Photosynthetic Processes and Light Response Model Fitting of Quercus acutissima Carruth. and Quercus variabilis Bl. in the Changjiang River Delta, China

Abstract

Plants have the capacity to fix CO₂ through photosynthesis. To reveal the photosynthetic processes of Quercus acutissima Carruth. and Quercus variabilis Bl., their net photosynthetic rates were quantified during the early and peak growing seasons. To evaluate forest photosynthetic efficiencies, the photosynthetic light response curves of Q. acutissima and Q. variabilis were fitted by the rectangular hyperbola model (RHM), non-rectangular hyperbola model (NHM), and modified rectangular hyperbola model (Ye model). The results revealed the following: (1) All daily variation curves of the net photosynthetic rate, stomatal conductivity, and transpiration rate were single-peaked. The peak times of the Q. acutissima and Q. variabilis’ net photosynthetic rates appeared at 12:00 am during the early growing season and 10:00 am during the peak growing season. (2) The photosynthetic capacities of both Q. acutissima and Q. variabilis during peak growing seasons were higher than during the early growing season. (3) The net photosynthetic rate was found to be positively correlated with stomatal conductivity, the transpiration rate, and photosynthetically active radiation, and it was negatively correlated with the intercellular CO₂ concentration. (4) The Ye model provided the best fit for the light response curves of Q. acutissima and Q. variabilis when compared with the rectangular hyperbola and nonrectangular hyperbola models. The photosynthetic performance of Q. acutissima was superior to that of Q. variabilis; thus, it can be employed as a priority tree species in carbon sink forests.

1. Introduction

Photosynthesis is a biological process that absorbs CO₂ and releases O₂ to balance their concentrations in the ambient atmosphere [1]. Through photosynthesis, forests serve as an important carbon sink for terrestrial ecosystems by fixing CO₂ [2]. Photosynthetic parameters are essential indicators for the evaluation of forest photosynthetic efficiencies. The photosynthetic light response method is an important research technique in plant physiology [3]. From light response curves, photosynthetic parameters such as the maximum net photosynthetic rate, light saturation point, light compensation point, dark respiration rate, and apparent quantum efficiency can be obtained. The photosynthesis of plants is also affected by their physiology (e.g., stomatal conductivity) and environmental factors (e.g., photosynthetically active radiation) [4,5,6]. As plants grow, the environment, as well as their own physiological conditions, are altered. Subsequently, their photosynthetic capacities change during different growing seasons. Thus, it is critical to elucidate the photosynthetic processes of plants and their impact factors during different growing seasons.

The main models for fitting photosynthetic light response curves include the rectangular hyperbola model (RHM), the nonrectangular hyperbola model (NHM), the Ye-modified model (modified rectangular hyperbola model, YZP), the exponential model, etc. The rectangular hyperbola model was proposed by Baly in 1935, who described the relationship between photosynthesis and irradiance thusly: the net photosynthetic rate increases sharply with greater photosynthetically active radiation under low light intensities and slowly with greater photosynthetically active radiation at moderate light intensities [7]. The rectangular hyperbola model has been applied to simulate the light response curve of Ziziphus jujuba Var., Populus Euramericana Cv., and Pinus pinea L. and achieved good results [8,9,10]. The nonrectangular hyperbola model was proposed by Thornley in 1976 based on the rectangular hyperbola model with the addition of curvilinear angle (θ) to adjust the curvature of the curve [11]. Lang found that the nonrectangular hyperbola was the best model for fitting the light response curve of Prunus sibirica L., Hippophae rhamnoides L., and Pinus tabulaeformis Carr. [12]. The modified rectangular hyperbola model was proposed by Ye in 2007, which was based on the rectangular hyperbola model with the addition of a limiting parameter (β) to handle photosynthetic inhibition data. Li discovered that the modified rectangular hyperbola model could well fit the photosynthetic light response curve under a wide range of soil water conditions [13]. The rectangular hyperbola and nonrectangular hyperbola models are good at fitting the light compensation point and apparent quantum efficiency. The photosynthetic parameters fitted by the Ye model describe not only the light response characteristics but also the molecular photosynthetic pigment characteristics [14] and reproduce the light response trends of electron transport and CO₂ absorption [15]. Previous studies on photosynthetic light response curves showed that there were differences in fitting the photosynthetic parameters of the same plant using different models. Thus, it is of particular importance to select the optimal light response model to investigate the photosynthetic attributes of plants [16]. For this study, based on earlier research and our preliminary validations [17,18], we selected rectangular hyperbola, nonrectangular hyperbola, and Ye-modified models to fit the light response curves.

Quercus acutissima Carruth. and Quercus variabilis Bl. are widespread across warm temperate and subtropical regions of China. They are important, highly adaptable tree species with strong water conservation and excellent carbon sequestration capacities. These trees are extensively distributed throughout the Yangtze River Delta region and are broadly accepted by researchers as carbon sink trees [19,20]. The Yangtze River Delta region is an important area affected by acid rain, with a 57.12% acid precipitation frequency [21]. Most previous studies into the photosynthetic parameters of Quercus acutissima and Quercus variabilis involved saplings [22,23], some of which were concentrated in arid and high-temperature regions [24]. Further, they were situated in regions that were less affected by acid rain, while leaf photosynthesis was impacted by acid rain to a certain extent [25]. It is very important to understand the photosynthetic capacities of Quercus acutissima and Quercus variabilis in this region.

