Quantifying Light Response of Leaf-Scale Water-Use Efficiency and Its Interrelationships With Photosynthesis and Stomatal Conductance in C₃ and C₄ Species

Abstract

Light intensity (I) is the most dynamic and significant environmental variable affecting photosynthesis (A_n), stomatal conductance (g_s), transpiration (T_r), and water-use efficiency (WUE). Currently, studies characterizing leaf-scale WUE–I responses are rare and key questions have not been answered. In particular, (1) What shape does the response function take? (2) Are there maximum intrinsic (WUE_i; WUE_i–max) and instantaneous WUE (WUE_inst; WUE_inst–max) at the corresponding saturation irradiances (I_i–sat and I_inst–sat)? This study developed WUE_i–I and WUE_inst–I models sharing the same non-asymptotic function with previously published A_n–I and g_s–I models. Observation-modeling intercomparison was conducted for field-grown plants of soybean (C₃) and grain amaranth (C₄) to assess the robustness of our models versus the non-rectangular hyperbola models (NH models). Both types of models can reproduce WUE–I curves well over light-limited range. However, at light-saturated range, NH models overestimated WUE_i–max and WUE_inst–max and cannot return I_i–sat and I_inst–sat due to its asymptotic function. Moreover, NH models cannot describe the down-regulation of WUE induced by high light, on which our models described well. The results showed that WUE_i and WUE_inst increased rapidly within low range of I, driven by uncoupled photosynthesis and stomatal responsiveness. Initial response rapidity of WUE_i was higher than WUE_inst because the greatest increase of A_n and T_r occurred at low g_s. C₄ species showed higher WUE_i–max and WUE_inst–max than C₃ species—at similar I_i–sat and I_inst–sat. Our intercomparison highlighted larger discrepancy between WUE_i–I and WUE_inst–I responses in C₃ than C₄ species, quantitatively characterizing an important advantage of C₄ photosynthetic pathway—higher A_n gain but lower T_r cost per unit of g_s change. Our models can accurately return the wealth of key quantities defining species-specific WUE–I responses—besides A_n–I and g_s–I responses. The key advantage is its robustness in characterizing these entangled responses over a wide I range from light-limited to light-inhibitory light intensities, through adopting the same analytical framework and the explicit and consistent definitions on these responses. Our models are of significance for physiologists and modelers—and also for breeders screening for genotypes concurrently achieving maximized photosynthesis and optimized WUE.

Introduction

Stomata control the balance between carbon flux driven by photosynthesis and water flux dominated by transpiration, which is characterized by water-use efficiency (WUE) at various scales (Sinclair et al., 1984; Gilbert et al., 2011; Eamus et al., 2016; Medlyn et al., 2017). WUE can thus indicate the natural selection on the balance between these fluxes (Hetherington and Woodward, 2003). Characterizing the environmental impacts on WUE among plant species and/or plant function types can advance our knowledge on differential plant adaptation strategies, and improve our prediction on consequences of environmental challenges (Avola et al., 2008; Egea et al., 2011; Zhou et al., 2014, 2016; De Kauwe et al., 2015; Köhler et al., 2016; Ahrar et al., 2017). For instance, plant species with the highest WUE would show the greatest fitness in dry habitats (Dudley, 1996; Zhou et al., 2019). WUE is also an important metric in crop breeding and genotype selection, especially for irrigated crops whose water use significantly affects crop productivity and profitability (Duursma et al., 2013; Flexas et al., 2013; Bota et al., 2016; Webster et al., 2016).

WUE can be estimated using different techniques, based on observations of leaf gas exchange, stable isotope discrimination, and eddy covariance fluxes (Medlyn et al., 2017). Among these techniques, WUE is most commonly estimated by measuring leaf gas exchange, facilitated by portable photosynthesis system allowing simultaneous measurement of leaf-scale carbon and water fluxes (Medrano et al., 2015). WUE derived from leaf gas exchange measurement is usually defined as the ratio of net CO₂ assimilation rate (A_n) to stomatal conductance for water vapor (g_s)—intrinsic water-use efficiency (WUE_i; von Caemmerer and Farquhar, 1981), or the ratio of A_n to transpiration rate (T_r)—instantaneous water-use efficiency (WUE_inst; Fischer and Turner, 1978) (see Table 1 for a summary of parameters and units). WUE_i can be used to compare photosynthetic characteristics independently of evaporative demand (Linares and Camarero, 2012). WUE_inst is a key determinant of whole-plant WUE as it summarizes plant dry mass production per unit of water loss (Sinclair et al., 1984; Duursma et al., 2013; but see Medrano et al., 2015 for constraints). WUE_i and WUE_inst have been widely used as an index of plant and vegetation performances in response to various environmental changes, such as changed water or light availabilities, vapor pressure deficit (VPD), temperature and CO₂ concentration (Aranda et al., 2007; Avola et al., 2008; Linares and Camarero, 2012; Duursma et al., 2013; Bota et al., 2016).

