Limitations of the Farquhar–von Caemmerer–Berry Model in Estimating the Maximum Electron Transport Rate: Evidence from Four C₃ Species

Simple Summary

Accurately measuring how plants convert sunlight into energy through photosynthesis is crucial for predicting crop yields and understanding plant responses to climate change. Scientists often use mathematical models, like the FvCB model, to estimate the maximum rate of electron transport in plants—a key factor in photosynthesis. However, this study found that two widely used versions of the FvCB model often overestimate this rate when tested on four common plant species, including wheat and ryegrass. By comparing model predictions with direct measurements, this research revealed that the models fail to account for energy losses caused by processes like photorespiration and nutrient absorption. The empirical model proposed by Ye et al. provided more accurate and reliable estimates. These findings highlight the need to improve existing models to better predict plant growth under changing environmental conditions. This work will help farmers, ecologists, and policymakers make more informed decisions about crop management and climate adaptation strategies, ensuring food security and ecosystem resilience in a warming world.

Abstract

The study evaluates the accuracy of two FvCB model sub-models (I and II) in estimating the maximum electron transport rate for CO₂ assimilation (J_A-max) by comparing estimated values with observed maximum electron transport rates (J_f-max) in four C₃ species: Triticum aestivum L., Silphium perfoliatum L., Lolium perenne L., and Trifolium pratense L. Significant discrepancies were found between J_A-max estimates from sub-model I and observed J_f-max values for T. aestivum, S. perfoliatum, and T. pratense (p < 0.05), with sub-model I overestimating J_A-max for T. aestivum. Sub-model II consistently produced higher J_A-max estimates than sub-model I. This study highlights limitations in the FvCB sub-models, particularly their tendency to overestimate J_A-max when accounting for electron consumption by photorespiration (J_O), nitrate reduction (J_Nit), and the Mehler reaction (J_MAP). An alternative empirical model provided more accurate J_f-max estimates, suggesting the need for improved approaches to model photosynthetic electron transport. These findings have important implications for crop yield prediction, ecological modeling, and climate change adaptation strategies, emphasizing the need for more accurate estimation methods in plant physiology research.

1. Introduction

As global environmental changes intensify, the ability to accurately estimate plant photosynthetic rates has become increasingly critical for predicting and adapting to future climate conditions. The light-driven electron transport chain in the photosynthetic apparatus is the fundamental force powering plant growth and development. A key parameter is the maximum electron transport rate for CO₂ assimilation (J_A-max), which represents the peak rate under light-saturated conditions and reflects the upper limit of energy conversion during photosynthesis. Therefore, accurate determination of J_A-max is essential for understanding plant responses to environmental factors such as light, CO₂ concentration, temperature, nutrition, and water availability [1,2,3,4,5,6].

To estimate J_A-max, both indirect and direct methods have been developed. The indirect method, based on the Farquhar–von Caemmerer–Berry (FvCB) model, estimates J_A-max by fitting the CO₂ response curve of photosynthesis (A_n–C_i curve) under light-saturated conditions. The FvCB model, which considers the enzymatic kinetics of Rubisco and the chemometrics of RuBP regeneration in C₃ species, is widely used for this purpose [2,3,5,6,7,8,9,10,11]. Direct methods include the non-rectangular hyperbolic model (NRH model) and a mechanistic model of the light response of electron transport rate (J–I curve) developed by Ye et al. [12,13]. These models estimate or calculate J_max by fitting the J–I curve, and the latter model considers light energy absorption and pigment molecule excitation in photosynthesis. However, these models are typically used to estimate J_max under constant CO₂ conditions and do not investigate the CO₂ response of photosynthesis in plants.