For this study, we continuously observed the photosynthetic diurnal variations of Q. acutissima and Q. variabilis in the Changjiang River Delta region for different growing seasons and simulated their photosynthetic light response curves using the rectangular hyperbola, nonrectangular hyperbola, and Ye models. This study endeavored to explore the photosynthetic processes and relationships between photosynthesis and eco-physiologicalfactors. Secondly, we aimed to select an optimal model to simulate the light response curves of Q. acutissima and Q. variabilis. Finally, we selected highly photosynthetically efficient Quercus spp. plants. Our results revealed the photosynthetic capacities of oak forests in the Yangtze Delta region and evaluated the photosynthetic efficiencies of individual oak trees. Further, this study provided a scientific basis to support the further study of forest carbon fixation in acid rain-impacted areas.

2. Materials and Methods

2.1. Site Description

This study was conducted at the Changjiang River Delta Forest Ecosystem National Positioning Station (E119°12′03″, N32°07′48″, 332.6 m) of the State Forestry and Grassland Administration. The site inhabits the middle foothills of Hollow Green Mountain, with a 20° southeast slope, in Jurong City, Jiangsu Province, East China (Figure 1), under a north subtropical monsoon climate. The mean annual temperature in this area is 15.2 °C, the mean frost-free period is 233 d, and the mean annual precipitation is 1055.6 mm. The soil is yellow-brown loam at pH 4.76 [26]. The dominant tree species are sawtooth oak (Q. acutissima) and oriental oak (Q. variabilis), with a small population of maple (Liquidamdar formosara), Chinese pistache (Pistacia chinensis), etc. The basic characteristics of the forest stands are shown in

Table 1. Basic characteristics of sample stands. Three sample squares of 20 m × 20 m were set up, wherein every 27 trees was measured.

Tree Species	Q. acutissima	Q. variabilis
Forest age/years	65	65
Tree height/m	19.24	17.78
Diameter/cm	26.64	25.08
Crown/m	4.6	4.1
Density/plants·hm−2	325	350
Crown density	0.5	0.47

Note: The forest survey was implemented according to the National Standard of the People’s Republic of China’s “Long-term positioning observation method of forest ecosystem” (GB/T33027-2016).

.

2.2. Climate Observation

The climate was observed continuously for 24 h every day for the entire year. The main meteorological factors observed at the experimental site were photosynthetically active radiation (PAR) (μmol m⁻² s⁻¹) and air temperature (°C). The photosynthetically active radiation was measured using a radiation sensor SK01-DP2 (MIDDLETON SOLAR Inc., Melbourne, VIC, Australia), while the air temperature was quantified with a thermohygrometer HMP155A (VAISALA Inc., Helsinki, Finland), which were both at 20 m above the ground surface (observation tower).

2.3. Measurement of Photosynthetic Characteristics and Light Response Curve

From 20 to 28 April and 6 to 14 July (both with clear skies), photosynthetic characteristic measurements were obtained every two hours from 6:00 am to 18:00 pm using a portable photosynthesizer LI-6400 (LI-COR Inc., Lincoln, OR, USA). Three healthy and fully expanded leaves were selected from the middle of the canopies of six standard Q. acutissima and Q. variabilis trees with height and diameter at breast height close to average values. The net photosynthetic rate, intercellular CO₂ concentration, transpiration rates, and stomatal conductivities were measured simultaneously. Finally, the arithmetic averages of the measurements were used as photosynthetic data for the early peak growing season (20 April to 30 May) and the peak growing season (1 July to 30 August), respectively. During the early growing season, the temperature ranged from 15 to 25 °C, air humidity from 34% to 50%, CO₂ concentration from 375 to 398 μmol mol^–1, and PAR from 1 to 1300 μmol m⁻² s⁻¹. During the peak growing season, the temperature ranged from 20 to 35 °C, air humidity from 45% to 91%, CO₂ concentration from 370 to 398 μmol mol^–1, and PAR from 1 to 1600 μmol m⁻² s⁻¹.

According to numerous studies, the most sensitive time for plant photosynthesis in response to light intensity is between 9:00 am and 11:00 am [27,28,29]. Consequently, for this study, we selected three leaves from three healthy Q. acutissima and Q. variabilis trees and made measurements from 9:00 am to 11:00 am each day under clear skies from 6 to 14 July. The sample chamber conditions were controlled, with the leaf temperature set at 25 °C, relative air humidity set at 60%, atmospheric CO₂ concentration set at 400 μmol mol⁻¹, an airflow rate of about 500 μmol s^–1, and light radiation intensities set at 0, 10, 20, 50, 100, 200, 400, 600, 800, 1000, 1200, 1400, 1600, 1800, and 2000 μmol m⁻² s⁻¹. Once the light intensities were adjusted, the leaves remained in the sample chamber for two min, with measurement times no less than two minutes.

2.4. Fitting Model of the Photosynthetic Light Response Curve

The photosynthetic light response curves of Q. acutissima and Q. variabilis were fitted using the rectangular hyperbola, nonrectangular hyperbola, and Ye models. The net photosynthetic rates and photosynthetically active radiation curves were quantified [30], while the maximum net photosynthetic rate, light compensation point, light saturation point, and dark respiration rate were estimated from the curve trend as the measured values of the characteristic parameters of light responses [12,31].