TABLE 1.

List of major model parameters defining the light response curves of photosynthesis (A_n), stomatal conductance (g_s), intrinsic water use efficiency (WUE_i), and instantaneous water use efficiency (WUE_inst).

Symbol	Definition	Unit
An	Net photosynthetic rate	μmol CO2 m–2 s–1
Anmax	Maximum net photosynthetic rate	μmol CO2 m–2 s–1
gs	Stomatal conductance	mol H2O m–2 s–1
gs–max	Maximum stomatal conductance	mol H2O m–2 s–1
I	Light intensity	μmol photons m–2 s–1
Isat	Saturation light intensity corresponding to maximum net photosynthetic rate	μmol photons m–2 s–1
Ig–sat	Saturation light intensity corresponding to maximum stomatal conductance	μmol photons m–2 s–1
Ii–sat	Saturation light intensity corresponding to maximum intrinsic water-use efficiency	μmol photons m–2 s–1
Iinst–sat	Saturation light intensity corresponding to maximum instantaneous water-use efficiency	μmol photons m–2 s–1
Rd	Mitochondrial CO2 release in the dark	μmol CO2 m–2 s–1
Tr	Transpiration rate	mmol H2O m–2 s–1
WUEi	Intrinsic water-use efficiency	μmol CO2 mol–1 H2O
WUEi–max	Maximum intrinsic water-use efficiency	μmol CO2 mol–1 H2O
WUEinst	Instantaneous water-use efficiency	μmol CO2 mmol–1 H2O
WUEinst–max	Maximum instantaneous water-use efficiency	μmol CO2 mmol–1 H2O
α, α0, α1, α2	Initial slope of light response curve of An, gs, WUEi and WUEinst	mmol H2O m–2 s–1
β, β0, β1, β2	Inhibitor coefficient of light response curve of An, gs, WUEi and WUEinst	m2 s μmol–1 photons
γ, γ0, γ1, γ2	Saturation coefficient of light response curve of An, gs, WUEi and WUEinst	m2 s μmol–1 photons
Ki	Residual intrinsic water-use efficiency	μmol CO2 mol–1 H2O
Kinst	Residual instantaneous water-use efficiency	μmol CO2 mmol–1 H2O

Light is often viewed as the most significant environmental variable affecting photosynthesis, stomatal behavior and WUE (Knapp and Smith, 1987; Aranda et al., 2007; McAusland et al., 2016). Plants in most ecosystems experience rapid short-term variability in light resource (Smith et al., 1989), which can cause continual transition of A_n, g_s, T_r, WUE_i, and WUE_inst throughout the growing season (Knapp and Smith, 1990; Knapp, 1993). However, studies characterizing the light response of WUE are rare (McAusland et al., 2016). It is largely unknown whether there is a maximum WUE_i or WUE_inst—and the corresponding saturation irradiance—for plants under dynamic irradiance conditions, or how plant species or plant function types (PFTs) would differ in their light responses of WUE_i and WUE_inst.

Characterization of the interrelationships among light responses of A_n, g_s, T_r, WUE_i and WUE_inst—which can be simultaneously measured—will be fundamental to the scaling-up modeling of WUE–I responses at the whole-plant and ecosystem scale. The foremost step toward this direction calls for a robust model, with which (1) the WUE_i and WUE_inst responses to a gradient of irradiance intensity (I) levels (WUE_i–I and WUE_inst–I response curve, respectively) can be characterized, and (2) the key quantities defining the response curves—such as the initial slope of the response curve, the maximum WUE and the corresponding saturation irradiance—can be quantified. Ideally, the model can accurately represent the differential WUE_i and WUE_inst responses among plant species or PFTs, such as that reported between C₃ and C₄ species with contrasting light responses of photosynthesis, stomatal functioning, and WUE (Pearcy and Ehleringer, 1984; Knapp, 1993). For a given A_n, g_s and T_r are higher in C₃ than C₄ plants, leading to higher WUE_i and WUE_inst in C₄ plants, which has higher utilization efficiency of CO₂ at relatively lower intercellular CO₂ concentration (Pearcy and Ehleringer, 1984). The objectives of this study were to develop a leaf-scale WUE–I model and assess the model performance against experimental field observations of C₃ and C₄ species in order to answer key questions of how best to model the light response of WUE_i and WUE_inst. In particular: (1) What shape does the leaf-scale WUE–I response function take? Is there a maximum WUE_i and/or WUE_inst—and the corresponding saturation irradiances for plants under dynamic irradiance conditions? (2) Can the model well represent the differential WUE_i–I and/or WUE_inst–I response characteristics between C₃ and C₄ species? By integrating the published A_n–I (Ye, 2007; Ye et al., 2013) and g_s–I (Ye and Yu, 2008) response function, we developed an explicit WUE–I modeling framework and hypothesized that the species-specific light response curves of WUE_i and WUE_inst can be quantitatively characterized using the same non-asymptotic function. The hypothesis was tested using an observation-modeling intercomparison on WUE_i–I and WUE_inst–I responses for field-grown C₃ [soybean (Glycine max L.)] and C₄ species [grain amaranth (Amaranthus hypochondriacus L.)] under high I condition in the growing season. Model performance against that of the non-rectangular hyperbola model was also evaluated.

