Photosynthetic CO2 response characteristics in canopy of Larix principis-rupprechtii Mayr. tree and practicability of three Models

Accurately predicting the crown photosynthesis of trees is important to understand the tree growth status and carbon circle in terrestrial ecosystem. However, modeling the photosynthetic carbon dioxide (CO2) response curves for individual tree are still challenging due to the complex canopy structure and changeable environmental conditions. Therefore, taking 16-old year Larix principis-rupprechtii Mayr. as the research material, the dynamic CO2 response models of photosynthesis, including rectangular hyperbolic model (RHM), the non-rectangular hyperbolic model (NRHM) and the modified rectangular hyperbolic model (MRHM), were used to simulate CO2 response curves of the crown. The fitting accuracy of the models depend on the comparison of determinants coefficients (R2), mean square errors (MSE) and Akaike information criterion (AIC). The results showed that the mean value of R2 (R2=0.9939 ∼ 0.9964) of MRHM was the highest, whereas MSE value (MSE=0.2185∼0.2627) and AIC value (AIC=-13.18∼-8.03) were the lowest. The CO2-saturated gross photosynthetic rate (Amax) and the saturation point (CiSP) obtained by MRHM were closest to the measured value respectively. Therefore, the MRHM fitted the CO2 response data well, and calculated the photosynthetic parameters directly and accurately, the fitted result showed α, Amax, CiSP, CiCP and RP were 0.04, 7.51 μmol·m-2s-1, 938.97 μmol·m-2, 67.54 μmol·m-2 and 0.60 μmol·m-2s-1, respectively. In addition, the difference on the photosynthetic CO2 response parameters values showed somewhat among different layers and orientations. In all, all data suggested that the modified rectangular hyperbolic model (MRHM) was an ideal model to fit the crown photosynthetic CO2 response curve of Larix principis-rupprechtii Mayr. These results are of great significance for parameter calibration of photosynthetic model and robust prediction of photosynthetic response in forest.


Introduction
As the largest CO 2 fluxes in carbon, energy and other cycles in the earth system, photosynthesis can assimilate atmospheric CO 2 and mitigate climate change, it is a critical component in the material cycle and energy flow of global terrestrial ecosystem [1][2][3]. CO 2 is one of the limiting factors of photosynthesis during plant growth stage, the change of its concentrations influences the accumulation of photosynthetic products [4][5][6][7]. For the trees, the crown canopy is the most direct part for photosynthesis to response to assimilating CO 2 . Therefore, it is a major research priority to develop understanding the mechanism of leaf photosynthetic response of canopy to CO 2 availability for improving forest productivity and ecological protection, especially for dynamic simulation of growth model and in parameterization of canopy photosynthesis.
The photosynthetic CO 2 response curves (A n -C i curves ) elaborate the relationship between net photosynthetic rate (A n ) and intercellular CO 2 concentration (C i ), the A n -C i curve has always been one of the hotspots in plant physiology, ecology and biochemistry, it can analyze the primary productivity of vegetation and forests [8][9]. To date, in order to investigate the response of net photosynthetic rate (A n ) to intercellular CO 2 concentration (C i ) of different plants, many A n -C i curves models, including Farquhar model (1980) and its modified model [1,[10][11][12][13], the rectangular hyperbola model (RHM) [14], Michaelis-Menten model (MMM) [15], the nonrectangular hyperbola model (NRHM) [16], the exponential model (EM) [17], and the modified rectangular hyperbola model (MRHM) [18][19], the modified exponential model (MEM) [20][21], may be used to describe the the photosynthetic CO 2 response curves (A n -C i curves) in different plants [1], various photosynthetic parameters, such as maximum net photosynthetic rate (A max ), initial carboxylation efficiency (α), CO 2 saturation point (C i SP ), CO 2 compensation point (C i CP), and light respiration rate (R p ), were used to assess the canopy photosynthetic capacity and other aspects of plants in different growth stage. However, RHM, MMM, NRHM, and EM were very complex, some photosynthetic parameters (such as A max and C i SP) couldn't be obtained directly from these models due to environmental changes [19,22], and the The C i SP calculated by the above models was clearly underestimated, whereas A max fitted by these models were overestimated [19]. In the contrary, due to the addition of two adjusting factors (β and γ) into the model, the MRHM can directly produce A max and C i SP, and overcome the shortcomings of above these models, the accuracy was very higher, the results were suitable for simulating A n -C i curves and photosynthetic parameters under different environmental conditions, it has been successfully applied to simulate CO 2 -response curves of many plants, such as Physalis pubescens L [23], Sapindus mukorossi [9], Alsophila spinulosa [8], Brassica napus L. [24], Nicotiana [25].
Larix principis-rupprechtii Mayr (Larch) plays a critical role in wood production, biodiversity protection, conservation of water and soil and forest ecosystem in Northern China. Due to its complexity, little was known about the application of various dynamic canopy photosynthetic CO 2response models in Larch, and the fitting effects and differences of these models on CO 2 -response remains largely elusive. Therefore, the determinant coefficients (R 2 ), mean square error (MSE), and Akaike information criterion (AIC) were used to evaluated the performance of three types of CO 2response models (such as RHM, NRHM, and MRHM ) in 16-years-old Larch. plantation. The specific objectives of the study are to select an optimal A n -C i curve model for fitting the A n -C i curves of Larch, and to explore the relationships between the parameters of the optimal A n -C i curve model and needle vertical and horizontal directions. The results will provide a theoretical guidance for further exploring the spatial heterogeneity of carbon sequestration capacity and accurately estimating photosynthetic characteristics of Larch needles at the crown level.