The rectangular hyperbola model (RHM) equation was expressed as follows:

$$P_n=\frac{\alpha I{P}_n{}_{\max }}{\alpha I+P_{n\max }}-R_d$$

(1)

where P_n is the net photosynthetic rate (μmol m⁻² s⁻¹), α is the initial quantum efficiency, I is the photosynthetic active radiation intensity (μmol m⁻² s⁻¹), P_nmax is the maximum net photosynthetic rate at light saturation (μmol m⁻² s⁻¹), and R_d is the dark respiration rate (μmol m⁻² s⁻¹)

The nonrectangular hyperbolic model (NHM) equation was expressed as follows:

$$P_n=\frac{\alpha I+P_n{}_{\max }-\sqrt{{\left(\alpha I+P_{n\max }\right)}^2-4\alpha \theta I{P}_{n\max }}}{2\theta }-R_d$$

(2)

where θ is the optical response curve angle of the curvature, with the other letters referring to the same as above.

The Ye model (the modified rectangular hyperbola model, YZP) equation was expressed as follows:

$$P_n=\alpha \frac{1-\beta I}{1+\gamma I}I-R_d$$

(3)

where β is the photoinhibition coefficient (m² s μmol⁻¹), γ is the light saturation coefficient (m² s μmol⁻¹), and the other letters have the same meanings as above.

The light saturation points, I_s (μmol m−² s⁻¹), for the rectangular hyperbola and nonrectangular hyperbola models were calculated using the equation below [32]. First, a linear regression of the photosynthetic active radiation, I, from 0 to 200 (μmol m−² s⁻¹) and the net photosynthetic rate, P_n, were used to obtain the apparent quantum efficiency (AQE) and dark respiration rate (R_d), with the equation expressed as follows:

$$P_n=\mathrm{m}\times I-{\mathrm{R}}_{\mathrm{d}}$$

(4)

where P_n is the net photosynthetic rate (μmol m⁻² s⁻¹), slope m is apparent quantum efficiency, and the R_d is the dark respiration rate (μmol m⁻² s⁻¹).

Then, the light saturation point, I_s, was calculated with Equation (4):

$$I_{\mathrm{s}}=\frac{P_{n\max }+R_{\mathrm{d}}}{m}$$

(5)

where P_nmax is the max net photosynthetic rate (μmol m⁻² s⁻¹), m is apparent quantum efficiency, and R_d is dark respiration rate (μmol m⁻² s⁻¹).

The light saturation point, I_s, in the Ye model was expressed as follows:

$$I_s=\frac{\sqrt{\left(\beta +\gamma \right)/\beta }-1}{\gamma }$$

(6)

where the net photosynthetic rate P_n is 0, and the light compensation point (I_c) (mol m⁻² s⁻¹) is the photosynthetically active radiation. As a result, for the RHM, NHM, and YZP models, the P_n was set to 0 to obtain the respective I_c values.

The formula of the light compensation point for the rectangular hyperbola model was expressed as follows:

$$I_{\mathrm{c}}=\frac{R_d{P}_{n\max }}{\alpha \left(P_{n\max }-R_d\right)}$$

(7)

The formula of the light compensation point for the nonrectangular hyperbolic model was expressed as follows:

$$I_{\mathrm{c}}=\frac{P_{n\max }{R}_d-\theta R_d^2}{\alpha \left(P_{n\max }-R_d\right)}$$

(8)

The formula of the light compensation point, for the Ye model was expressed as follows:

$$I_{\mathrm{c}}=\frac{\alpha -R_d\gamma -\sqrt{{\left(\alpha -R_d\gamma \right)}^2-4\alpha \beta R_d}}{2\alpha \beta }$$

(9)

The maximum net photosynthetic rate equation for the Ye model was expressed as follows:

$$P_{n\max }=\alpha {\left(\left.\frac{\sqrt{\beta +\gamma }-\sqrt{\beta }}{\gamma }\right)\right.}^2-R_{\mathrm{d}}$$

(10)

2.5. Model Evaluation

To evaluate the goodness of fit for the three models, the root-mean-square error (RMSE), mean absolute percentage error (MAPE), and determination coefficient (R²) were calculated using empirical formulae. The determination coefficient was established by fitting the light response curve with Matlab 2020, while the RMSE and MAPE were calculated using the equations below [33]:

$$RMSE=\sqrt{\frac{1}{n}{{\displaystyle \sum _{i=1}^n\left(Y_{m,i}-Y_{0,i}\right)}}^2}$$

(11)

where Y_m,i is the predicted value of the model, and Y_0,i is the observed value, as shown below:

$$MAPE=\frac{1}{n}{\displaystyle \sum _{i=1}^n\left|\left.\frac{Y_{m,i}-Y_{0,i}}{Y_{0,i}}\right|\right.}\times 100\%$$

(12)

2.6. Data Analysis

The net photosynthetic rate and eco-physiological factor data were processed using Excel 2017 and SPSS (V 19, Armonk, NY, USA) for correlation analysis. Origin software(Version 2018, Northampton, MA, USA) was employed to plot the dynamic photosynthetic daily change characteristics and photosynthetic light response curves. Matlab software (Version 2020, Natick, MA, USA) was employed to build the rectangular hyperbola, nonrectangular hyperbola, and Ye models.

