Effects of photosynthetic models on the calculation results of photosynthetic response parameters in young Larix principis-rupprechtii Mayr. plantation

Accurately predicting the crown photosynthesis of trees is necessary for better understanding the C circle in terrestrial ecosystem. However, modeling crown for individual tree is still challenging with the complex crown structure and changeable environmental conditions. This study was conducted to explore model in modeling the photosynthesis light response curve of the tree crown of young Larix principis-rupprechtii Mayr. Plantation. The rectangular hyperbolic model (RHM), non-rectangular hyperbolic model (NRHM), exponential model (EM) and modified rectangular hyperbolic model (MRHM) were used to model the photosynthetic light response curves. The fitting accuracy of these models was tested by comparing determinants coefficients (R2), mean square errors (MSE) and Akaike information criterion (AIC). The results showed that the mean value of R2 of MRHM (R2 = 0.9687) was the highest, whereas MSE value (MSE = 0.0748) and AIC value (AIC = -39.21) were the lowest. The order of fitting accuracy of the four models for Pn-PAR response curve was as follows: MRHM > EM > NRHM > RHM. In addition, the light saturation point (LSP) obtained by MRHM was slightly lower than the observed values, whereas the maximum net photosynthetic rates (Pmax) modeled by the four models were close to the measured values. Therefore, MRHM was superior to other three models in describing the photosynthetic response curve, the accurate values were that the quantum efficiency (α), maximum net photosynthetic rate (Pmax), light saturation point (LSP), light compensation point (LCP) and respiration rate (Rd) were 0.06, 6.06 μmol·m-2s-1, 802.68 μmol·m-2s-1, 10.76 μmol·m-2s-1 and 0.60 μmol·m-2s-1. Moreover, the photosynthetic response parameters values among different layers were also significant. Our findings have critical implications for parameter calibration of photosynthetic models and thus robust prediction of photosynthetic response in forests.


Introduction
As the largest carbon flux in global carbon (C) cycling, photosynthesis can assimilate CO 2 from the atmosphere and thus dedicating to climate change mitigation. It plays a crucial role in the material cycle and energy flow of forest ecosystems [1][2][3]. In addition to the stage of leaf development and genetic constitution of plant, photosynthesis is also strongly affected by surrounding environmental conditions (e.g., light, leaf, CO 2 concentration, humidity and temperature etc.), during which intensity of light and its availability particularly determine the amount of C assimilated by photosynthesis [4][5][6][7]. For the trees, the canopy is the most direct part for photosynthesis to response to incoming solar irradiance. Therefore, better understanding the mechanism of crown leaf photosynthesis response to light availability is thus critical for maintaining forest productivity and management, in particular for dynamic simulation growth models and in parameterization of crown photosynthesis.
Light response curves (Pn-PAR curves) describe the relationship between net photosynthetic rate (P n ) and photosynthetically active radiation (PAR), and provide information about the photosynthetic efficiency of plants (e.g. quantum yield, the maximum photosynthetic capacity, light compensation point and leaf radiation use efficiency of leaves) [8][9][10]. The simulation of Pn-PAR curves are becoming increasingly important to study the photosynthetic response process of plants to the environment, and analyze the primary productivity of vegetation and forests [1,[11][12][13]. A series of photo-physiological core parameters, such as maximum net photosynthetic rate (P max ), apparent quantum yield (AQY), light-saturation point (LSP), light-compensation point (LCP), and dark respiration rate (R d ), can be used to assess the canopy photosynthetic rate and capacity of plants in different growth stage. To date, in order to investigate the response of net photosynthetic rate (P n ) to light intensity of different plants, many models, including the rectangular hyperbola model (RHM) [14,15], the nonrectangular hyperbola model (NRHM) [16,17], the exponential model (EM) [18,19], and the modified rectangular hyperbola model (MRHM) [20], have been widely applied in modeling the photosynthetic light-response curve (P n -PAR curve) [1,12]. However, RHM, NRHM, and EM are very complex, some photo-and biochemical parameters (such as P max and LSP) are subject to environmental conditions and cannot be calculated directly using these models when light intensity are above zero [21][22][23][24], and the fitted values of photosynthetic parameters were significantly different from the measured ones [20,25]. In the contrary, owing to the addition of two adjusting factors (β and γ) into this model, which made the model highly advantageous in fitting the photo-inhibition and light saturation stages [20,26], the MRHM can directly produce P max and LSP, and overcome the limitation of above three models, the accuracy were higher and the results were suitable for fitting P n -PAR curve and photosynthetic parameters under various environmental conditions [20,24,26,27], it has been successfully applied in simulating light-response curves of many plants, such as Keteleeria calcarea [28], Pinu stabulaeformis Carr. [29], Pinus koraiensis [30], Betula utilis [31].
Larix principis-rupprechtii Mayr (Larch)., one of the main species of the total area of all plantations in Northern China, plays an important role in wood production, biodiversity protection, and forest ecological construction, due to its advantages of fast growth, strong adaptability, and high economic value. To the best of our knowledge, little attention has been paid to the application of a variety of dynamic crown photosynthetic light-response models in Larch, and the fitting effect and differences of light responses by these models remains unclear. Therefore, the determinant coefficients (R 2 ), mean square error (MSE), and Akaike information criterion (AIC) were used to evaluated the performance of four types of light-response models(such as RHM, NRHM, EM, and MRHM) in 16-years-old Larch. Planation. The objectives of the study were to select an optimal P n -PAR curve model for fitting the P n -PAR curves of Larch, and to explore the relationships between the parameters of the optimal P n -PAR curve model and leaf vertical positions. The results are helpful to further explore the spatial heterogeneity of carbon sequestration capacity of Larch needles in canopy, and provide a basis for accurately estimating photosynthetic physiological characteristics and the productivity of its plantation.