Materials and Methods

Analytical Models

A non-asymptotic model has been previously developed and tested to well characterize the light response of photosynthesis (Ye, 2007; Ye et al., 2013), with its simplified form as follows:

$$A_{\text{n}}=\mathrm{\alpha }\frac{1-\mathrm{\beta }I}{1+\mathrm{\gamma }I}{\text{I-R}}_{\text{d}}$$ (1)

where α is the initial slope of light response curve of photosynthesis, I is the irradiance, and β and γ are the photoinhibition coefficient and saturation coefficient, respectively, and R_d is the dark respiratory rate. The key model parameters are listed in Table 1.

The saturation irradiance (I_sat) corresponding to the light-saturated photosynthetic rate (A_nmax) can be calculated as follows:

$$I_{\text{sat}}=\frac{\sqrt{(\mathrm{\beta }+\mathrm{\gamma })/\mathrm{\beta }}-1}{\mathrm{\gamma }}$$ (2)

$$A_{\text{nmax}}=\mathrm{\alpha }{\left(\frac{\sqrt{\mathrm{\beta }+\mathrm{\gamma }}-\sqrt{\mathrm{\beta }}}{\mathrm{\gamma }}\right)}^2-R_{\text{d}}$$ (3)

Eq. 1 has been widely used to characterize photosynthetic light response curves of various plant species under different environmental conditions, highlighting its better performance than that of rectangular (Baly, 1935) and non-rectangular hyperbolic models (Thornley, 1976; Wargent et al., 2011; Xu et al., 2012a, b; Song et al., 2015; Chen et al., 2016). The rectangular and the non-rectangular hyperbolic models have been reported to overestimate A_nmax (dos Santos et al., 2013), and cannot quantify I_sat (Gomes et al., 2006; dos Santos et al., 2013; Song et al., 2015; Chen et al., 2016).

Meanwhile, a model of the same non-asymptotic form as Eq. 1 has been developed and tested to well characterize the light response of stomatal conductance (Ye and Yu, 2008), as follows:

$$g_{\text{s}}={\mathrm{\alpha }}_0\frac{1-{\mathrm{\beta }}_{0}I}{1+{\mathrm{\gamma }}_{0}I}I+g_{\mathrm{s0}}$$ (4)

where α₀ is the initial slope of light response curve of stomatal conductance, g_s0 is the residual stomatal conductance, and β₀ and γ₀ are two coefficients that are independent of I (Ye and Yu, 2008). Most existing stomatal conductance models cannot quantify the g_s–max or the corresponding I_g–sat under changing irradiance conditions (Dewar, 2002; Buckley et al., 2003; Buckley and Mott, 2013; Flexas et al., 2013). The g_s–I model developed by Ye and Yu (2008) can well characterize the g_s–I response, from which key parameters defining the g_s–I response—such as g_s–max and I_g–sat—can be easily obtained.

The saturation irradiance (I_g–sat) corresponding to the light-saturated stomatal conductance (g_s–max) can be calculated as follows:

$$I_{\mathrm{g}-\mathrm{sat}}=\frac{\sqrt{\left({\mathrm{\beta }}_0+{\mathrm{\gamma }}_0\right)/{\mathrm{\beta }}_0}-1}{{\mathrm{\gamma }}_0}$$ (5)

$$g_{\text{smax}}={\mathrm{\alpha }}_0{\left(\frac{\sqrt{{\mathrm{\beta }}_0+{\mathrm{\gamma }}_0}-\sqrt{{\mathrm{\beta }}_0}}{{\mathrm{\gamma }}_0}\right)}^2+g_{\mathrm{s0}}$$ (6)

Here, we hypothesize that the light response of WUE_i can be characterized using the same non-asymptotic form as that of the A_n–I (Eq. 1) and g_s–I (Eq. 4) response functions, as follows:

$${\text{WUE}}_{\text{i}}={\mathrm{\alpha }}_1\frac{1-{\mathrm{\beta }}_{1}I}{1+{\mathrm{\gamma }}_{1}I}I-K_i$$ (7)

where α₁ represents the initial slope of light response curve of WUE_i, β₁, and γ₁ are coefficients that are independent of I, and K_i is the residual intrinsic water-use efficiency. The saturation irradiance (I_i–sat) corresponding to the maximum WUE_i (WUE_i–max) can be calculated as follows:

$$I_{\text{i}-\text{sat}}=\frac{\sqrt{({\mathrm{\beta }}_1+{\mathrm{\gamma }}_1)/{\mathrm{\beta }}_1}-1}{{\mathrm{\gamma }}_1}$$ (8)

$${\text{WUE}}_{\text{i}-\text{max}}={\mathrm{\alpha }}_1{\left(\frac{\sqrt{{\mathrm{\beta }}_1+{\mathrm{\gamma }}_1}-\sqrt{{\mathrm{\beta }}_1}}{{\mathrm{\gamma }}_1}\right)}^2-K_i$$ (9)