3. Results

3.1. Diurnal Dynamics of Photosynthetic Parameters

3.1.1. Diurnal Variations of Net Photosynthetic Rates

The daily trend of the net photosynthetic rates of Q. acutissima and Q. variabilis was a single-peaked curve for both the early and peak growing seasons, as shown in Figure 2A. During the early growing season, the peak net photosynthetic rates of Q. acutissima and Q. variabilis were 4.40 and 4.07 μmol m⁻² s⁻¹, respectively, and the peak time appeared at 12:00 am. During the peak growing season, the peak net photosynthetic rates of Q. acutissima and Q. variabilis were 6.87 and 5.05 μmol m² s⁻¹, respectively, and the peak time appeared at 10:00 am. The peak net photosynthetic rate during the peak growing season occurred two hours earlier than during the early growing season, and the mean daily net photosynthetic rates of both Q. acutissima and Q. variabilis during the peak growing season were higher than during the early growing season. The average daily net photosynthetic rate of 1.94 μmol m² s⁻¹ was higher than that of Q. variabilis (1.86 μmol m⁻² s⁻¹) during the early growing season but not significant (p = 0.12). During the peak growing season, the average daily net photosynthetic rate of Q. acutissima was 4.16 μmol m⁻² s⁻¹, compared with 3.10 μmol m⁻² s⁻¹ for Q. variabilis.

3.1.2. Diurnal Variation of Transpiration Rate

Plant transpiration is intimately linked to photosynthesis, which facilitates carbon assimilation and the diffusion and transportation of CO₂ from the ambient atmosphere to leaf flesh cells. As illustrated in Figure 2D, the daily trends of Q. acutissima and Q. variabilis transpiration were consistent with the photosynthetic rate (both in a single-peaked pattern), whereas the peak transpiration rate for Q. acutissima occurred at 12:00 at 0.80 mol m⁻² s⁻¹ during the early growing season, with a daily mean transpiration rate of 0.377 mol m⁻² s⁻¹. The peak transpiration rate of Q. variabilis also occurred at 12:00 am at 0.67 mol m² s⁻¹, whereas the daily mean transpiration rate was 0.36 mol m⁻² s⁻¹. The peak transpiration rate for Q. acutissima appeared at 12:00 at 0.06 mol m⁻² s⁻¹, and the daily mean transpiration rate was 1.11 mol m⁻² s⁻¹ during the peak growing season. The peak transpiration rate for Q. variabilis occurred at 12:00 am at 0.05 mol m⁻² s⁻¹, and the mean daily transpiration rate was 0.91 mol m⁻² s⁻¹. The daily mean transpiration rates of Q. acutissima and Q. variabilis during the peak growing season were higher than those of the early growing season, with the transpiration rate of Q. acutissima being higher than that of Q. variabilis.

3.1.3. Diurnal Variation of Stomatal Conductivity

Stomata are the channels through which CO₂ and water ingress and egress leaves, where stomatal conductivity reflects the capacity of leaves to exchange CO₂ and water with the ambient environment. The daily variation of stomatal conductivity was unimodal (Figure 2B) and corresponded to the daily trend of the net photosynthetic and transpiration rates. The daily average stomatal conductivities of Q. acutissima and Q. variabilis were lower during the early growing season than during the peak growing season. At 12:00 am, the peak stomatal conductivity of Q. acutissima was 0.03 mol m⁻² s⁻¹, whereas that of Q. variabilis was 0.03 mol m⁻² s⁻¹. The peak stomatal conductivity of Q. acutissima was 0.06 mol m⁻² s⁻¹ at 12:00 am and 0.05 mol m⁻² s⁻¹ at 12:00 am during the peak growing season. The mean daily stomatal conductivity for Q. acutissima was 0.02 mol m⁻² s⁻¹ and 0.02 mol m⁻² s⁻¹ for Q. variabilis during the early growing season. During the peak growing season, the mean daily stomatal conductivity was 0.03 mol m² s⁻¹ for Q. acutissima and 0.03 mol m⁻² s⁻¹ for Q. variabilis.

3.1.4. Diurnal Variation of Intercellular CO₂

Intercellular CO₂ is the primary raw material for photosynthesis in leaves, where its concentration reflects its strength. As shown in Figure 2C, the daily intercellular variations in CO₂ exhibited a trend of being low in the afternoon and high in the morning and evening during both the early growth and peak seasons. Figure 2 reveals that, as the solar radiation increased, leaf photosynthesis commenced, after which the intercellular CO₂ concentration gradually decreased to reach its low point at midday. The lowest CO₂ concentrations for Q. acutissima and Q. variabilis were 157.18 and 187.25 μmol mol⁻¹, respectively, during the early growing season and 140.25 and 151.70 μmol mol⁻¹, respectively, during the peak growing season. The concentration of intercellular CO₂ steadily increased as photosynthesis weakened in the afternoon. During the early growing season, the average intercellular CO₂ concentrations for Q. acutissima and Q. variabilis were 212.36 and 241.27 μmol mol⁻¹, respectively. During the peak growing season, the intercellular CO₂ concentrations for Q. acutissima and Q. variabilis were 158.61 and 187.01 μmol mol⁻¹, respectively. The concentration of intercellular CO₂ for Q. variabilis was higher than that of Q. acutissima during both the early and peak growing seasons. Furthermore, with more robust photosynthesis, the intercellular CO₂ concentration was lower. As shown in Figure 2C, the intercellular CO₂ concentrations of Q. acutissima and Q. variabilis reached a valley at 10:00 am, in conjunction with the peaking net photosynthetic rate.