Ethics statement
Conflicts of interest. The authors declare no conflict of interest. Ethical approval. The authors declare that this article does not contain any research with humans or animal subjects.

Site description and sample tree selection
The experiments were conducted in the field at the the scientific research base of the State Forestry and Grassland Bureau established by Hebei Agricultural University, and the practice Base for postgraduate training of Forestry Master's Degree in Hebei Agricultural University. which is located in Saihanba Forest Farm of Weichang County of Hebei Province in the northern China (Fig 1, Table 1). The farm was mainly composed with Larixprincipis-rupprechtii, Populusdavidiana, Betula platyphylla, and Quercus mongolica. The total forest coverage is approximately 82.6%, including 72.6% plantation.
Three sample plots (20 m width × 30 m length) were set up within 16-year-old Larch plantations of the same habitat. The diameter at breast height (DBH, cm) and tree height (H, m) were measured for all trees with the D >5 cm in each plot, and the mean D (Dm) for three plots were calculated independently. Then, three sample trees, whose D values respectively was similar to Dm of the three plots, were selected to represent experimental materials. According to the previous studies, for trees, the upper limit of the P n -PAR curves was significantly different within different crown whorls in the vertical direction [32][33][34]. Thus, we divided the crowns of three sample trees respectively into three vertical layers with the trisection of crown

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Effects of photosynthetic models on the photosynthesis in young Larix principis-rupprechtii Mayr. plantation depth (the distance from the top of the tree to the base of its live crown, CD), and each layer was divided into two parts in horizontal direction (sunny and shaded) (Fig 2) [35].

Measurements of the light-response process
The light responses of photosynthesis were measured using a portable photosynthetic gas analysis system (LI-6400, LI-COR, Inc., Lincoln, Nebraska, USA) coupled with a standard red-blue light-emitting diode (LED) radiation source (85% red, emission peak at 655 nm + 15% blue, emission peak at 465 nm) (Li-6400-02B, LI-COR, Inc., Lincoln, NE, USA), photosynthetic active radiations (PAR) intensities were set at thirteen lever of 2000, 1500, 1200, 1000, 800, 600, 400, 200, 150, 100, 50, 25, and 0 μmol (photons) m -2 s -1 ). Before measuring, the instrument was preheated and calibrated each time, these sample needles were kept for 10-20 min at a CO 2 concentration of 380 μmol (photons) m -2 s -1 and a PAR value of 1,400 μmol (photons) m -2 s -1 in the leaf chamber, which reach a steady state around the needles. Then, the sample needles were allowed to equilibrate to 20˚C conditions for a minimum time of 2 min and a maximum of 3 min before the data were logged during the measurement of the P n -PAR curves. The measurements (experiments) were conducted from 8:30 a.m. to 16:30 p.m. on a cloud-free periods day, with an air temperature at 24-26˚C and a relative humidity at 30-40%, the fixed exposure time for each level of PAR was set at 2-3 min, these methods are described previously [32,33]. The data for the P n -PAR curves were measured once every half month during the growing season (approximately from 15th June to 10th August) in 2018 and 2019