Since g_s controls leaf T_r at a given VPD (Duursma et al., 2013), we hypothesize that the light response of WUE_inst can also be characterized using the same non-asymptotic function as that of WUE_i–I response function (Eq. 7), as follows:

$${\text{WUE}}_{\text{inst}}={\mathrm{\alpha }}_2\frac{1-{\mathrm{\beta }}_{2}I}{1+{\mathrm{\gamma }}_{2}I}I-K_{\text{inst}}$$ (10)

where α₂ represents the initial slope of light response curve of WUE_inst, β₂ and γ₂ are coefficients that are independent of I, and K_inst is the residual instantaneous water-use efficiency. The saturation irradiance (I_inst–sat) corresponding to the maximum WUE_inst (WUE_inst–max) can be calculated as follows:

$$I_{\text{inst}-\text{sat}}=\frac{\sqrt{({\mathrm{\beta }}_2+{\mathrm{\gamma }}_2)/{\mathrm{\beta }}_2}-1}{{\mathrm{\gamma }}_2}$$ (11)

$${\text{WUE}}_{\text{inst}-\text{max}}={\mathrm{\alpha }}_2{\left(\frac{\sqrt{{\mathrm{\beta }}_2+{\mathrm{\gamma }}_2}-\sqrt{{\mathrm{\beta }}_2}}{{\mathrm{\gamma }}_2}\right)}^2-K_{\text{inst}}$$ (12)

In this study, we tested if Eqs. 7 and 10 can well characterize the species-specific WUE–I response characteristics against model-oriented field observations and the simulations using the non-rectangular hyperbola model—in terms of the initial slope of light response curve of WUE (α₁ and α₂, respectively), the maximum WUE_inst (WUE_i and WUE_inst–max, respectively), and the saturation irradiance (I_i–sat and I_inst–sat, respectively).

Study Site and Plant Material

The field observations on one C₃ species—soybean (Glycine max L.) and one C₄ species—grain amaranth (A. hypochondriacus L.) were conducted at the Yucheng Comprehensive Experiment Station of the Chinese Academy of Sciences, located at the irrigation district of the Yellow River Basin in the North China Plain. This region is dominated by the warm-temperate semi-humid monsoon climate and is suitable for planting soybean and grain amaranth with high yields. This region has ample energy resource, and the light intensity in the growing season usually reaches ∼2000 μmol m^–2 s^–1 in sunny days. Soybean and grain amaranth were planted in field on May 3rd and June 15th 2012, respectively. All plants were kept under moist condition throughout the experiment.

Light Response Curve Measurement

The leaf gas exchange measurements were conducted after 45 days of growth in field—June 16th for soybean and July 29th for grain amaranth. Fully expanded sun-exposed leaves of four plants for each species were measured using a portable photosynthesis system (LI-6400, Li-Cor Inc., Lincoln, NE, United States). Before each measurement, the leaf was acclimated in the chamber to achieve stable gas exchange, with reference CO₂ concentration maintained at 380 μmol CO₂ mol^–1, irradiance intensity maintained at 2000 μmol photon m^–2 s^–1, and leaf temperature maintained at 35°C. After the leaf acclimated to the cuvette environment, the photosynthetic light response curve measurements were conducted with a descending gradient of irradiance intensity levels, as follows: 2000, 1800, 1600, 1400, 1200, 1000, 800, 600, 400, 200, 150, 100, 80, 50, and 0 μmol m^–2 s^–1. At each irradiance level, leaf gas exchange was monitored to ensure reaching steady-state plateau before data-logging. VPD was kept stable during measurements (Supplementary Figure S1). The A_n–I, g_s–I, WUE_i–I, and WUE_inst–I response curves were fitted by Eqs. 1, 4, 7, and 10, respectively. I_sat, I_g–sat, I_i–sat, and I_inst–sat values were calculated following Eqs. 2, 5, 8, and 11, respectively. A_nmax, g_s–max, WUE_i–max, and WUE_inst–max values were calculated following Eqs. 3, 6, 9, and 12, respectively.