3.1.5. Correlation Analysis of Net Photosynthetic Rate and Eco-Physiological Factors

We observed physiological indicators such as the net photosynthetic rate, stomatal conductivity, and transpiration rate, as well as associated environmental factors, including photosynthetically active radiation (PAR) and temperature, during the early and peak growing seasons. To better comprehend how the net photosynthetic rate responded to eco-physiological factors, it was correlated with the stomatal conductivity, intercellular CO₂ concentration, transpiration rate, photosynthetically active radiation, and air temperature (

Table 2. Correlation coefficients between net photosynthetic rate and eco-physiological factors during different growing seasons. PAR: photosynthetically active radiation. Significant values are indicated: **, p < 0.01.

Species	Growing Period	Stomatal Conductivity	Internal CO2 Concentration	Transpiration Rate	Air Temperate	PAR
Q. acutissima	Early	0.890 **	−0.789 **	0.854 **	0.202	0.789 **
	Peak	0.980 **	−0.650 **	0.968 **	0.258	0.626 **
Q. variabilis	Early	0.748 **	−0.737 **	0.617 **	0.281	0.510 **
	Peak	0.942 **	−0.776 **	0.944 **	0.295	0.598 **

). The net photosynthetic rate was found to be significantly positively correlated with the stomatal conductivity, transpiration rate, and photosynthetically active radiation (p < 0.01); significantly negatively correlated with the intercellular CO₂ concentration (p < 0.01); and insignificantly correlated with the temperature (p < 0.05). The strongest correlation was found between the net photosynthetic rate and stomatal conductivity, and the correlation coefficient increased over time. The correlation coefficient between the net photosynthetic rate and stomatal conductivity was 0.89 during the early growing season and 0.98 during the peak growing season, which indicated that the stomatal conductivity had an increased effect on the net photosynthetic rate during the peak growing season. During both the early and peak growing seasons, the correlation coefficient between the net photosynthetic rate and transpiration rate of Q. acutissima was greater than that of Q. variabilis, which was consistent with the response pattern of the net photosynthetic rate on the stomatal conductivity of Q. acutissima. The correlation coefficients between the net photosynthetic rate and stomatal conductivity for Q. acutissima and Q. variabilis were greater than those between the net photosynthetic rate and photosynthetically active radiation. This implied that the stomatal conductivity had a greater impact on the net photosynthetic rate than the photosynthetically active radiation.

3.1.6. Photosynthetic Light Response Model and Photosynthetic Parameters

The dynamic variations in the photosynthetic light response curve for the three models were similar when the PAR was <200 μmol m⁻² s⁻¹ (Figure 3 B–D). Specifically, the net photosynthetic rate increased rapidly with greater photosynthetically active radiation, and the predicted values fitted by the three models were close to those measured. When the PAR was >200 μmol m⁻² s⁻¹, the imitative effects of the three photosynthetic light response models on the light response curves were varied. In the Ye model, the net photosynthetic rates of Q. acutissima and Q. variabilis gradually decreased when the PAR exceeded the light saturation point (Figure 3D). In the rectangular hyperbola model, the net photosynthetic rate increased slightly as the PAR increased (Figure 3B). whereas in the nonrectangular hyperbola model, the light response curve trended to smoothing. Changes in the photosynthetic light response curve predicted by the Ye model were consistent with the measured curves when the PAR was >200 μmol m⁻² s⁻¹ (Figure 3A,D).

The light saturation point refers to the light intensity when the photosynthetic intensity of a plant reaches its peak. According to

Table 3. Photosynthetic parameters of Quercus acutissima Carruth. and Quercus variabilis Bl. fitted by the three models. Different lowercase letters (i.e., a, b, c) in the same column indicate a significant difference between different models of the same species (p < 0.05). Different capital letters (i.e., A, B, C) in the same column indicate a significant difference between different species of the same model (p < 0.05). RHM: rectangular hyperbola model; NHM: nonrectangular hyperbola model; YZP: Ye model; LSP: light saturation point; LCP: light compensation point; R_d: dark respiration; and the same below.

Species	Models	LSP/μmol m−2 s−1	LCP/μmol m−2 s−1	Rd/μ mol m−2 s−1	Pnmax/μmol m−2 s−1	MAPE/%	RMSE	R2
Q. acutissima	RHM	296.28bA	7.24aA	0.68cA	5.00aA	20.47	0.68	0.85
	NHM	169.77aA	7.67aA	0.24aA	4.29aA	17.86	0.56	0.90
	YZP	607.24cA	8.14abA	0.42bA	4.85aA	15.37	0.20	0.99
	Measured value	783.33dA	9.86bA	0.29aA	4.65aA	—
Q. variabilis	RHM	326.84aA	22.67aB	1.76aB	5.36bA	27.18	0.37	0.95
	NHM	239.65aA	34.55aB	1.43aB	4.78abA	25.38	0.24	0.98
	YZP	651.69bA	27.53aB	1.65aB	3.67aB	24.37	0.10	0.99
	Measured value	666.67bB	26.00aB	1.55aB	3.630aB	—

, the light saturation points (LSP) of the measured curves for Q. acutissima and Q. variabilis were 783.33 and 666.67 μmol m⁻² s⁻¹, respectively. The ANOVA revealed that the light saturation point of Q. acutissima was significantly greater than that of Q. variabilis (p < 0.05), which meant that Q. acutissima utilized more light energy than Q. variabilis. The light saturation points of the rectangular hyperbola and nonrectangular hyperbola models for Q. acutissima were 62.965% and 78.78%, respectively, which were lower than the measured values, while that of the Ye model was 24.10% lower than the measured values. The light saturation points of the rectangular hyperbola and nonrectangular hyperbola models for Q. variabilis were 45.53% and 60.057% lower than the measured values, respectively, while that of the Ye model was 8.62% lower than those measured. This indicated that the light saturation points of the Ye model were closer to the measured values and had a better fit.

