Non-rectangular Hyperbola Model Research Articles

Simulating short-term light responses of photosynthesis and water use efficiency in sweet sorghum under varying temperature and CO2 conditions.

Climate change, characterized by rising atmospheric CO2 levels and temperatures, poses significant challenges to global crop production. Sweet sorghum, a prominent C4 cereal extensively grown in arid areas, emerges as a promising candidate for sustainable bioenergy production. This study investigated the responses of photosynthesis and leaf-scale water use efficiency (WUE) to varying light intensity (I) in sweet sorghum under different temperature and CO2 conditions. Comparative analyses were conducted between the A n-I, g s-I, T r-I, WUEi-I, and WUEinst-I models proposed by Ye etal. and the widely utilized the non-rectangular hyperbolic (NRH) model for fitting light response curves. The Ye's models effectively replicated the light response curves of sweet sorghum, accurately capturing the diminishing intrinsic WUE (WUEi) and instantaneous WUE (WUEinst) trends with increasing I. The fitted maximum values of A n, g s, T r, WUEi, and WUEinst and their saturation light intensities closely matched observations, unlike the NRH model. Despite the NRH model demonstrating high R 2 values for A n-I, g s-I, and T r-I modelling, it returned the maximum values significantly deviating from observed values and failed to generate saturation light intensities. It also inadequately represented WUE responses to I, overestimating WUE. Across different leaf temperatures, A n, g s, and T r of sweet sorghum displayed comparable light response patterns. Elevated temperatures increased maximum A n, g s, and T r but consistently declined maximum WUEi and WUEinst. However, WUEinst declined more sharply due to the disproportionate transpiration increase over carbon assimilation. Critically, sweet sorghum A n saturated at current atmospheric CO2 levels, with no significant gains under 550 μmol mol-1. Instead, stomatal closure enhanced WUE under elevated CO2 by coordinated g s and T r reductions rather than improved carbon assimilation. Nonetheless, this response diminished under simultaneously high temperature, suggesting intricate interplay between CO2 and temperature in modulating plant responses. These findings provide valuable insights into photosynthetic dynamics of sweet sorghum, aiding predictions of yield and optimization of cultivation practices. Moreover, our methodology serves as a valuable reference for evaluating leaf photosynthesis and WUE dynamics in diverse plant species.

Addressing the long-standing limitations of double exponential and non-rectangular hyperbolic models in quantifying light-response of electron transport rates in different photosynthetic organisms under various conditions.

The models used to describe the light response of electron transport rate in photosynthesis play a crucial role in determining two key parameters i.e., the maximum electron transport rate (J max) and the saturation light intensity (I sat). However, not all models accurately fit J-I curves, and determine the values of J max and I sat. Here, three models, namely the double exponential (DE) model, the non-rectangular hyperbolic (NRH) model, and a mechanistic model developed by one of the coauthors (Z-P Ye) and his coworkers (referred to as the mechanistic model), were compared in terms of their ability to fit J-I curves and estimate J max and I sat. Here, we apply these three models to a series of previously collected Chl a fluorescence data from seven photosynthetic organisms, grown under different conditions. Our results show that the mechanistic model performed well in describing the J-I curves, regardless of whether photoinhibition/dynamic down-regulation of photosystem II (PSII) occurs. Moreover, both J max and I sat estimated by this model are in very good agreement with the measured data. On the contrary, although the DE model simulates quite well the J-I curve for the species studied, it significantly overestimates both the J max of Amaranthus hypochondriacus and the I sat of Microcystis aeruginosa grown under NH4 +-N supply. More importantly, the light intensity required to achieve the potential maximum of J (J s) estimated by this model exceeds the unexpected high value of 105 μmol photons m-2 s-1 for Triticum aestivum and A. hypochondriacus. The NRH model fails to characterize the J-I curves with dynamic down-regulation/photoinhibition for Abies alba, Oryza sativa and M. aeruginosa. In addition, this model also significantly overestimates the values of J max for T. aestivum at 21% O2 and A. hypochondriacus grown under normal condition, and significantly underestimates the values of J max for M. aeruginosa grown under NO3 -N supply. Our study provides evidence that the 'mechanistic model' is much more suitable than both the DE and NRH models in fitting the J-I curves and in estimating the photosynthetic parameters. This is a powerful tool for studying light harvesting properties and the dynamic down-regulation of PSII/photoinhibition.