Data Analysis

All statistical tests were performed using the statistical package SPSS 18.5 statistical software (SPSS, Chicago, IL, United States). The analysis of variance (ANOVA) was used to assess species effects. Paired-sample t tests were conducted to test whether there were significant differences between fitted and measured values of quantitative traits (α, A_nmax, I_sat, α₀, g_s–max, I_g–sat, α₁, WUE_i–max, I_i–sat, α₂, WUE_inst–max, I_inst–sat, etc.). Goodness of fit of the mathematical model to experimental observations was assessed using the coefficient of determination (r² = 1–SSE/SST, where SST is the total sum of squares and SSE is the error sum of squares).

Results

Light Response Curves of A_n, g_s, and T_r

The increase of I led to a rapid initial increase of A_n (Figures 1A,B), g_s (Figures 1C,D), and T_r (Figures 1E,F) for both C₃ and C₄ species. However, the initial increase rate of A_n was 100-fold higher than that of g_s for both species (Tables 2 and 3). The high coefficient of determination (r²) values indicated that the species-specific A_n–I response curves fitted by Eq. 1—and the g_s–I response curves fitted by Eq. 4—were highly representative of the observations for both species (Figure 1).

FIGURE 1.

Irradiance (I) responses of net photosynthetic rate (A_n) (A,B), stomatal conductance (g_s) (C,D) and transpiration rate (T_r) (E,F) for C₃ [soybean (Glycine max)] and C₄ species [grain amaranth (Amaranthus hypochondriacus)], respectively. In plots (A) and (B), solid lines were fitted using Eq. 1 and dashed lines were fitted using the non-rectangular hyperbola model (Eq. S1). In plots (C) and (D), solid lines were fitted using Eq. 4. Data are the mean ± SE (n = 4).

TABLE 2.

Fitted (Eq. 1) and measured (Obs.) values of parameters defining the light response curve of photosynthesis for C₃ (soybean) and C₄ species (grain amaranth).

Species	α		Anmax (μmol m–2 s–1)		Isat (μmol m–2 s–1)		β (m2 s μmol–1)		γ (m2 s μmol–1)		Rd (μmol m–2 s–1)
	Eq. 1	Obs.	Eq. 1	Obs.	Eq. 1	Obs.	Eq. 1	Obs.	Eq. 1	Obs.	Eq. 1	Obs.
Soybean	0.059 ± 0.005a	–	21.25 ± 0.53b	21.79 ± 0.58	1925.38 ± 60.30a	1800.00 ± 81.65	(1.20 ± 0.10) × 10–4	–	(1.25 ± 0.16) × 10–3	–	4.36 ± 0.46a	4.90 ± 0.29a
Grain amaranth	0.069 ± 0.001a	–	63.36 ± 2.46a	–	2186.67 ± 101.21a	–	(2.07 ± 0.15) × 10–4	–	(1.08 ± 0.29) × 10–4	–	4.18 ± 0.35a	4.99 ± 0.30a

The parameters are initial slope of the A_n–I curve (α), the maximum net photosynthetic rate (A_nmax) and the corresponding saturation irradiance (I_sat), photoinhibition coefficient (β), saturation coefficient (γ), and dark respiration rate (R_d). All values are the means ± SE (n = 4). Different letters denote statistically significant differences (P ≤ 0.05) between soybean and grain amaranth within each column of fitted (Eq. 1) or measured (Obs.) values. There is no statistically significant difference between fitted (Eq. 1) and measured (Obs.) values for each parameter. See Table 1 for definitions of abbreviations.

TABLE 3.

Fitted (Eq. 4) and measured (Obs.) values of parameters defining the light response curve of stomatal conductance for C₃ (soybean) and C₄ species (grain amaranth).

Species	α0		gs–max (mol m–2 s–1)		Ig–sat (μmol m–2 s–1)		β0 (m2 s μmol–1)		γ0 (m2 s μmol–1)		gs0 (mol m–2 s–1)
	Eq. 4	Obs.	Eq. 4	Obs.	Eq. 4	Obs.	Eq. 4	Obs.	Eq. 4	Obs.	Eq. 4	Obs.
Soybean	(3.5 ± 0.9) × 10–4a	–	0.26 ± 0.01	0.26 ± 0.02	2291.90 ± 259.17	1800.00 ± 81.65	(1.7 ± 0.7) × 10–4	–	(8.6 ± 5.5) × 10–4	–	0.06 ± 0.01a	0.07 ± 0.01a
Grain amaranth	(7.3 ± 3.0) × 10–4a	–	–	–	–	–	(-5.6 ± 6.1) × 10–4	–	(6.1 ± 5.5) × 10–3	–	0.09 ± 0.01a	0.11 ± 0.02a

The parameters are initial slope of the g_s–I curve (α₀), coefficients β₀ and γ₀, the maximum stomatal conductance (g_s–max) and the corresponding saturation irradiance (I_g–sat), and the residual stomatal conductance (g_s0). All values are the means ± SE (n = 4). Different letters denote statistically significant differences (P ≤ 0.05) between soybean and grain amaranth within each column of fitted (Eq. 4) or measured (Obs.) values. There is no statistically significant difference between fitted (Eq. 4) and measured (Obs.) values for each parameter. See Table 1 for definitions of abbreviations.