The minimum light intensity required by plants for photosynthesis is defined as the light compensation point. As shown in Table 3, the light compensation point (LCP) predicted by the rectangular hyperbola model for Q. acutissima was 7.24 μmol m⁻² s⁻¹; for the nonrectangular hyperbola model, it was 7.68 μmol m⁻² s⁻¹. These values were 26.55 % and 22.18% lower than the measured LCP (9.86 μmol m⁻² s⁻¹), respectively. The light compensation point predicted by the Ye model (8.14 mol m⁻² s⁻¹) was 17.51% lower than the measured value. The LCP predicted by the rectangular hyperbola model for Q. variabilis was 12.82% lower than the measured value. Further, the LCP predicted by the nonrectangular hyperbola and Ye models were 32.89% and 5.88% higher, respectively, than the measured value.

For this study, the respiration rate value at a light intensity of zero was used as the measured dark respiration rate. Because of ignoring the photorespiration, the actual dark respiration rate was greater than or equal to the measured respiration rate. The predicted dark respiration rates of the three models for Q. variabilis were not significantly different from the measured values. However, for Q. acutissima, only the predicted dark respiration rate of the nonrectangular hyperbola model was closer to the measured values, while the predicted dark respiration rates of the rectangular hyperbola and Ye models were 137.02% and 43.94% higher, respectively, than the measured values. According to Table 3, the dark respiration rate of Q. acutissima was significantly lower than that predicted or measured for Q. variabilis (p < 0.05), which was 81.39% lower than for Q. variabilis. In the Ye model, Q. acutissima had a 74.86% lower dark respiration rate than Q. variabilis, where the lower the dark respiration rate, the less CO₂ content was released. This meant that, under the same conditions, Q. acutissima had a higher carbon storage capacity than Q. variabilis.

The highest net photosynthetic rate was the critical parameter in defining the photosynthetic potential. For the rectangular hyperbola and Ye models of Q. acutissima, the maximum net photosynthetic rates predicted were 7.68% and 4.30% greater, respectively, than the measured values. However, there were difference between photosynthetic parameters predicted by different models. The predicted maximum net photosynthetic rate of the rectangular hyperbola model was 47.63% significantly higher than that measured for Q. variabilis (p < 0.05). While, the predicted maximum net photosynthetic rates of the nonrectangular hyperbola and Ye models were 31.57% (p = 0.08) and 1.02% (p= 0.95) higher than the measured values, respectively. The measured maximum net photosynthetic rate of Q. acutissima was 28.02% higher than that of Q. variabilis (p < 0.05). Similarly, the maximum net photosynthetic rate of Q. acutissima predicted by the Ye model was considerably higher than that of Q. variabilis (p < 0.05).

The imitative effects of the three models were tested via three indicators, including the root-mean-square error (RMSE), mean absolute percentage error (MAPE), and coefficient of determination (R²). The RMSE measures the differences between the observed and predicted values and reflects the dispersion of errors. The MAPE characterizes the average errors of multiple predictions for evaluating the fitting accuracy of the model to the existing data, while R² can determine the degree of model fitting. The lower the MAPE and RMSE, the closer the R² is to one, which indicates a better fit. The RMSE of the fitted curves of the three Q. variabilis models were 0.37, 0.25, and 0.10, respectively, while the RMSE of the fitted curves of the three models for Q. acutissima were 0.678, 0.57, and 0.20 respectively. The RMSE of the Ye model was the smallest of the three models. In terms of the model-fitting accuracy for the Q. acutissima and Q. variabilis light response curves, the Ye model had the best fitting accuracy for Q. acutissima with an error rate of 15.37%, followed by the nonlinear hyperbolic model with an error rate of 17.86%. The Ye model had the best fitting accuracy for Q. variabilis with an error rate of 24.37%, followed by the nonlinear hyperbolic model (25.38%). The R² values for all three models of Q. variabilis were greater than 0.90, whereas the R² for the fitted curve of Q. acutissima was 0.99 in the Ye model. In summary, the Ye model performed better than the rectangular hyperbola and the non-rectangular hyperbola models in terms of fitting the photosynthetic parameters (e.g., maximum net photosynthetic rate, light saturation point, and light compensation point). Further, its model evaluation index RMSE was lower, the R² was closer to one, and the fitting accuracy was higher. This signified that the Ye model was better suited for fitting the net photosynthetic light response curves of Q. acutissima and Q. variabilis.