Spring irrigation with magnetized water affects soil water-salt distribution, emergence, growth, and photosynthetic characteristics of cotton seedlings in Southern Xinjiang, China

BackgroundSpring irrigation with freshwater is widely used to reduce soil salinity and increase the soil water content in arid areas. However, this approach requires a huge amount of freshwater, which is problematic given limited freshwater resources. Utilizing brackish water for spring irrigation in combination with magnetized water technology may be a promising alternative strategy.ResultsThe objective of this study was to evaluate the effects of four spring irrigation methods (freshwater spring irrigation (FS), magnetized freshwater spring irrigation (MFS), brackish water spring irrigation (BS), and magnetized brackish water spring irrigation (MBS)) on soil water and salt distribution, emergence, growth, and photosynthetic characteristics of cotton seedlings. The results showed that for both freshwater and brackish water, magnetized water irrigation can increase the soil water content for improved desalination effect of irrigation water. Additionally, spring irrigation with magnetized water promoted cotton emergence and seedling growth. Compared with FS treatment, cotton finial emergence rate, emergence index, vigor index, plant height, stem diameter, and leaf area index of MFS treatment increased by 6.25, 7.19, 12.98, 15.60, 8.91, and 20.57%, respectively. Compared with BS treatment, cotton finial emergence rate, emergence index, vigor index, plant height, stem diameter, and leaf area index of MBS treatment increased by 27.78, 39.83, 74.79, 26.40, 14.01, and 57.22%, respectively. Interestingly, we found that spring irrigation with magnetized water can increase the chlorophyll content and net photosynthetic rate of cotton seedlings. The rectangular hyperbolic model (RHM), non-rectangular hyperbolic model (NRHM), exponential model (EM), and modified rectangular hyperbolic model (MRHM) were used to fit and compare the cotton light response curve, and MRHM was determined to be the optimal model to fit the data. This model was used to calculate the photosynthetic parameters of cotton. Compared with FS treatment, the net photosynthetic rate (Pnmax), dark respiration rate (Rd), light compensation point (Ic), light saturation point (Isat), and the range of available light intensity (ΔI) of MFS were increased by 5.18, 3.41, 3.18, 2.29 and 2.19%, respectively. Compared with BS treatment, the Pnmax, Rd, Ic, Isat and ΔI of MBS were increased by 26.44, 29.48, 30.05, 5.13, and 2.27%, respectively.ConclusionThe results show that spring irrigation with magnetized brackish water may be a feasible method to reduce soil salt and increase soil water content when freshwater resources are insufficient.

Forest Management Model based on Photosynthesis Model and Market Simulation

In order to mitigate the impact of climate change, it is necessary to make rational use of forest resources for carbon cycle. Firstly, based on the actual data of tomato single leaf light and rate, this paper establishes rectangular hyperbolic model, exponential model and non-rectangular hyperbolic model, and photosynthesis model based on light and effective radiation, temperature and carbon dioxide concentration of three environmental factors. Finally, it is analyzed through simulation experiments, The improved rectangular hyperbolic model with the best simulation effect is determined. The model based on photosynthesis designed in this paper is helpful to the decision-making of forest management.

Photosynthesis: Theory and Experiment

The approach we developed earlier to describe the chains of conjugate enzymatic reactions of the photosynthesis process for the first time made it possible to propose a strict mathematical model of non-rectangular hyperbola, which describes the dependence of the speed of photosynthesis on the intensity of light (I), the concentration of CO2 and the interaction of these two factors. The fundamental parameters of this model are light (IK) and carbon dioxide (CK) substrate constants, as well as hyperbola curvature (), conjugation parameters (rIP and rCP) and maximum photosynthesis rate (Pm). Special straightening coordinates are proposed, in which the entire hyperbole family has the form of a straight line. The main parameters can only be found when constructing experimental data in straightening coordinates. The proposed non-rectangular hyperbola model is applicable both for describing the process of photosynthesis in seaweed and higher plants, and for absorbing vitamin B12 by algae, and the dependence of the rate of food consumption by zooplankton and fish.

Phytoplankton Primary Productionin the Coastal Water surrounding Shantar Archipelago

Our studies were carried out in July 2016, in the Uda Bay and the Academy Bay (including the Ulban Bay and Nikolay Bay). The primary production (PP) of phytoplankton in the photic zone was calculated from the thickness of the euphotic zone, as well as by the concentration of chlorophyll а, and the assimilation numbers of phytoplankton. We used for calculations a modified nonrectangular hyperbola model, for photosynthetic light-response curves of phytoplankton. The formation of PP is a function of the supply of nutrients to the photic zone from the underlying waters by intense tidal currents under conditions of weak stratification. The high concentrations of humus substances in Uda Bay limited the growth of phytoplankton. The values of integra-ted PP varied between Uda Bay to Academy Bay from 250–1000 to 1069–4268 mgC m–2 day–1.