Soybean exhibited a single-peaked pattern for both A_n–I and g_s–I responses, characterized by the increase of A_n and g_s with the increasing I until reaching the A_nmax and g_s–max at the corresponding I_sat and I_g–sat, respectively (Figures 1A,C and Tables 2 and 3). Compared with Eq. 1, the non-rectangular hyperbola model (Supplementary Eq. S1) showed similarly high r² value in simulating A_n–I response curves but significantly overestimated the A_nmax (Figures 1A,B and Supplementary Table S1). Paired-sample t tests showed there were no significant differences between the fitted values and the measured values of A_nmax, I_sat, g_s–max, and I_g–sat for soybean (Tables 2 and 3). Grain amaranth kept increasing its A_n and g_s within the range of irradiance intensity applied during measurements (0–2000 μmol photon m^–2 s^–1), without showing an observational A_nmax, I_sat, g_s–max, or I_g–sat (Figures 1B,D and Tables 2 and 3). Grain amaranth showed relatively higher (not significant) initial increase rate of g_s, characterized by an initial slope of the light response curve of g_s (α₀) (Figure 1 and Tables 2 and 3).

Light Response Curves of WUE_i and WUE_inst

Within the low range of irradiance intensity, WUE_i and WUE_inst of both species increased almost linearly with the increasing I. Both soybean and grain amaranth exhibited a single-peaked WUE_i–I and WUE_inst–I response pattern, respectively. In particular, both species showed an increase of WUE_i and WUE_inst with the increasing I until reaching the species-specific WUE_i–max and WUE_inst–max at the corresponding species-specific saturation irradiance levels (I_i–sat and I_inst–sat, respectively) (Figure 2 and Tables 4 and 5). However, soybean showed significantly lower observed and fitted WUE_i–max and WUE_inst–max (P ≤ 0.05) than grain amaranth (Figure 2 and Tables 4 and 5). The two species showed no significant difference in I_i–sat, I_inst–sat or the initial increase rate of WUE_i or WUE_inst—characterized by a maximal slope of the light response curves (α₁ and α₂, respectively) (Figure 2 and Tables 4 and 5).

FIGURE 2.

Irradiance (I) response of intrinsic water-use efficiency (WUE_i) (A,B) and instantaneous water-use efficiency (WUE_inst) (C,D) for C₃ [soybean (Glycine max)] and C₄ species [grain amaranth (Amaranthus hypochondriacus)], respectively. In plots (A) and (B), solid lines were fitted using Eq. 7 and dashed lines were fitted using the non-rectangular hyperbola model (Eq. S2). In plots (C) and (D), solid lines were fitted using Eq. 10 and dashed lines were fitted using the non-rectangular hyperbola model (Eq. S3). Data are the mean ± SE (n = 4).

TABLE 4.

Fitted (Eq. 7) and measured (Obs.) values of parameters defining the light response curve of intrinsic water-use efficiency for C₃ (soybean) and C₄ species (grain amaranth).

Species	α1		WUEi–max (μmol mol–1)		Ii–sat (μmol m–2 s–1)		β1 (m2 s μmol–1)		γ1 (m2 s μmol–1)		Ki (μmol mol–1)
	Eq. 7	Obs.	Eq. 7	Obs.	Eq. 7	Obs.	Eq. 7	Obs.	Eq. 7	Obs.	Eq. 7	Obs.
Soybean	1.53 ± 0.25a	–	87.66 ± 3.38b	89.24 ± 3.26b	1153.95 ± 101.89a	1250.00 ± 262.99a	(8.49 ± 0.62) × 10–5	–	(7.52 ± 0.89) × 10–3	–	74.92 ± 6.16a	75.35 ± 5.98a
Grain amaranth	0.87 ± 0.19a	–	131.32 ± 7.83a	133.99 ± 7.63a	1417.60 ± 90.68a	1150.00 ± 125.83a	(1.21 ± 0.30) × 10–4	–	(3.72 ± 1.26) × 10–3	–	40.35 ± 4.24b	49.03 ± 5.69b

The parameters are initial slope of the WUE_i–I curve (α₁), the maximum intrinsic water-use efficiency (WUE_i–max) and the corresponding saturation irradiance (I_i–sat), and coefficients β₁ and γ₁ and K_i. All values are the means ± SE (n = 4). Different letters denote statistically significant differences (P ≤ 0.05) between soybean and grain amaranth within each column of fitted (Eq. 7) or measured (Obs.) values. There is no statistically significant difference between fitted (Eq. 7) and measured (Obs.) values for each parameter. See Table 1 for definitions of abbreviations.

TABLE 5.

Fitted (Eq. 10) and measured (Obs.) values of parameters defining the light response curve of instantaneous water-use efficiency for C₃ (soybean) and C₄ species (grain amaranth).