Photosynthesis-light response curve-fitting model and its parameters
The rectangular hyperbola model, the nonrectangular hyperbola model, the exponential model, and the modified rectangular hyperbola model were used to fit the light-response curves and to estimate photosynthetic parameters. The environmental conditions (CO 2 concentration, temperature and humidity) are given. The expressions and parameters of the four models were as follows: The rectangular hyperbola model (RHM) [15,36] was represented to the following form: Where: P n represents the net photosynthetic rate (μmol (photon) m -2 �s -1 ), a represents the initial quantum efficiency at low light intensities [22], P max represents the maximum net photosynthetic rate (μmol (photon) m -2 �s -1 ), R d represents the respiration rate in the dark (μmol (photon) m -2 �s -1 ), and I represents the PAR. α, P max , and R d are the main parameters to used describe the characteristics of the P n -PAR. Α is the initial slope of the P n -PAR when PAR is 0--200 μmol�m -2 �s -1 , which indicates the plants' light use efficiency [37][38][39].
The P max and LSP cannot be calculated directly using RHM, therefore, P max was estimated and calculated by using the nonlinear least squares method under high light intensity [36,40,41], LSP could be expressed respectively as: where: A (AQE) represents apparent quantum efficiency; LSP represents the light saturation point (μmol (photon) m -2 �s -1 ); R d is as described above. A was obtained by fitting the light response data which PAR is equal to or less than 200 μmol (photon) m -2 s -1 ) Where: LCP represents the light compensation point (μmol (photon) m -2 �s -1 ); LSP, A, P max , R d are as described above.
The nonrectangular hyperbola model (NRHM) [42] was represented to the following form: ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi where: P n indicates the net photosynthetic rate (μmol (photon) m -2 �s -1 ); θ (0 < θ < 1) indicates the convexity (curvilinear angle) (dimensionless); and α, I, P max, and R d are as described above.
The LSP was calculated by. Formula 3.
The LCP can be obtained by: Where: LCP represents the light compensation point (μmol (photon) m -2 �s -1 ); k, α, P max , R d are as described above.
The expressions for the exponential model (EM) [18] was represented to the following form: Where: e indicates the base of natural logarithm, α, I, P max , P n , and R d are as described above.
The LSP was calculated by. Formula 3, The LCP was calculated by. Formula 8.
The P max , LCP and LSP were expressed on the modified rectangular hyperbola model in Eqs 10, 11, and 12, respectively: LSP ¼ ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ffi ðb þ gÞ=b where LCP, LSP, α, β, γ, and R d are as described above.

Model assessment and validation
The fitting quality of the different models were assessed by mean square errors (MSE), determinants coefficients (R 2 ), 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. 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.
Determinants coefficients (R 2 ) represents the fitting degree of net photosynthetic rate and light intensity.
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 the equations above represented 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 [43].

Statistical analyses
The measured light-response data are collated and analyzed and expressed as mean ± standard deviation (SD) of three replicates. Statistical analyses of the data were performed using twoway analysis of variance (ANOVA) by GraphPad Prism 8.0 or the SPSS software (version 18.0) and Duncan tests. Parameter values which are significantly different (p<0.05) are indicated by different letters.