4. Discussion

4.1. Relationships between Photosynthetic Rates and Eco-Physiological Factors

During the early and peak growing seasons, diurnal changes in the net photosynthetic rates of Q. acutissima and Q. variabilis were unimodal, which was consistent with Zhao et al. and Fan et al. [34,35], but they diverged from the study of Wang et al. [33]. These researchers thought that this was due to the stomatal conductivity, which limited the availability of CO₂ at higher temperatures [36]. During the peak growing season, the net photosynthetic rates of Q. acutissima and Q. variabilis were significantly greater than during the early growing season, which was consistent with the changes in leaf stomatal conductivity. The main factor that influenced the net photosynthetic rates of Q. acutissima and Q. variabilis was stomatal conductivity. Table 1 shows that the correlation coefficients between the stomatal conductivities and net photosynthetic rates of Q. acutissima and Q. variabilis were 0.89 and 0.75, respectively, during the early growing season, which increased to 0.98 and 0.94 during the peak growing season. This was consistent with the study of Liang, who found that the stomatal factor was the primary driver behind changes in the net photosynthetic rate [37]. Stomatal conductivity steadily increased with stomatal expansion from the early to peak growing seasons, which stimulated photosynthesis [38]. Atmospheric temperatures, vapor pressure deficits, and relative humidity can affect stomatal opening and closing [39] and indirectly affect the net photosynthetic rate. In addition to stomatal factors, stomatal opening and closing had an indirect impact on the photosynthetic rate. Photosynthetic active radiation in conjunction with stomatal factors were important external factors that influenced the net photosynthetic rates of Q. acutissima and Q. variabilis. Wu et al. discovered that photosynthetically active radiation had a greater impact on sunny plants such as Q. acutissima and Pinus sylvestris [40]. This was due to photosynthetically active radiation that induced the generation of adenosine triphosphate (ATP) and nicotinamide adenine dinucleotide phosphate (NADPH), which assimilated carbon in the dark reaction stage [41]. The photosynthetic rate and intercellular CO₂ concentrations were negatively associated, which indicated that more intense photosynthesis consumed additional CO₂. This was because the intercellular CO₂ concentrations affected the photochemical efficiency of photosystem II [42]. The photosynthetic rate was significantly positively correlated with the transpiration rate, which was consistent with the study of Kim [43]. As stomata conductivity reflects the extent to which stomata open, both photosynthesis and transpiration employ stomata as channels. Thus, both of them increased with higher stomata conductivity.

4.2. Comparison of Photosynthesis–Light Response Models

Currently, the rectangular hyperbola, nonrectangular hyperbola, and Ye models are the most commonly utilized photosynthesis light response models [44], and they play important roles in fitting photosynthetic light response curves, while also predicting photosynthetic parameters [9]. The Ye model can accurately reflect the inhibition of the net photosynthetic rate with higher light intensities during photosynthesis in Q. acutissima and Q. variabilis, while the rectangular hyperbola and nonrectangular hyperbola models cannot indicate the inhibition of photosynthesis under strong light conditions [45]. This is due to the mathematical expressions for the rectangular hyperbola and nonrectangular hyperbola models lacking the asymptote of the poles [46]. Thus, they cannot simulate the decreasing photosynthetic rate under higher light intensities. Conversely, the Ye model is based on the rectangular hyperbola model with the addition of correction parameters to bring the fitted curve closer to the actual measurement [30]. Deng et al. discovered that the Ye model fitted the Q. variabilis photosynthesis–light response curve better than the rectangular hyperbola or nonrectangular hyperbola models [22].

Since photosynthetic parameters reflect the capacity of plants to utilize light energy [45], the adaptabilities of the three models to the light response curves of Q. acutissima and Q. variabilis were compared. Both the rectangular hyperbola and nonrectangular hyperbola models had lower light saturation points than the actual curve, which was consistent with the studies of Xu and Xi [47,48]. This was due to the light saturation points of the rectangular hyperbola and nonrectangular hyperbola models not being directly obtainable, which had to be calculated using Richardson’s hypothetical empirical formula [49]. The light saturation point of Q. acutissima predicted by the Ye model was significantly lower than the measured value, while the predicted light saturation point of Q. variabilis was not significantly different from the measured value. This indicated that the prediction of the light saturation point of Q. variabilis using the Ye model was superior to that of Q. acutissima. The prediction of the light compensation point (LCP) for Q. acutissima and Q. variabilis via the three models revealed differences. The LCP of Q. acutissima predicted by the Ye model was closer to the measured curve than that of the rectangular hyperbola and nonrectangular hyperbola models, while the LCP of Q. variabilis predicted by the three models was not significantly different from that of the measured value. The differences between the models may have been due to the smaller LCP of Q. acutissima, which was more photonically sensitive under low light conditions [50]. The dark respiration rate of Q. acutissima predicted by the nonrectilinear hyperbolic model was closer to the measured value, while the dark respiration rates predicted by the rectangular hyperbola and Ye models were significantly larger than the measured values. This signified that the prediction of the dark respiration rate of Q. acutissima by the nonrectilinear hyperbolic model was better than those projected by the rectangular hyperbola and Ye models. The predicted dark respiration rates of Q. variabilis using the three models were not significantly different from the measured values, which indicated that all three models were suitable for fitting the Q. variabilis dark respiration rate.