Site description and sample tree selection
This study was conducted in the Saihanba Forest Farm of Chengde City, Hebei Province, northern

Determination of CO 2 -response curve
The CO 2 -response curves (A n -C i curves ) for different needle positions were determined by a portable photosynthetic gas exchange system equipped with a 2 × 3 cm LED Light Source (LI-COR6400, LI-COR Inc., Lincoln, Nebraska, USA ). Photosynthetic photon flux density was held at 1200 µmol m -2 s -1 , temperature of leaf chamber of 24-26℃, relative humidity of 30-40% during the determination of A-C i curves. Measurements of the response curves of photosynthesis to intercellular CO 2 concentration (A n -C i ) started at external CO 2 concentration of 400 µmol mol -1 , then decreased stepwise to 50 µmol mol -1 and increased stepwise to 2000 µmol mol -1 , resulting in a sequence 400, 300, 200, 100, 50, 0, 150, 250, 400, 600,1000, 1500 and 2000 µmol mol -1 . The experiment were conducted between 8:00 and 16:00 under cloud-free skies, the measurement data for the A n -C i curves were obtained from June to August of 2020 and 2022. These methods were described previously [26][27].

Photosynthesis CO 2 -response (A n /C i ) curve-fitting model
As the most frequently model for fitting A n -C i curves, the rectangular hyperbola model (RHM), the nonrectangular hyperbola model (NRHM), and the modified rectangular hyperbola model (MRHM) were well described in the literature [19,[30][31][32].
The rectangular hyperbola model (RHM) was represented to the following form : Where: A n , μmol m -2 s -1 , is the photosynthetic capacity; C i , μmol·mol -1 , is the intercellular CO 2 concentration; α is initial carboxylation efficiency (dimensionless) when C i =0 μmol m -2 ; A max , μmol m -2 s -1 , is the maximum photosynthetic capacity; R p is light respiration rate, it is estimated from the A n /C i curve at C i = 0 µmol mol -1 .
The A max and C i SP cannot be calculated directly using RHM, therefore, A max was estimated and calculated by using the nonlinear least squares method [33], C i SP (saturation CO 2 point, μmol m -2 s -1 ) and C i CP (CO 2 compensation point, μmol m -2 s -1 ) were expressed on the rectangular hyperbola model in equations. 2 and 3 respectively.
Where: CE, μmol m -2 , is the carboxylation efficiency ( CE is the slope at C i < 200 µmol mol -1 ); and R p are as described above.

Nonrectangular hyperbola model
The nonrectangular hyperbola model (NRHM) was represented to the following form: where: θ (0 < θ < 1) indicates the convexity (curvilinear angle) (dimensionless); and A n α, C i , A max, and R p are as described above.
The C i SP and C i CP was calculated by formula 2, 5 respectively.
where: C i CP, α, θ, I, A max, and R p are as described above.
The A max , C i SP and C i CP were expressed on the modified rectangular hyperbola model in equations. 8, 9, and 10 respectively: Where:A max , α, β, γ, C i CP, R p are as described above.