Pn in response to PAR
To describe the relationships between P n and PAR, photosynthetic light-response curves (P n -PARs) of Larch was studied. The results showed that light response curves (P n -PAR) fitted by NRHM, EM and MRHM from different layers were of similar tendency, while RHM were difficult to implement because the curves increased gradually with no extreme. Taking the middle layer as an example, the P n -PAR curves could be divided into three stages, the net photosynthetic rate (P n ) increased linearly (rapidly) with the augments of photosynthetic available radiation (PAR) in the first stage, where PAR < 200 μmol (photon) m -2 s -1 , then increased nonlinearly up to the maximum P n, in the second stage, the maximum P n is 6.00 μmol (photons) m -2 s -1 when PAR is 600 μmol (photons) m -2 s -1 , and decreased gradually with increasing PAR in the third stage (Fig 3). At the same PAR, needles under upper layer had a higher P n than those of the middle and lower leaves, and P n values under different leaf layer could be ranked as: Upper layer >Middle layer >lower layer.

Fitting and comparison of photosynthesis-light response curves
The fitting results showed the fitting P n values of the four models were very close to the measured values actually when the PAR was low (PAR <100 μmol (photons) m -2 s -1 ), the gap increased with an increasing PAR, and the difference in P n was more remarkable. The P n value simulated by NRHM, MRHM, and EM was slightly greater than measured value when PAR values are 200-2000 μmol (photons) m -2 s -1 , and the simulated pattern of P n -PAR curves showed similar trend, the light-response curve was best described by three models, especially when light intensity (PAR) is beyond P max (Fig 3). However, the P n value simulated by the RHM increased with the increasing PAR, the fitting error was too large to use directly ( Fig  3A1-3A3). In addition, the mean value of R 2 (range from 0.9748 to 0.9930) of the MRHM model was the highest among the four models, and MSE value (MSE range from 0.0646 to 0.0866 μmol (photons) m -2 s -1 ) and AIC value (range from -45.7887 to -34.8321 respective) of the MRHM were significantly smaller than those of other three models in upper, middle and lower layer respectively (Table 2). In addition, MRHM model was superior to other three models in south and north orientation.

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Effects of photosynthetic models on the photosynthesis in young Larix principis-rupprechtii Mayr. plantation

Fitting analysis of the photosynthetic parameters based on the models
The Fitting value of photosynthetic parameters were used to estimate the fitting quality of the model, its accuracy and rationality are affected by the model and layer [16,19,20,27]. Therefore, it is very important to study the fitting effect of different models, different layers and different orientations on light response parameter of needle leaves. The results showed P max calculated from the RHM, NRHM and EM were closer to the measured value in the up layer, and was slightly greater than the measured values in the middle and lower layer. The light saturation point (LSP) obtained by above three models were much lower than the measured values in the up, middle and lower layer respectively. The fitted values of P max and LSP by MRHM were close to the measured values in each layer respectively. In addition, the LSP values were significant difference between MRHM and the other three models, while the P max and LCP values were no significant difference, the a values of each model, which are the quantum efficiency at low irradiance, ranged from 0 to 0.125 [44], R d value was closer among four models (Fig 4).
In the different layers, some simulated values of P n -PAR response parameters revealed somewhat different, there was no significant difference for LSP LCP and R d in upper and middle layers, but was significant difference in lower layers, the values of α and P max were significant for in each layer. In addition, the layer is one of the main factors of affecting the light

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Effects of photosynthetic models on the photosynthesis in young Larix principis-rupprechtii Mayr. plantation response parameters (e.g. a, P max , LCP) (Fig 4, S1 Table). Some simulated values of P n -PAR response parameters calculated by MRHM was more accurate than those obtained from other three models (Fig 5, S1 Table). The photosynthetic parameters which were fitted by four models showed no significant difference between north and south direction (Fig 6, S3 Table).

