynthetic fractionations, processes such as bark photosynthesis and refixation, or different C storage and remobilization dynamics could explain the ¹³C offset between wood and sugars (Gessler & Ferrio, 2022).

The value $\overline{b}$ = 25.5‰ was determined with whole wood, but it would need to be readjusted if using cellulose, which is known to be c. 1‰ more enriched than wood (Harlow et al., 2006). Values for $\overline{b}$ are empirically derived from a linear regression with the form of the simplest model Δ_3‐sim. If one were to use the comprehensive model, or some intermediate version of it, this would lead to an error if $\overline{b}$ were not adequately readjusted (Bloomfield et al., 2019). An example of an intermediate version is presented in Ubierna & Farquhar (2014) that adds the contribution of photorespiration to the simplest ¹³C discrimination model, which could be useful when large gradients in temperature, O₂ or CO₂ are expected. Photorespiratory contribution to total discrimination in recent assimilates is c. 1.1‰, but we ignore how much of that translates into wood biomass δ¹³C.

When is Δ_3‐sim not enough?

Using Δ_3‐sim can be an acceptable compromise for many applications, but it will not suffice when the processes investigated are dynamic enough – across time or species – that they cannot be accounted for with a unique and constant $\overline{b}$ value. That is typically the case of applications measuring instantaneous observed discrimination (Δ_obs) to derive physiological parameters. Then, the model of choice should be Δ_3‐com because any model simplification, error or uncertainty will be compounded in the value of the derived parameter. In these situations, even ignoring small effects can have a significant impact; for example, mesophyll conductance was overestimated when ternary effects were ignored (Farquhar & Cernusak, 2012). If the aim is to derive iWUE from Δ_obs, mesophyll conductance should be accounted for, but respiratory fractionations, boundary layer conductance and ternary effects are far less influential (Ma et al., 2021). If the focus is interpreting diurnal trends in discrimination, Δ_3‐sim will not be able to explain some processes occurring at low fluxes. For example, a comprehensive model was needed to produce good estimations of iWUE early in the morning (Stangl et al., 2019) or to explain large Δ_obs at dawn and dusk (Wingate et al., 2007). Interpreting intra‐annual trends in tree rings can require models with more than one substrate pool (Offermann et al., 2011).

As illustrated, there are multiple examples where isotope signals cannot be retrieved with Δ_3‐sim. However, for broader scale Δ_p‐based applications, the simplest Δ_3‐sim model is likely to suffice when an appropriate $\overline{b}$ is used. Besides its simplicity, Δ_3‐sim indirectly accounts for photosynthetic and post‐photosynthetic effects through the empirically derived value of $\overline{b}$ providing a useful framework to interpret isotope ratios of plant biomass. We encourage scientists to refrain from using $\overline{b}$ = 27‰ across the board and instead use tissue‐specific values. The values for $\overline{b}$ for both leaves and wood are cross‐species averages and the one for sugars is based on Leppä et al.'s Scots pine sucrose data and supported by results from other species (Brugnoli et al., 1988; Scartazza et al., 1998; Monti et al., 2006). Variation in $\overline{b}$ exists across species and environmental conditions (Cernusak & Ubierna, 2022). Future research should investigate variation of $\overline{b}$ and how it relates to the many processes lumped into this parameter.