With rising atmospheric CO₂ levels, understanding C₃ plant responses to elevated CO₂ is crucial. The FvCB model is a key tool for investigating this response and has been extensively applied to study plant physiology under various conditions [4,5,6,14,15,16,17,18,19,20,21,22]. The FvCB model estimates key parameters like J_A-max, the maximum carboxylation rate (V_cmax), triose phosphates utilization (V_TPU), day respiration rate (R_d), and mesophyll conductance (g_m), which are vital for crop yield prediction, ecological modeling, and global carbon cycling [4,5,6,17,20,23,24,25,26]. However, J_A-max in the FvCB model is indirectly estimated, necessitating a modeling–observation intercomparison approach to assess its accuracy under different conditions.

The FvCB model’s development involves two equations for estimating J_A-max by fitting the A_n–C_i curve of C₃ plants. One assumes RuBP regeneration is limited by NADPH alone (sub-model I) [2,5,6,7,27,28,29], while the other assumes co-limitation by NADPH and ATP (sub-model II) [5,8,23,27,30,31]. Sub-model I is often favored for its accuracy in estimating J_A-max across diverse environmental conditions. In contrast, sub-model II is employed by others to explore the photosynthetic physiology and ecology of C₃ plants under varied environmental conditions [5,8,23,27,30,32].

However, in practice, it is uncertain whether RuBP regeneration in C₃ plants is limited by NADPH alone or co-limited by NADPH and ATP, leading to uncertainty in model selection and J_A-max estimation accuracy. Therefore, it is essential to verify the consistency of J_A-max values estimated by the two sub-models with observed values, especially under varying environmental conditions.

Our objective in this study is to simultaneously measure the A_n–C_i and J–C_i curves for Triticum aestivum L., Silphium perfoliatum L., Lolium perenne L., and Trifolium pratense L. at saturating irradiance (I_sat), fit the A_n–C_i curves using both FvCB sub-models to estimate J_A-max values, and compare these with observed values (J_f-max) to determine the more accurate sub-model. It also seeks to investigate reasons and solutions if estimated J_A-max values differ from observed values, providing new criteria for evaluating RuBP regeneration limitation assumptions in the FvCB model.

2. Material and Methods

2.1. Plant Material

Four species were used as test materials. T. aestivum (Jimai 22) is a widely cultivated wheat variety in Shandong Province, China. S. perfoliatum, native to the tallgrass prairie regions of North America, was introduced to China from Korea in 1979 by the Institute of Botany, Chinese Academy of Sciences, and is now used as a high-quality forage species. L. perenne (cv. Zhongxin 830) was developed through multigenerational hybridization between hexaploid and octoploid parental lines (H4372 × woH90) by the Crop Breeding and Cultivation Research Institute of the Chinese Academy of Agricultural Sciences. T. pratense is native to China and is widely used for forage and ornamental purposes. The seeds used in this study were obtained from Jinan Tianshundifeng. Agricultural Technology Co., Ltd., Jinan, China. The experimental site was located at Yucheng Station in the southwest of Yucheng County, Chinese Academy of Sciences, Shandong Province. The plants were sown on 15 October 2022 and maintained under standard field conditions. Data collection was performed on sunny days from 28 April 2023 to 10 May 2023. T. aestivum was in the booting to flowering stage, with an approximate plant height of 60–70 cm, and the flag leaf was selected for testing. S. perfoliatum was also in vigorous vegetative growth, with an approximate plant height of 30 cm, and the second leaf fully unfolded from top was selected for testing. L. perenne was in the booting stage, with an approximate plant height of 1.3 m. The first leaf beneath the flag leaf was selected for testing. T. pratense was in a period of vigorous vegetative growth with an approximate plant height of 15 cm, and mature leaves at the top were selected for testing.