Species	α2		WUEinst–max (μmol mmol–1)		Iinst–sat (μmol m–2 s–1)		β2 (m2 s μmol–1)		γ2 (m2 s μmol–1)		Kinst (μmol mmol–1)
	Eq. 10	Obs.	Eq. 10	Obs.	Eq. 10	Obs.	Eq. 10	Obs.	Eq. 10	Obs.	Eq. 10	Obs.
Soybean	0.035 ± 0.006a	–	2.42 ± 0.17b	2.47 ± 0.16b	1182.74 ± 63.01a	1300.00 ± 191.49a	(9.38 ± 1.29) × 10–5	–	(6.34 ± 0.82) × 10–3	–	1.78 ± 0.19a	1.80 ± 0.19a
Grain amaranth	0.037 ± 0.008a	–	6.99 ± 0.50a	7.03 ± 0.52a	1649.05 ± 260.38a	1300.00 ± 100.00a	(1.21 ± 0.32) × 10–4	–	(2.83 ± 0.83) × 10–3	–	1.81 ± 0.24a	2.24 ± 0.32a

The parameters are initial slope of the WUE_inst-I curve (α₂), coefficients β₂ and γ₂ and K_inst, the maximum instantaneous water-use efficiency (WUE_inst–max), and the corresponding saturation irradiance (I_inst–sat). All values are the means ± SE (n = 4). Different letters denote statistically significant differences (P ≤ 0.05) between soybean and grain amaranth within each column of fitted (Eq. 10) or measured (Obs.) values. There is no statistically significant difference between fitted (Eq. 10) and measured (Obs.) values for each parameter. See Table 1 for definitions of abbreviations.

The high r² values indicated that WUE_i–I response curves fitted by Eq. 7—and the WUE_inst–I response curves fitted by Eq. 10—were highly representative of the observations of both species (Figure 2 and Tables 4 and 5). There were no significant differences between fitted and observed values in WUE_i–max, WUE_inst–max, I_i–sat, I_inst–sat, K_i, or K_inst (Tables 4 and 5). Compared with Eqs. 7 and 10, the non-rectangular hyperbola model (Supplementary Eqs. S2 and S3, respectively) showed similarly high r² values but significantly overestimated WUE_i–max and WUE_inst–max for the two species (Supplementary Tables S2 and S3).

Discussion

Our WUE_i–I and WUE_inst–I models represented cultivar-specific response curves over a wide range of light intensities extremely well (r² ≥ 0.996), including the decline of WUE_i and WUE_inst beyond the saturation irradiances which the NH models cannot represent due to the asymptotic function. Our models can also return values for WUE_i–max, WUE_inst–max, I_i–sat, and I_inst–sat, which were in very close agreement with the measured values. The NH models cannot characterize the decline in WUE_i and WUE_inst induced by high light, leading to overestimations of WUE_i–max and WUE_inst–max (Supplementary Tables S2 and S3).

Interrelationships of Light Responses of Photosynthesis, Stomatal Conductance, and Water-Use Efficiency

WUE_i and WUE_inst increased rapidly within low range of I, mainly driven by the uncoupled rapidity of photosynthetic and stomatal responses (Figures 1, 2 and Tables 4 and 5; Knapp and Smith, 1990; McAusland et al., 2016). In this study, both C₃ and C₄ species showed 100-fold higher initial increase rate of A_n (α) than that of g_s (α₀) (Tables 2 and 3). The rapid initial increase of WUE_i and WUE_inst—characterized by α₁ and α₂, respectively—occurred at low g_s (and at low I), when small increase in g_s exerted the greatest impacts on A_n and T_r (Hetherington and Woodward, 2003). The occurrence of the greatest A_n and T_r increase at low g_s also determined that α₁ would be much higher than α₂ for a given species (Figure 2 and Tables 4 and 5).

With the increasing I (from 0 to ∼800 μmol m^–2 s^–1), faster photosynthesis response than stomatal response led to the decline of intercellular CO₂ concentration (C_i) (Supplementary Figure S1; McAusland et al., 2016), causing further opening of stomatal pores (Mott, 1988) which allowed for diffusion of ambient CO₂ into the leaf (Hetherington and Woodward, 2003). Further increase of g_s—beyond the low g_s range—led to minimal increase of A_n and T_r (Hetherington and Woodward, 2003), such that WUE_i and WUE_inst flattened quickly after reaching the WUE_i–max and WUE_inst–max (Figure 2). Further increase of I beyond I_i–sat and I_inst–sat led to a decrease in WUE_i and WUE_inst. To reach A_nmax, both soybean and grain amaranth would have to show a decrease of WUE_i (or WUE_inst) from WUE_i–max (or WUE_inst–max) (Figures 1, 2).