4.3. Comparison of Net Photosynthetic Rates with Other Regions

In this study, the net photosynthetic rate of Q. variabilis was similar to that of the Funiu Mountain area but lower than that of this species on Taihang Mountain and other regions [49]. The net photosynthetic rate of Q. acutissima in this study was closer to that of Nanjing, Chuzhou, and Wanyuan [34,51] but lower than that of Fei County, Kunming [52]. According to

Table 4. Comparison of net photosynthetic rates of Q. acutissima and Q. variabilis in different regions. These data were obtained during July and August.

Species	Area	Daily MEAN Net Photosynthetic Rate/μmol·m−2·s−1	Annual Rainfall/mm	Mean Annual Temperature/°C	Precipitation pH	Latitude/N	Climatic Zone	Reference
Q.variabilis	Funiu Mountain	3.26	1100	12~14.1	-	32°45′	Temperate	[49]
	Taihang Mountain	7.62	641.7	12.4~14.3	5.13	35°01′	Temperate	[35]
	Beijing	7.72	669.1	10.8	5.21	40°29′	Temperate	[54]
	Jurong	3.10	1055	15.2	4.87	32°07′	Subtropics	This study
Q.acutissima	Kunming	6.20	1035	15	7.80	-	Subtropics	[52]
	Feixian	6.79	856.4	20	5.35	117°96′	Temperate	[51]
	Chuzhou	3.65	1050	15	5.06	118°08	Subtropics	[51]
	Wanyuan	3.67	1100	15	4.74	108°06′	Subtropics	[51]
	Nanjing	4.47	1100	15.1	4.87	31°35′	Subtropics	[34]
	Jurong	4.16	1055	15.2	4.87	31°59′	Subtropics	This study

, we found that higher precipitation translated to a lower net photosynthetic rate. Following 15 years of continuous observation of terrestrial ecosystems in Qinghai and Tibet, Xu et al. discovered that the net primary productivity decreased with higher precipitation [53]. Wang et al. found that the net photosynthetic rate of Q. variabilis in northern habitats (Beijing) was significantly higher than in southern habitats (Yunnan), which received more precipitation [54]. Furthermore, acid rain had a significant impact on the net photosynthetic rate. Kunming, which has the same annual average temperature and precipitation, has a higher net photosynthetic rate than Nanjing and Jurong, which might have been due to the pH of the rainfall. Acid rain had a positive effect on the leaf photosynthetic rate when the pH was above 5.0 and had a negative effect when below this level [25]. It is known that the annual average precipitation pH value was 4.87 in the Changjiang River Delta [21] and 7.28 in Kunming city [55]. Thus, it was obvious that the pH of precipitation can inhibit photosynthesis in the oak forests of the Changjiang River delta. Differences in the photosynthetic capacities of Q. variabilis in different regions were also influenced by latitude. Xiong et al. discovered that latitude had a significant impact on Q. variabilis photosynthesis [56]. Liu et al. also found that, at high latitudes, Q. variabilis had higher dark respiration rates, whereas, at low latitudes, it had higher maximum net photosynthetic rates and lower light compensation points [57]. This was thought to be attributed to increases in the chlorophyll and nitrogen contents of Q. variabilis leaves with increasing latitude.

4.4. Comparison of Photosynthetic Parameters between Q. acutissima and Q. variabilis

The daily average net photosynthetic rate of Q. acutissima was significantly greater than that of Q. variabilis during the early and peak growing seasons, and its maximum net photosynthetic rate (referring to photosynthetic potential) was also greater than that of Q. variabilis. This indicated that Q. acutissima possessed a stronger photosynthetic capacity and superior carbon sequestration efficiency. As the trees grew, the photosynthetic capacity of Q. acutissima differed even more significantly from that of Q. variabilis. The light compensation point reflects the photosynthetic capacity of plants under low light conditions. The light compensation point of Q. acutissima was significantly smaller than that of Q. variabilis, which implied that the photosynthetic capacity of Q. acutissima was superior under low light conditions. The dark respiration rate is an important parameter that characterizes plant respiration, where the higher the value, the more CO₂ is released. The dark respiration rate of Q. acutissima was 0.289 mol m⁻² s⁻¹, which was significantly lower than that of Q. variabilis (1.553 mol m⁻² s⁻¹). This suggested that the number of carbohydrates consumed by Q. acutissima was smaller than that of Q. variabilis. Specifically, when all other conditions were equivalent, the quantity of CO₂ fixed by Q. acutissima was greater than that of Q. variabilis. In summary, Q. acutissima had a higher photosynthetic carbon sequestration capacity than Q. variabilis, which makes it a priority candidate species for carbon sink forests.

5. Conclusions

By synthesizing data from photosynthetic processes and fitting the photosynthetic light response curves, we assessed the photosynthetic characteristics of Q. acutissima and Q. variabilis and their photosynthetic efficiencies. Our results indicated the following: (1) The photosynthetic capacities of Q. acutissima and Q. variabilis significantly increase with their growth. (2) Stomatal conductivity was the most important physiological factor that affected photosynthesis in Q. acutissima and Q. variabilis, where photosynthetically active radiation was the most critical environmental factor. (3) The Ye model was the optimal model for fitting the light response curves of Q. acutissima and Q. variabilis. (4) The photosynthetic efficiency of Q. acutissima was higher than that of Q. variabilis; thus, it can serve as a priority species for carbon sink forests in the Changjiang River delta region. In the future, investigations into the processes and kinetics of acid rain that affect the photosynthesis of Q. acutissima and Q. variabilis need to be conducted, as does an evaluation of carbon fixation capacities in acid rain areas.