2.2. Gas Exchange and Chl Fluorescence Measurement

From 28 April 2023 to 10 May 2023, A_n–I curves were measured for each study plant with an open-path gas exchange system (LI-6400; Li-Cor, Lincoln, NE, USA), equipped with a leaf chamber fluorometer (6400-40; Li-Cor). Measurements were taken between 9:30 and 11:30 and between 14:30 and 17:00 on sunny days. The ambient [CO₂] concentration was maintained at 420 μmol mol⁻¹ for 15 or 13 light levels in the following order (first to last): 2000, 1800, 1600, 1400, 1200, 1000, 800, 600, 400, 200, 150, 100, 80, 50, and 0 μmol m⁻² s⁻¹ for L. perenne and T. aestivum; 1600, 1400, 1200, 1000, 800, 600, 400, 200, 150, 100, 80, 50, and 0 μmol m⁻² s⁻¹ for T. pratense; and 1400, 1200, 1000, 800, 600, 400, 200, 150, 100, 80, 50, and 0 μmol m⁻² s⁻¹ for S. perfoliatum. The plants were allowed to acclimate to changes in light intensity for approximately 2–3 min before measurements were logged; it took about 50 min to complete an entire A_n–I curve. After data collection, we employed a mechanistic model of A_n–I in PMSS (http://photosynthetic.sinaapp.com, accessed on 15 May 2024) to simulate the A_n–I curves, determining the saturating irradiance (I_sat) to be 1200, 900, 2000, and 2000 μmol m⁻² s⁻¹ for T. aestivum, S. perfoliatum, L. perenne, and T. pratense, respectively. Then A_n–C_i and J–C_i curves were simultaneously recorded at saturating irradiance for 12 CO₂ concentrations in the following order (first to last measurement): 1600, 1400, 1200, 1000, 800, 600, 420, 300, 200, 100, 60, and 0 μmol mol⁻¹. To ensure steady-state conditions, the plants were given approximately 5 min to acclimate to ambient CO₂ (420 μmol mol⁻¹) in the gas exchange chamber before beginning each A_n–C_i and J–C_i curve, and then logged. It took approximately 45 min to complete a single A_n–C_i and J–C_i curve. The two FvCB sub-models in PMSS (http://photosynthetic.sinaapp.com, accessed on 16 May 2024) were then used to simulate the A_n–C_i curves and obtain the J_A-max values for the four C₃ plants.

2.3. J_A-max Estimated by the FvCB Model

Electron transport and concomitant proton transfer in the chloroplast’s thylakoids produces NADPH and ATP [10]. For steady-state C₃ leaf photosynthesis, the carbon assimilation rate is assumed to be limited either by Rubisco-catalyzed carboxylation or by regeneration of RuBP, which is controlled by the electron transport rate [2,5,6,7,10,28,29,31,33,34]. When calculating the electron transport-limited rate of CO₂ assimilation (A_j), there are many equations for estimating J_A-max [5,10]. Among these, two FvCB sub-models are commonly used to estimate the J_A-max value [5,10,31].

Sub-model I can be expressed as follows [2,5,6,7,10,28,29,31]:

$$A_{\mathrm{j}}=J{\displaystyle \frac{C_{\mathrm{i}}-{\Gamma }_{\ast }}{4C_{\mathrm{i}}+8{\Gamma }_{\ast }}}-R_{\mathrm{d}}$$

(1)

where C_i is the intercellular CO₂ concentration, Γ_∗ is the CO₂ compensation point in the absence of day respiratory rate, and R_d is the daily respiration rate.

In sub-model II, the limitation is co-determined by both NADPH and ATP availability, and the equation takes a slightly different form [5,10,23,27,30,31,35]:

$$A_{\mathrm{j}}=J{\displaystyle \frac{C_{\mathrm{i}}-{\Gamma }_{\ast }}{4.5C_{\mathrm{i}}+10.5{\Gamma }_{\ast }}}-R_{\mathrm{d}}$$

(2)

At the saturation irradiance, the value of J estimated by sub-model I and sub-model II represents the maximum electron transport rate for carbon assimilation (J_A-max). In addition, through simple mathematical analysis, both sub-models I and II exhibit asymptotic functions without extreme values. They, while similar, provide different estimates for J_A-max based on assumptions regarding the biochemical limitations of photosynthesis. Mathematical analysis shows that the J_A-max estimated by sub-model I is greater than that estimated by sub-model II, because the denominator in Equation (2) is larger than that in Equation (1) for any same value of Γ_∗ and C_i. The difference in the denominator reflects the additional ATP requirement per unit of CO₂ fixation when accounting for photorespiration and other processes.