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

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.

Comparison of several models for estimating gross primary production of drip-irrigated maize in arid regions

Gross primary productivity (GPP) is the total amount of carbon absorbed by green plants through photosynthesis. As an important part of the global carbon cycle, photosynthesis is the process of converting solar energy into chemical energy. Therefore, accurate estimation of GPP is important for understanding the regional and global carbon flux variations. Based on the flux data of spring maize under drip irrigation in northwest China during 2014∼2018, this study compared and evaluated the simulation accuracy of several models for estimating GPP under different growing seasons and environmental conditions, and optimized the rectangular hyperbolic (RH) model. The results showed that none of these models consistently had the highest simulation accuracy over a 5-year period. The total GPP simulated by the light response photosynthetic models was closer to the observed value than the light use efficiency (LUE) model and stomatal conductance models. Under different growing stages and environmental conditions, the simulation accuracy of different models was different: (1) RH model had the best simulation effect when the maize was completely covered (i.e. LAI>2), but stomatal conductance-photosynthesis-transpiration coupling (SMPT-SB) model had the best simulation effect in the early growing stage; (2) when the soil water content was high, RH model has the best simulation effect. On the contrary, the simulation effect of the non-rectangular hyperbolic (N-RH) model was slightly better than other models; (3) the LUE model has a strong dependence on light conditions. Therefore, when Rn≤100, all the other 8 models except the LUE model could well simulate GPP. When Rn>100, the RH model had the best simulation effect; (4) when VPD≤1.5, the simulation accuracy of RH model was the highest; when VPD>1.5, SMPT-SB had the best simulation effect. To obtain parameters in the models more quickly and accurately, we improved the RH model by establishing the relationship between maximum photosynthetic rate (Pmax) and leaf area index (LAI), initial quantum efficiency (α) and LAI, and obtained the RH-LAI model. Compared with the RH model, the simulation accuracy of the improved RH-LAI model was improved. And the reliability of the RH-LAI model was verified in other sites. Therefore, the research results showed that in the regions with fewer observation indexes, we can use the RH-LAI model with a simple structure and convenient calculation to calculate the daily GPP by integrating it on the time scale.

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.

Quantifying light response of photosynthesis: addressing the long-standing limitations of non-rectangular hyperbolic model

Light intensity (I) fluctuates rapidly and is the most important environmental factor affecting photosynthesis. Accurate characterization of light-response curve of leaf-scale photosynthesis (PN-I curve) is fundamental for understanding PN-I relations at the whole-plant and ecosystem scales. A robust PN-I model should be accurate in reproducing PN-I curves over light-limited, light-saturated, and photoinhibitory I levels, and ideally returning key quantitative traits defining the curves, including initial slope of increase (α), dark respiration rate (RD), the maximum net photosynthetic rate (PNmax), and the corresponding saturation intensity (Isat). We need to improve a model reproduction of (1) PN-I responses over low I levels and (2) the widely reported decline of PN at photoinhibitory I levels. Our observation-modelling comparison, shown by the widely used non-rectangular hyperbolic model, led to (1) underestimation of RD, (2) overestimation of PNmax, and (3) failure in reproducing the photoinhibitory response when I surpassed the cultivar-specific Isat. In contrast, our model addressed the above limitations extremely well. The results highlighted the accuracy and robustness of our model, especially in (1) returning key traits defining the curve and (2) reproducing the curve over both low [i.e., 0-50 μmol(photon) m-2 s-1] and photoinhibitory I levels (i.e., beyond Isat).

Comparison of the Photosynthetic Capacity of Phragmites australis in Five Habitats in Saline‒Alkaline Wetlands.