Model assessment and validation
The performance of the different models were assessed by determinants coefficients (R 2 ), mean square errors (MSE), and Akaike information criterion (AIC), the best combination with the largest R 2 value and smallest MSE and AIC value represented the higher fitting accuracy.
Determinants coefficients (R 2 ) represents the fitting degree of net photosynthetic rate.
Mean square error (MSE) was the average of squared forecast errors, it is the specific value of the sum of squared errors to the number of errors.
Akaike information criterion (AIC) is a fined technique based on in-sample fit to estimate the likelihood of a model to predict/estimate the future values.
where y i, ŷ i and y i in 11, 12, and 13 equations is the measured value, the fitted value and the mean of the measured values, respectively n is the number of observations. k is the number of estimated parameters [34].

Statistical analysis
The photosynthetic data were expressed as mean ± standard error (SE) of five independent experiments. All statistical data analyses were performed using the software GraphPad Prism 8.0 or the SPSS 18.0 (SPSS, Chicago, IL, USA). the mean values in photosynthetic parameters were significantly different at the level of 0.05 by different lowercase letters. Error bars represent the standard of the mean values of three biological replicates.

Spatial and temporal distribution characteristics of A n -C i
To describe the relationships between A n and C i , photosynthetic CO 2 -response curves (A n -C i ) of Larch was studied. The results showed the variation of A n for needles with increasing C i . The A n -C i curves could be divided into three phases, A n increased rapidly as C i was below 300 µmol mol -1 , then increased nonlinearly up to the maximum A n when C i was 300-1000 µmol mol -1 , and decreased gradually beyond 1000 µmol mol -1 in the third stage. The A n -C i curves of needles under the different canopies showed similar tendency, the A n values were very closer in the different canopy layers when the C i was low (C i < 300 μmol m -2 ), the gap increased with an increasing C i , and the difference in A n was more remarkable. At the same C i , A n under UP needles was higher than that of the MD and LW needles, respectively, and A n values could be ranked as: upper layer > middle layer > lower layer (Fig 2, Table S1). The results indicated that needles in the upper layer have relatively higher photosynthesis, whereas those in the lower canopy layer have relatively lower photosynthesis, they are playing mutually a critical role in the canopy photosynthesis.  Table S2) showed the A n -C i curves of needles under the different layers and different models . The A n values fitted by the RHM, NRHM and MRHM were very close to the measured values actually when the C i was low (C i <300 μmol m -2 ), the A n values simulated by three models were slightly greater than measured values when C i values > 300 μmol m -2 , and the pattern of A n -C i curves simulated by three models showed similar tendency, as C i was above 1000 μmol m -2 , the A n value simulated by the MRHM remained stable or decreased slowly, whereas the A n value simulated by the RHM and NRHM increase slowly. The mean value of R 2 (range from 0.9939 to 0.9964) of the MRHM model was the highest among the three models, and MSE value (MSE range from 0.2185 to 0.2627 ) and AIC value (range from-13.18 to -8.03 respective) of the MRHM were significantly smaller than those of other two models in UP, MD and LW respectively (Table. 1). Therefore, MRHM was superior to other two models in describing the photosynthetic CO 2 response curve.    In addition, the A max, and R p values were significant difference between MRHM and the other two models in the upper layer, while the a, and C i CP values were no significant difference among three models, the C i SP was significant difference between MRHM and the other two models in the different layers (Fig 5, Table S4). Therefore, MRHM could fit the photosynthetic response curve well , and better explain the saturation phenomenon of photosynthesis to CO 2 concentrations.  Table S5) showed the comparison of photosynthetic parameters of the different canopy layers. Taking the measured value and(or) the fitted value by MRHM for example, the values of A max and R p in the upper layer were significantly higher than that in the lower layer, and showed no difference from in the middle layer, while the value of C i CP in the upper was significantly lower than that in the lower layer, and showed no difference from in the middle layer.

Comparison of the photosynthetic parameters in the different canopy layer
The values of C i SP showed no difference in different canopy layers, the difference of a was consistent with A max in the vertical direction. In addition, the significant differences of the measured values of photosynthetic parameters in the different layers were consistent with the fitting values of MRHM model, and were different from those of other two models.