2.4. An Empirical Model for the CO₂ Response of Electron Transport Rate (Model 1)

The empirical model of CO₂ response of the electron transport rate for photosynthetic organisms (including C₃, C₄, CAM species, algae, and photosynthetic bacteria) [36] is:

$$J_{\mathrm{f}}=\alpha {\displaystyle \frac{1-\beta C_{\mathrm{i}}}{1+\gamma C_{\mathrm{i}}}}+J_0$$

(3)

where J is electron transport rate, α, β, and γ are three coefficients independent of C_i, and J₀ is the electron transport rate, while C_i = 0 μmol·mol⁻¹.

Saturation CO₂ concentration (C_isat) corresponds to the maximum electron transport rate (J_f-max), and J_f-max can be obtained as follows:

$$C_{\mathrm{isat}}={\displaystyle \frac{\sqrt{\frac{\left(\beta +\gamma \right)}{\beta }}-1}{\gamma }}$$

(4)

and

$$J_{\mathrm{f}-\max }=\alpha {\left({\displaystyle \frac{\sqrt{\beta +\gamma }-\sqrt{\beta }}{\gamma }}\right)}^2+J_0$$

(5)

By fitting the J–C_i curves using Equation (3), the values of C_isat and J_f-max can be obtained from Equations (4) and (5), respectively.

These values can then be directly compared with the observed values to verify the accuracy of Equation (3). No significant differences were found between the estimated J_f-max values and observed J_f-max values (see

Table 1. Comparison of estimated J_A-max values from fitting A_n–C_i curves with the FvCB sub-models, J–C_i curves using the empirical model proposed by Ye et al. [36], and observed J_f-max values from LI-6400 for four C₃ species (mean ± SE, n = 3). Estimated J_A-max and observed J_f-max values within one plant that are significantly different (p < 0.05) are marked with different superscript letters (e.g., 214.88 ± 3.31 ^b and 247.48 ± 3.60 ^a), while those that are not significantly different (p > 0.05) share the same superscript letter (e.g., 247.48 ± 3.60 ^a and 250.17 ± 4.33 ^a). Units of J_A-max and J_f-max: μmol m⁻² s⁻¹.

Species	Fitted JA-max Values by FvCB Sub-Model I	Fitted JA-max Values by FvCB Sub-Model II	Fitted Jf-max Values by Empirical Model	Observed Jf-max Values by Li-6400
Triticum aestivum	316.53 ± 5.42 b	363.02 ± 6.07 a	291.47 ± 0.65 c	293.78 ± 3.13 c
Silphium perfoliatum	224.04 ± 2.47 c	255.74 ± 2.73 a	237.76 ± 1.36 b	235.76 ± 0.98 b
Lolium perenne	276.18 ± 7.20 b	315.66 ± 8.57 a	297.03 ± 10.23 b	283.85 ± 3.36 b
Trifolium pratense	214.88 ± 3.31 b	247.48 ± 3.60 a	256.19 ± 6.17 a	250.17 ± 4.33 a

). Consequently, our results indicate that Equation (3) is an effective model for simulating J–C_i curves and for calculating C_isat and J_f-max.