Water shortages have an important impact on the photosynthetic capacity of Phragmites australis. However, this impact has not been adequately studied from the perspective of photosynthesis. An in-depth study of the photosynthetic process can help in better understanding the impact of water shortages on the photosynthetic capacity of P. australis, especially on the microscale. The aim of this study is to explore the photosynthetic adaptation strategies to environmental changes in saline‒alkaline wetlands. The light response curves and CO2 response curves of P. australis in five habitats (hygrophilous, xerophytic, psammophytic, abandoned farmland, paddy field drainage) in saline‒alkaline wetlands were measured at different stages of their life history, and we used a nonrectangular hyperbolic model to fit the data. It was concluded that P. australis utilized coping strategies that differed between the growing and breeding seasons. P. australis in abandoned farmland during the growing season had the highest apparent quantum efficiency (AQE) and photosynthetic utilization efficiency for weak light because of the dark environment. The dark respiration rate of P. australis in the drainage area of paddy fields was the lowest, and it had the highest values for photorespiration rate, maximum photosynthetic rate (Pmax), photosynthetic capacity (Pa), biomass, maximum carboxylation rate (Vcmax), and maximum electron transfer rate (Jmax). The light insensitivity of P. australis increased with the transition from growing to breeding season, and the dark respiration rate also showed a downward trend. Moreover, Vcmax and Jmax would decline when Pmax and Pa showed a declining trend, and vice versa. In other words, Vcmax and Jmax could explain changes in the photosynthetic capacity to some extent. These findings contribute to providing insights that Vcmax and Jmax can directly reflect the variation in photosynthetic capacity of P. australis under water shortages in saline‒alkaline wetlands and in other parts of world where there are problems with similarly harmful environmental conditions.

Modeling Light Response of Electron Transport Rate and Its Allocation for Ribulose Biphosphate Carboxylation and Oxygenation.

Accurately describing the light response curve of electron transport rate (J–I curve) and allocation of electron flow for ribulose biphosphate (RuBP) carboxylation (J C–I curve) and that for oxygenation (J O–I curve) is fundamental for modeling of light relations of electron flow at the whole-plant and ecosystem scales. The non-rectangular hyperbolic model (hereafter, NH model) has been widely used to characterize light response of net photosynthesis rate (A n; A n–I curve) and J–I curve. However, NH model has been reported to overestimate the maximum A n (A nmax) and the maximum J (J max), largely due to its asymptotic function. Meanwhile, few efforts have been delivered for describing J C–I and J O–I curves. The long-standing challenge on describing A n–I and J–I curves have been resolved by a recently developed A n–I and J–I models (hereafter, Ye model), which adopt a nonasymptotic function. To test whether Ye model can resolve the challenge of NH model in reproducing J–I, J C–I and J O–I curves over light-limited, light-saturated, and photoinhibitory I levels, we compared the performances of Ye model and NH model against measurements on two C3 crops (Triticum aestivum L. and Glycine max L.) grown in field. The results showed that NH model significantly overestimated the A nmax and J max for both species, which can be accurately obtained by Ye model. Furthermore, NH model significantly overestimated the maximum electron flow for carboxylation (J C-max) but not the maximum electron flow for oxygenation (J O-max) for both species, disclosing the reason underlying the long-standing problem of NH model—overestimation of J max and A nmax.

Sugarcane leaf photosynthetic light responses and their difference between varieties under high temperature stress

Leaf photosynthetic light response (PLR) of six sugarcane (Saccharum officinarum L.) varieties with a high sugar content was measured in the field. PLR curves were fitted by the rectangular hyperbola (RH) model, the nonrectangular hyperbola (NRH) model, and the Ye model, respectively. Photoinhibition occurred under warm and humid environment for all tested sugarcane varieties except for GT02-467 with the photosynthetic rate reduced significantly. The Ye model was the best for PLR curve fitting, especially when photoinhibition occurred. Nearly all PLR parameters estimated by the Ye model were better than the other two models. Some PLR parameters correlated with each other. A significant negative correlation was found between the photoinhibition coefficient and the photosaturation coefficient. The varieties with high light-use efficiency (e.g., YZ99-91 and YZ01-1413) are suitable for dense planting under warming climate, while the varieties with strong ability for dim light use (e.g., GT02-467 and MT69-421) would be appropriate for planting at a high density under warming and dimming climate in the future.

Photosynthetic CO<sub>2</sub> response to soil water and its simulation using different models in leaves of two species

CO2 concentrations and soil moisture conditions are important factors in photosynthesis of trees. This study investigated the photosynthetic CO2 responses in the leaves of Prunus sibirica L. and Pinus tabulaeformis Carr. under eight soil water conditions in a semiarid loess hilly region. CO2-response curves and physiological parameters were fitted using a rectangular hyperbola model, nonrectangular hyperbola model, exponential equation, and modified rectangular hyperbola model. Results revealed the relative soil water content (RWCs) for P. sibirica required to maintain higher photosynthetic rate ranging from 46.5 to 81.6%, and that for P. tabulaeformis ranging from 35.4 to 84.5%. When RWCs exceeded these ranges, the net photosynthetic rate of both species decreased. CO2-response curves and three parameters, carboxylation efficiency, CO2-compensation point, and photorespiration rate, were well fitted by the four models when RWCs was appropriate for P. sibirica and P. tabulaeformis. When RWCs exceeded the optimal ranges, only the modified rectangular hyperbola model could precisely simulate the CO2-response curves and photosynthetic parameters of both species.