Discussion
As a critical method in elucidating the relationship between the net photosynthetic rate and CO 2 concentrations, the A n -C i curve can identify many photosynthetic parameters and evaluate the photosynthetic capacity of plants [35]. Therefore, choosing an appropriate CO 2 -response curve model is helpful to fit crown photosynthesis and to estimate plant photosynthetic capacity. In the study, A n increased initially and then decreased gradually with the increase of C i (Fig 3), which was in accordance with the study report of leaf A n -C i curves of some plants [36]. The results implied CO 2 absorbed by plants exceeded the needs of plants, the assimilation of the excessive CO 2 would restricted enzymatic reaction rates in the chloroplasts and lead to delaying growth of Larch. In addition, the variation of A n response to C i maintained the state of upper layer > middle layer > lower layer at the whole growth stage, the differences of the A n -C i curve among different canopy layers might be associated with leaf characteristics, higher chlorophyll a/b ratios, relative depth into crown, etc [26,37].
The fitting of CO 2 -response curve model is a critical means to describe the response mechanism of A n to C i and to evaluate the photosynthetic efficiency [35]. In the study, the fitting effects of three CO 2 -response models on the A n -C i curves of the larch were compared in the different layers and orientations. the fitting effects of RHM and NRHM on A n -C i curves were better (R 2 >0.9) at the first stage (Fig 2), however, these two models could not fit the decline process of A n -C i curves when C i was above 1000 μmol m -2 , which indicated that the application and fitting accuracy of above two models were not suitable for fitting A n -C i of the larch. Compared with RHM and NRHM, the MRHM could fully fit the curve of net photosynthetic rate decreasing with the increase of CO 2 , and could reflect the actual CO 2 saturation, it had a greater R 2 and smaller MSE and AIC than other two models in simulating A n -C i response of needles (Table. 1). In addition, some photosynthetic parameters fitted by RHM and NRHM deviated greatly from the measured values, the fitted values of photosynthetic parameters (such as α, A max , C i SP, C i CP) by MRHM were close to the measured values (Fig 5), which was consistent with the study of leaf A n -C i curves of some plants at growth [5,[38][39]. Therefore, the unique structure of MRHM was more flexible in simulating different trends of A n -C i curves [33].
The photosynthetic parameters were somewhat different in different models and canopy layers.
A max , α, C i CP and Rp were significant difference in different layers (Fig 6a, 6c-6e), and was no significantly different in different models (Fig 5a, 5c-5e), while C i SP was no significant difference in different canopy layers (Fig 6b) and significantly different in different models (Fig 5b).
Additional, the photosynthetic parameters showed no significant difference in the horizontal directions (Fig 7, Table S6). It can be seen that canopy layer was one of the main factors of affecting the photosynthetic parameters (Fig.4), the model and orientation were not an important factor that affects the photosynthetic capacity of needles. The spatial variability may be due to the comprehensive effects of genetic diversity, different producing areas and environmental factors of trees [40].
In all, we considered the MRHM could fit well the A n -C i curves of larch, and better reflect the changes of photosynthetic parameters in different canopy layers. However, the data, obtained from five sample trees of Larix principis rupprechtii during the growing stage in 2020 and 2021, are of some limitation for the spatial heterogeneity and complexity. Therefore, many studies are needed further to examine the relationship between P n and C i based on more detailed data from different sample trees of different habitat conditions, the optimal CO 2 -response curve model was selected to better understand the mechanisms of the photosynthetic physiological ecology of plants over other forest ecosystems.

Conclusion
In the study, the A n -C i curves and photosynthetic parameters were measured in different canopy layers and orientations of five planted L. principis-rupprechtii trees by three models at the whole growth. The results showed that the modified rectangular hyperbola model (MRHM) could simulate A n -C i curve well and analyze the CO 2 -response data more accurately, the fitted values of photosynthetic parameters were as follows: α, A max , C i SP, C i CP and R P were 0.04, 7.51 μmol·m -2 s -       Table   Table 1 Fitting accuracy of different A n -C i.
Supporting Information S1 Table. the variation of A n for needles with increasing C i。 (DOC) S2