2.5. Statistical Analyses

The two FvCB sub-models and the empirical J–C_i model proposed by Ye et al. (available via the PMSS web platform, http://photosynthetic.sinaapp.com) were used to simulate the A_n–C_i and J–C_i curves to determine the J_A-max values for the four plants. PMSS integrates these models and uses Simulated Annealing and the Metropolis Algorithm to fit photosynthetic parameters to user-provided data. Data are expressed as the means ± standard error. Student’s t-tests were used to compare the J_A-max values estimated by the two FvCB sub-models with the corresponding observed J_f-max values. Data were analyzed by one-way analysis of variance (ANOVA) at p < 0.05 (p-significance level) using SPSS 18.5 statistical software (SPSS, Chicago, IL, USA). Figures were generated using Origin 7.0 (Origin Lab, Northampton, MA, USA) and Adobe Illustrator CS6 (Adobe, San Jose, CA, USA). The goodness of fit between the experimental observations and the line of best fit obtained from mathematical modeling were assessed using the coefficient of determination (R²), calculated as R² = 1 − SSE/SST, where SST is the total sum of squares, and SSE is the error sum of squares.

3. Results

3.1. A_n–C_i Curve Analysis

The CO₂ assimilation rates of all four C₃ species showed a typical A_n–C_i response under saturating irradiance (Figure 1). At CO₂ concentrations below approximately 500 μmol·mol⁻¹, A_n increased rapidly, reflecting the Rubisco-limited phase. As CO₂ concentration continued to increase, A_n also increased, but at a slower pace, particularly for T. aestivum (Figure 1A,B), S. perfoliatum (Figure 1C,D), and L. perenne (Figure 1E,F), which reached a plateau, indicating C_i transit points from RuBP-limited to triose-phosphate-utilization-limited (TPU-limited) photosynthesis (C_i,TPU). Notably, the carbon assimilation rate of S. perfoliatum showed a slight decrease after reaching C_i,TPU (Figure 1C,D).

3.2. Comparison of J_max Estimates

Comparison of J–C_i curves under saturating irradiance (derived from fitted A_n–C_i curves in Figure 2) revealed significant differences between observed J_max (J_f-max) values and estimated J_max values using the two FvCB sub-models in all species (Figure 3). For T. pratense, sub-model I significantly underestimated J_max compared to observed values (p < 0.05) (Figure 3A, Table 1), while sub-model II did not (p > 0.05). For S. perfoliatum, both sub-models significantly differed from observed values (p < 0.05), with sub-model I underestimating and sub-model II overestimating J_max (Figure 3B, Table 1). For L. perenne, the J_max values estimated by sub-model I were not significantly different from observed values (p > 0.05), but sub-model II significantly underestimated J_max (p < 0.05) (Figure 3C, Table 1). For T. aestivum, both sub-models significantly overestimated J_max (p < 0.05) (Figure 3D, Table 1). Sub-model II consistently produced higher J_max estimates than sub-model I across all species. The R_d and Γ_∗ parameters were identical between the two sub-FvCB models (Supplementary Table S1). In contrast, the Ye empirical J–C_i model accurately reproduced both the CO₂ response trends of J and the J_max values for all four plants, showing no significant difference from measured values (p > 0.05) (Figure 3A–D, Table 1).

4. Discussion

4.1. Why Can Current Technology Validate the Estimation of J_A-max by the FvCB Model?

At present, advanced experimental methodologies, such as chlorophyll fluorescence-based techniques, provide a more comprehensive understanding of electron partitioning. As elucidated by von Caemmerer [10] and Long and Bernacchi [23], J_f supports not only J_A, but also photorespiration (J_O), nitrate-to-ammonium conversion (J_Nit), and Mehler ascorbate peroxidase (MAP)-reaction-driven oxygen uptake (J_MAP). This relationship can be expressed as J_f = J_A + J_O + J_Nit + J_MAP.

This relationship underscores that J_f must exceed J_A under any environmental conditions. When J_A-max is inferred from the A_n–C_i curve—a method that indirectly estimates J_A-max—the sub-models consider only the electron transport rate dedicated to carbon assimilation (J_A-max). This approach neglects other electron-consuming processes, including J_O, J_Nit, and J_MAP. Conversely, the maximum J_f (J_f-max) values, which are directly obtained from the J–C_i curve, represent the total electron transport rate (J_f) originating from photosystem II (PSII). This differentiation is critical, because J_A represents just a portion of the overall electron flow, suggesting that the J_A-max derived from the FvCB sub-models should invariably be lower than the observed J_f-max across various environmental conditions. Hence, the J_A-max estimated by the two FvCB sub-models should consistently be lower than the observed J_f-max. This criterion is fundamental for evaluating the credibility of the FvCB model’s estimation of J_A-max.