Leaf photosynthetic light response of summer maize: comparison of models and analysis of parameters

An experiment was performed in order to study the applicability of light-response models for summer maize (Zea mays L.) by using rectangular hyperbola model, nonrectangular hyperbola model, exponential model, binomial regression model, and modified rectangular hyperbola model (Ye model), respectively. Our results showed that the fitted effect of Ye model was best and photosynthetic parameters were closest to the observation. The photoinhibition coefficient was significantly negatively correlated with the light-saturation point (Is), the light-saturation coefficient (γ), and maximum net photosynthetic rate at light-saturation point (PNmax), respectively. PNmax and Is, apparent quantum yield, and γ performed significantly positive relationship, respectively. When the soil volumetric water content varied from 13 to 21%, PNmax had significant positive correlation with the soil water content and stomatal conductance. Under water and temperature stress, the net photosynthetic rate decreased and photoinhibition occurred, which could be well simulated by the Ye model. It seems that Ye model would have more applications, especially for the regions with strong solar radiation.

Photosynthetic model for citrus cultivar Huangguogan

Grafting is an effective measure to improve the photosynthetic rate of citrus. The light responses of photosynthesis in leaves of two-year old grafted Huangguogan (citrus cultivar Huangguogan), Huanggougan / Trifoliate (HG/PT), Huanggougan / Tangerine (HG/CR), and Huanggougan / Ziyang Xiangcheng (HG/CJ) were studied using the LI-COR 6400 portable photosynthesis system. Light-response curves and photosynthetic parameters were analyzed and fitted using the rectangular hyperbola model (RHM), the exponential model (EM), the non rectangular hyperbola model (NRHM), and the modified rectangular hyperbola model (MRHM). The results showed that: (1) Grafting can change the photosynthetic characteristics of Huangguogan, and the value of photosynthesis rate of HG/CJ is the greatest; (2) The light-response curves of net photosynthetic rate (PN), the light compensation point (LCP), and the dark respiration rate (RD) were well fitted using the above four models. The modified rectangular hyperbola was the best model in fitting the data; the nonrectangular hyperbola model was the second, and the rectangular hyperbola model was the poorest one.

Light-response curve of photosynthesis and model fitting in leavesof Mangifera indica under different soil water conditions

A pot experiment was performed to study the light-response curve of photosynthesis (PN-PAR curve) of Mangifera indica and the applicability of light-response models under different soil water conditions. The experimental data were fitted and analyzed using the rectangular hyperbola model, the nonrectangular hyperbola model, the exponential model, the modified rectangular hyperbola model, and the kinetic model. The results showed that the optimal range of relative soil water content (RSWC) for the normal photosynthesis of M. indica was 45.1-77.3%. The modified rectangular hyperbola model could well fit the PN-PAR curves and photosynthetic parameters under wide range of soil water conditions (RSWC 23.3-77.3%). The rectangular hyperbola model, the nonrectangular hyperbola model, the exponential model, and the kinetic model could only be used to fit the PN-PAR curves of M. indica under mild and moderate drought stress (RSWC 45.1-77.3%).

[Light response process and simulation of Dendrocalamopsis oldhami in the process of gradual water loss.]

The photosynthesis response of the leaves of 2-year-old potted Dendrocalamopsis oldhami seedlings under continuous and multistage soil moisture was measured and analyzed by using a porta-ble photosynthetic system (Li-6400) during the natural water consumption process from artificial watering to saturated soil water. The results showed that there was less obvious photoinhibition in leaves of D. oldhami grown in the region where the relative soil water content (SRWC) was from 53.5% to 95.6%. There was a higher net photosynthetic rate in relative water deficit environment with the relative soil water content from 53.5% to 69.6%. When SRWC was below 33.6%, there was a significant photoinhibition. When the relative soil water changed, the Pn max value simulated by rectangular hyperbola model was much higher than measured value. The simulated light saturation point (LSP) value fitted by the rectangular hyperbola model, the non-rectangular hyperbola model and the exponential model was much lower than the measured value, and the simulation of the light-response curve under extreme water shortage conditions had larger differences between the fitted values and the observed data. Both the stomatal limitation value (Ls) and water use efficiency (WUEinst) showed a similar response process as the relative soil water decreased. Both of them increased first and then decreased, with the maximum value appeared in the range of 53.5%≤SRWC≤69.6%. Such a result showed a similarity and representative with the Pn max of photosynthesis light-response processes under changing soil moisture. The optimal humidity management range of SRWC for normal photosynthesis in leaves of D. oldhami was from 53.5% to 69.6%. In addition, it had good adaptability to higher soil water content (69.6%≤SRWC≤95.6%). Rectangular hyperbola modified model could well simulate the light-response of photosynthesis under different soil water conditions (23.1%≤SRWC≤95.6%), while the other three models had their own limitations.