Discussion
The light response curve (P n -PAR curve) is an important tool for describing the response of the P n to PAR, identifying a series of photosynthetic parameters and evaluating the photosynthetic efficiency of plants [11,45,46]. Therefore, constructing of P n -PAR curve and choosing the appropriate model are helpful to simulate canopy photosynthesis and predict plant productivity [47,48]. In the study, the net photosynthetic rate increased initially and then decreased gradually with the increase of PAR (Fig 3), which was consistent with the study of leaf P n -PAR curves of some plants in different growth stages [49,50]. The results indicated light energy absorbed by plants exceeded the needs of plants, the absorption of the excessive light energy would restricted photosynthetic mechanism and series of enzymatic reaction rates in the chloroplasts and result in photo-inhibition of Larch. The upper limit value of P n -PAR curve maintained the state of upper layer >middle layer > lower layer during the whole growth period, which was also proved in other Larch species [32], indicated that the metabolic capacity was

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Effects of photosynthetic models on the photosynthesis in young Larix principis-rupprechtii Mayr. plantation closely related to the light environment [34]. The differences of the P n -PAR curve among different canopies might be associated with leaf characteristics, solar elevation angle, higher chlorophyll a/b ratios, relative depth into crown (RDINC), etc [32,51]. Additional, The photosynthetic parameters which were fitted by four models showed no significant difference between north and south direction, which was consistent with that of previous study [52].
The fitting of light-response model is an important method to describe the response mechanism of P n to PAR and evaluate the photosynthetic efficiency [45]. Among four models, the P n value simulated by the RHM consistently increased with the increasing PAR with no stable or declined trend (Fig 3A1-3A3), indicated that RHM was more suitable for fitting consistently increased type of P n -PAR curves. This result agreed with the previous study [53]. Compared to the other three models, the determinants coefficients (R 2 ) value of the MRHM was the highest, and mean square errors (MSE) value and Akaike information criterion (AIC) value were the lowest ( Table 2), indicated that MRHM performed better than other three models [23]. In addition, some fitted values of photosynthetic parameters (e.g P max and LSP) were close to the measured values (Fig 4, S1 Table), Ye [20] has proved that the unique structure of MRHM made it more flexible in simulating different trends of P n -PAR curves.
Compared with data fitted (Fig 3) and error analysis (Table 2) on the P n -PAR curves of the needles at different leaf canopy, there was no significant difference for LSP, LCP and R d in upper and middle layers, but was significant difference in lower layers. However, the values of a and P max were significant in each layer. The P n in the upper canopy was significantly higher than those in the middle and lower canopy, which was not consistent with that of previous study [53]. The different may be due to the comprehensive effects of genetic diversity, different producing areas and environmental factors of trees [54]. It can be seen that layer was one of the main factors of affecting the light response parameters (e.g. a, P max , LCP) (Fig 4, S1 Table).
Based on the above discussion, we considered that the light response process and photosynthetic parameter (P max , LSP, LCP, and R d ) fitting by the MRHM models was more reliable (S2 Table). and MRHM could fit well the P n -PAR curves of Larch (Fig 4, S2 Table). In addition, the P n -PAR of the middle leaf layer can better reflect the changes in leaf layer photosynthetic parameters. However, the results, obtained in the vigorous growth period of Larix principis rupprechtii from June to August, are of spatial and temporal limitation in Saihanba, the further studies are needed to better understand the mechanisms of the photosynthetic physiological ecology of plants to the environment.

Conclusion
This study describe canopy photosynthesis for Larix principis rupprechtii plantation, the P n -PAR curves and photosynthetic response parameters were measured under different layer of three planted L. principis-rupprechtii trees by different models during the growing season. The results showed that the fitting effect of MRHM model was superior to those of other three models and it could analyze the light-response data more accurately, the selection of the middle layer of the plant is the best when measuring the photosynthetic performance of the whole tree in combining with the analysis of fitting precision (Fig 3), the accurate values were as follows: α, P max , LSP, LCP and R d were 0.06, 6.08 μmol�m -2 s -1 , 931.08 μmol�m -2 s -1 , 11.45 μmol�m -2 s -1 and 0.61 μmol�m -2 s -1 , respectively. This study not only helps to further explore the spatial heterogeneity of carbon sequestration capacity of Larix principis rupprechtii leaves in canopy, but also provides a scientific and effective guidance for accurately estimating the productivity of Larix principis rupprechtii plantation.
Supporting information S1 Table. P n -PAR response parameters of leaves in different layers of Larch. Black letter 'a' indicates significant differences between models, red letter 'a' indicates significant differences among different layers. (DOC) S2