4.2. What Explains the Discrepancies Between Estimated J_A-max and Observed J_f-max?

The discrepancies between estimated J_A-max and observed J_f-max values, particularly for T. aestivum, highlight a need for a deeper examination of the underlying assumptions in the FvCB sub-models. For T. aestivum, the observed J_f-max values consistently fall below the J_A-max estimates from both sub-models (Figure 1A,B and Figure 3A; Table 1), posing difficulties in interpretation within the context of the FvCB model. When considering consumption of J_O, J_Nit, and J_MAP, the J_A-max value derived from the FvCB model should be considerably lower than the observed J_f-max value, not alarmingly higher. From this, we can deduce that the J_A-max for T. aestivum, as estimated by the FvCB model, is unreasonable. Upon scrutinizing these results through the perspective of mathematical interpolation, it becomes evident that the coefficients for C_i and Γ_∗ in Equation (1) might be overstated. It is only when these coefficients for C_i and Γ_∗ are reduced that the estimated J_A-max has the potential to fall below the J_f-max. For S. perfoliatum and L. perenne, analogous findings were observed; the J_A-max values were found to be overestimated when accounting for consumption of J_O, J_Nit, and J_MAP (Figure 1C–F and Figure 3B,C; Table 1).

For example, in the case of T. aestivum, when consumption of J_O, J_Nit, and J_MAP is neglected, the coefficient of Γ_∗ in the denominator of Equation (1) must be adjusted to approximately 7.02 (a value less than 8) to ensure that the J_A-max value remains lower than the J_f-max values. This adjustment implies that 0.57 mol of CO₂ is released in the photorespiratory pathway for every mol of RuBP oxygenated, which exceeds the theoretical value of 0.5 mol [7]. However, this conclusion conflicts with the widely accepted consensus that 1 mol of O₂-bound RuBP releases 0.5 mol of CO₂ [2,5,7,10,27,28,29,31,37]. Therefore, the claim that the amount of CO₂ released in the photorespiratory pathway exceeds the theoretical value of 0.5 mol per mol of RuBP oxygenation appears to be unsupported.

To further evaluate this discrepancy, von Caemmerer’s theory provides an alternative perspective [10]. Specifically, if the Q cycle operates (H⁺/e⁻ = 3), the J_A-max for carbon assimilation can be estimated by $A_{\mathrm{j}}=J{\displaystyle \frac{C_{\mathrm{i}}-{\Gamma }_{\ast }}{3C_{\mathrm{i}}+7{\Gamma }_{\ast }}}-R_{\mathrm{d}}$. Under this assumption, the calculated J_A-max value is (240.02 ± 4.09) μmol m⁻² s⁻¹, which is significantly lower than the measured value of (293.78 ± 3.13) μmol m⁻² s⁻¹ (Table 1).

4.3. Can a More Comprehensive Framework Improve J_A-max or J_f-max Estimation?

Given the challenges associated with the FvCB sub-models, alternative approaches, such as the empirical model proposed by Ye et al. [36], offer a promising solution. This model directly calculates J_f-max from J–C_i curves, bypassing the need for indirect estimation via A_n–C_i fitting. In this study, the empirical model produced J_f-max values that closely matched observed J_f-max values across all four species (Figure 3, Table 1). Most importantly, this approach accounts for the whole-chain electron transport rate, providing a more accurate representation of photosynthetic electron transport. This is especially relevant when considering other key parameters in the FvCB model, such as V_cmax, V_TPU, R_d, and g_m.