Modelling temporal variation of parameters used in two photosynthesis models: influence of fruit load and girdling on leaf photosynthesis in fruit-bearing branches of apple.

Several studies have found seasonal and temporal variability in leaf photosynthesis parameters in different crops. This variability depends upon the environment, the developmental stage of the plant and the presence or absence of sinks. Girdling involves the removal of the bark and phloem down to the youngest xylem all around the stem and prevents export of photoassimilates out of the stem. The load of developing fruits has often been reported to influence the individual net leaf photosynthesis rate (Pn) in tree crops. In this study, we chose (1) to model the key parameters of photosynthesis models of leaves (Pgmax, Rd, α and θ) as a function of time and using these two means (girdling and low fruit load) to alter the source-sink balance and (2) to compare three models: the rectangular and non-rectangular hyperbola model by Thornley, as well as the non-rectangular hyperbola model by Marshall and Biscoe. Six-year-old fruit-bearing branches of 10-year-old apple trees were used to study and model the seasonal variation of photosynthetic parameters in leaves of vegetative shoots, as a function of global fruit load (at the branch level), with or without girdling, during the growing season of 2015. Three treatments were applied: control, low load (LL) or low load + girdling (LLG). For each fruit-bearing branch, light-response curves of Pn for two leaves of vegetative shoots were measured at two different positions, proximal and distal. The model of Marshall and Biscoe was the most accurate for the simulation of Pn in fruit-bearing branches of apple trees with time (season) and the three treatments applied. The present study proposed a way to model the photosynthesis rate by temporal and environmental variables only. A proper validation of this model will be necessary to extend its utilization and appreciate its predictive capacity fully.

[Simulation on photosynthetic-CO2 response of Quercus variabilis and Robinia pseudoacacia in the southern foot of the Taihang Mountain, China.]

In this study, leaf photosynthetic CO2-response curves of Quercus variabilis and Robinia pseudoacacia were measured using a Li-6400XT photosynthetic measurement system in the southern foot of the Taihang Mountain, China. The rectangular hyperbola model (RH), nonrectangular hyperbola model (NRH) andYe model (YZP) were used to fit photosynthetic-CO2 response curves and compare photosynthetic parameters, including the maximum net photosynthetic rate (Amax), the initial carboxylation rate (η), light respiration rate (Rp), CO2 compensation point (CCP) and CO2 saturation point (CSP). Compared with the NRH and YZP models, Amax, η, Rp and CCP obtained by the RH model were higher, and were 59.8%, 128.6%, 133.4% and 19.8% higher than the measured values. The accuracy of the RH model was lower and its relative error was higher than that of the NRH and YZP models.Compared with the RH and YZP models, Amax fitted by the NRH model was higher, and was 11.1% higher than the measured value. η, Rp and CCP fitted by the NRH model were closer to the measured values. CO2 saturation phenomenon of photosynthesis could be simulated by the YZP model, and Amax and CSP were fitted well. Amax, Rp and CCP in the shaded leaves of Q. variabilis were 31.3%, 5.2% and 14.3% lower than those in the sunlit leaves. Amax, Rp and CCP in shaded leaves of R. pseudoacacia were 23.5%, 11.0% and 5.4% more than those in the sunlit leaves. η in the shaded leaves of Q. variabilis and R. pseudoacacia were 6.9% and 7.0% higher than those in the sunlit leaves, respectively. Rp and CCP of R. pseudoacacia leaves had linear relationships with temperature (T) and photosynthetic active radiation (PAR), and η had a significant relationship with stomatal conductance (gs). η of Q. variabilis leaves was linearly correlated with PAR and gs, and CCP was affected by T and relative humidity. Amax of Q. variabilis leaves had significant positive linear relationships with RH and gs.