Differential Light Responses of Water-Use Efficiency Between C₃ and C₄ Species

The observation-modeling intercomparison in this study highlighted the differential single-peaked WUE_i–I and WUE_inst–I responses—besides differential A_n–I and g_s–I responses—between C₃ and C₄ species (Figure 2 and Tables 4 and 5). C₄ species (grain amaranth) showed higher WUE_i and WUE_inst than C₃ species (soybean), suggesting its better leaf-scale optimization of carbon uptake versus water loss than C₃ species (Figures 1, 2 and Tables 2, 4, and 5). This may be due to higher photosynthetic capacity and rapidity of stomatal response (α₀) in C₄ species under changing irradiance conditions (Figure 1 and Tables 2 and 3), which facilitate relatively closer coupling between A_n and g_s in C₄ species than C₃ species (McAusland et al., 2016).

Moreover, this study identifies greater interspecific difference in WUE_inst than that in WUE_i—at high I range when WUE_i and WUE_inst flatten (Figure 2 and Tables 4 and 5). C₃ species (soybean) showed larger discrepancy between its WUE_i–I and WUE_inst–I responses than that of C₄ species (grain amaranth). This may be due to differential water use strategies between C₃ and C₄ species—C₄ species holds smaller T_r change per unit of g_s change in relative to C₃ species (Knapp, 1993). These results quantitatively demonstrate that the differential WUE_i–I responses between C₃ and C₄ species would not necessarily mirror their differential WUE_inst–I responses (Figure 2).

These results support previous studies reporting that water conservation—in terms of high WUE—is an important consequence of the C₄ photosynthetic pathway (besides high carbon gain rate) at different scales including single leaf, whole plant, and even whole communities (Ludlow and Wilson, 1972), contributing to the success of C₄ species in high irradiance environments (Pearcy and Ehleringer, 1984; Knapp, 1993).

Model Significance

By providing (1) analytical models characterizing the single-peaked light responses of WUE_i and WUE_inst and (2) key quantitative traits defining WUE_i–I and WUE_inst–I response differences between C₃ and C₄ species, this study provides a practical and robust modeling approach—in a form potentially applicable to WUE–I models at whole-plant and/or ecosystem scale. In particular, the key quantitative traits—the initial increase rates of WUE_i (α₁) and WUE_inst (α₂) besides that of A_n (α) and g_s (α₀), the maximum WUE_i (WUE_i–max) and WUE_inst (WUE_inst–max) besides that of A_n (A_nmax) and g_s (g_s–max), and the corresponding saturation irradiances—will directly help physiologists and modelers investigate the interrelationships among photosynthesis, stomatal behavior, and WUE under changing irradiance conditions.

Meanwhile, the above quantitative traits allow for easier and more extensive evaluation of light-intensity consequences on carbon and water relations among different species and/or PFTs. Such quantitative information, gathered on a wider range of species and/or PFTs, could allow (1) a deeper understanding of interspecific variation in light response strategies (Knapp, 1993; Hetherington and Woodward, 2003; McAusland et al., 2016), and (2) a realistic representation of adaptive WUE–I response differences among PFTs into ecosystem modeling.

The explicit models developed in this study can be viewed as an initial step toward filling the gap between investigating the trends of interspecific variation in short-term leaf-scale WUE–I responses and translating the variation into improved process representation in models of plant and ecosystem scales. The findings in this study remain to be validated (1) with species of different growth form and PFT membership (e.g., slower-growing woody species), which could hold different light response strategies (Knapp and Smith, 1989), (2) with daily and seasonal integrals and/or whole-plant estimates of WUE that sometimes could show a low correlation with short-term leaf-scale WUE observations (Medrano et al., 2015), and (3) when leaf gas exchange is subjected to compound effects of other climatic conditions in current and future climate change scenarios.

Conclusion

The newly developed models (Eqs. 7 and 10, respectively) allow robust reproduction of the differential single-peaked WUE_i–I and WUE_inst–I trends between C₃ and C₄ species and easy parameterization of key traits defining the trends (α₁, I_i–sat, K_i and WUE_i–max, α₂, I_inst–sat, K_inst, and WUE_inst–max). The models can be employed for fast and accurate assessment of plant WUE_i and WUE_inst responses—besides that of photosynthetic and stomatal responses using a consistent modeling framework—across all light-limited, light-saturated, and photoinhibitory light intensities. These findings are useful (1) for breeders screening for ideal genotypes target with maximized photosynthesis capacity and optimized WUE, (2) for plant physiologists quantifying intra- and/or inter-specific variation in leaf-scale WUE–I responses, and (3) for modelers working on better representation of the coupling between carbon and water processes under dynamic irradiance conditions.

Data Availability Statement

The datasets generated for this study are available on request to the corresponding author.

Author Contributions

Z-PY and S-XZ drafted the work. All authors contributed substantially to the completion of this work and critically revised the work. Z-PY, H-JK, and Y-GL secured the funding.

Conflict of Interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fpls.2020.00374/full#supplementary-material