However, while the empirical model demonstrates superior accuracy, its lack of mechanistic detail limits its applicability in broader physiological studies. For instance, the biological significance of its coefficients in the empirical model remains unclear, and it does not explicitly link electron transport with ATP synthesis or the co-limitation of NADPH and ATP. As such, it should be regarded as a transitional tool, complementing the FvCB model while paving the way for more integrative approaches.

4.4. Should We Rethink the Estimation of J_A-max?

The discrepancies in J_A-max estimations by the FvCB sub-models reveal the necessity for prudent application and interpretation of these models. When considering consumption of J_O, J_Nit, and J_MAP, the consistent overestimation by sub-model II across four species and by sub-model I for S. perfoliatum, L. perenne, and T. aestivum, specifically for T. aestivum (Figure 3, Table 1) underscore the imperative to incorporate a deeper understanding of electron partitioning into model development. From a mathematical perspective, it is expected that the J_A-max values derived from fitting the A_n–C_i curves of the four plant species using $A_{\mathrm{j}}=J{\displaystyle \frac{C_{\mathrm{i}}-{\Gamma }_{\ast }}{3C_{\mathrm{i}}+7{\Gamma }_{\ast }}}-R_{\mathrm{d}}$ would be lower than the corresponding J_f-max values. Similarly, the J_A-max values obtained by fitting the A_n–C_i curves of S. perfoliatum and L. perenne using this equation are also anticipated to be lower than their respective J_f-max values.

4.5. How Does Overestimating J_A-max Affect Agricultural and Environmental Research?

The implications of overestimating J_A-max extend across multiple scientific and practical domains, with significant consequences for both agricultural and environmental research. In agricultural contexts, inflated J_A-max values can lead to unrealistic yield projections, potentially resulting in suboptimal resource allocation and misguided management practices. Farmers and policymakers relying on these overestimations may make decisions that do not align with actual crop performance, leading to inefficiencies in resource use and potential economic losses.

In ecological modeling, inaccuracies in J_A-max estimates can significantly compromise our understanding of carbon flux dynamics and energy conversion efficiencies. This distortion can affect predictions of carbon sequestration capacity and plant responses to environmental changes, ultimately undermining the accuracy of climate models and ecological forecasts. Such inaccuracies may also hinder efforts to predict and mitigate the impacts of climate change on natural ecosystems.

Furthermore, the potential consequences for climate change adaptation strategies are particularly concerning. Inaccurate J_A-max assessments could lead to flawed predictions of plant resilience and adaptability under elevated CO₂ concentrations and changing environmental conditions. This, in turn, could hinder the development of effective strategies for maintaining ecosystem stability and ensuring food security in the face of global climate change. Misguided adaptation strategies based on overestimated J_A-max values may fail to address the actual challenges posed by climate change, potentially exacerbating vulnerabilities in agricultural and natural systems.

While our study highlights these limitations in the examined species, the broader applicability of these findings requires further verification through additional research encompassing a wider range of plant species and environmental conditions. Future studies should focus on developing more accurate estimation methods and refining existing models to better capture the complex physiological processes underlying photosynthetic efficiency. By improving the precision of J_A-max estimates, researchers can enhance the reliability of predictions in agricultural and environmental research, ultimately supporting more informed decision-making and sustainable resource management.

5. Conclusions

This study evaluated the accuracy of two widely used sub-models of the FvCB model in estimating the maximum electron transport rate for CO₂ assimilation across four C₃ plant species. Our results revealed that both sub-models frequently overestimated the electron transport rate, particularly in T. aestivum, highlighting key limitations in their current formulations. By comparing these estimates with observed values obtained from direct measurements, we demonstrated that the empirical model proposed by Ye et al. provided more accurate and reliable estimates. These findings underscore the importance of refining photosynthetic models to more accurately reflect the physiological realities of plant electron transport. Improved models are essential for advancing research in plant physiology, enhancing crop yield predictions, and developing effective responses to climate change.