构建一个普适性的植物叶片气孔导度(g_s)对CO₂浓度响应(g_s-C_a)的模型, 对定量研究植物叶片g_s对CO₂浓度的响应变化尤为必要。该研究运用便携式光合仪(LI-6400)测量了大豆(Glycine max)和小麦(Triticum aestivum)光合作用对CO₂的响应曲线(A_n-C_a), 在比较传统的Michaelis-Menten模型(M-M模型)和叶子飘构建的CO₂响应模型拟合大豆和小麦A_n-C_a效果的基础上, 构建了g_s-C_a响应新模型。然后用新构建的模型拟合大豆和小麦的g_s-C_a曲线, 并将拟合结果与传统模型的拟合结果, 以及与其对应的观测数据进行比较, 以判断所构建模型是否合理。结果显示: 叶子飘构建的A_n-C_a模型可较好地拟合大豆和小麦的A_n-C_a曲线, 确定系数(R²)均高达0.999。M-M模型拟合大豆和小麦的A_n-C_a曲线时的R²虽然也较高, 但在较高CO₂浓度时的拟合曲线偏离观测曲线。因此, 基于叶子飘的A_n-C_a模型构建g_s-C_a模型更为可行。新构建的g_s-C_a模型可较好地拟合大豆和小麦的g_s-C_a曲线, R²分别为0.995和0.994, 而且还可以直接给出最大气孔导度(g_s-max)、最小气孔导度(g_s-min), 以及与g_s-min相对应的CO₂浓度值(C_s-min)。拟合得到大豆和小麦的g_s-max分别为0.686和0.481 mol·m^-2·s^-1, 与其对应的观测值(分别为0.666和0.471 mol·m^-2·s^-1)之间均不存在显著差异; 同样, 拟合得到的大豆和小麦的g_s-min分别为0.271和0.297 mol·m^-2·s^-1, 与其对应的观测值(分别为0.279和0.293 mol·m^-2·s^-1)之间也均不存在显著差异; 此外, 新构建的g_s-C_a模型给出大豆和小麦的C_s-min值分别为741.45和1 112.43 μmol·mol ^-1, 与其对应的观测值(732.78和1 200.34 μmol·mol ^-1)也不存在显著差异。由此可见, 该研究新构建的g_s-C_a模型可作为定量研究植物叶片气孔导度对CO₂浓度变化的有效数学工具。

Aims To quantify the responses of stomatal conductance (g_s) to CO₂ concentration (g_s-C_a) under current and future climate conditions, it is necessary to build a generally applicable model suitable for simulating this process at plant leaf levels.

Methods The response curves (A_n-C_a) of photosynthesis of soybean (Glycine max) and wheat (Triticum aestivum) to CO₂ were fitted using data collected from a portable photosynthetic apparatus (LI-6400). Based on the comparison between the traditional Michaelis-Menten model (M-M model) and the CO₂ response model developed by Ye, a new g_s-C_a response model was proposed. Then, the measured g_s-C_a curves of soybean and wheat were fitted with the new model. The model results were compared with those of the traditional model and the corresponding observation data to judge the rationality of the model.

Important findings The A_n-C_a model developed by Ye could fit well the A_n-C_a curve of soybean and wheat, and the coefficient of determination (R²) is as high as 0.999. Although the R ² values of M-M model fitting the A_n-C_a curves of soybean and wheat were also high, the fitting curves deviated from the observation at higher CO₂ concentrations. Meanwhile, M-M model greatly overestimated the maximum photosynthetic rate and could not estimate the saturation CO₂ concentrations. Therefore, it was more feasible to developg_s-C_a model based on the A_n-C_a model of Ye. The new model of g_s-C_a could fit well the g_s-C_a curves of soybean and wheat, and the R ² were 0.995 and 0.994, respectively. Moreover, the maximum stomatal conductance (g_s-max), the minimum stomatal conductance (g_s-min) and the CO₂ concentration corresponding to g_s-min (C_s-min) could also be generated directly. g_s-max of soybean and wheat fitted by the g_s-C_a model was 0.686 and 0.481 mol·m^-2·s^-1, respectively, and there was no significant difference between the fitted values and corresponding observation values (0.666 and 0.471 mol·m^-2·s^-1, respectively). The new model of g_s-C_a could also obtain the minimum g_s (g_s-min) of soybean and wheat (0.271 and 0.297 mol·m^-2·s^-1, respectively), and there was also no significant difference between the fitted values and corresponding observation values (0.279 and 0.293 mol·m^-2·s^-1, respectively). In addition, the new model of g_s-C_a generated the C_s-min values of 741.45 and 1 112.43 μmol·mol ^-1for soybean and wheat, respectively, and also showed no significant difference from the observed value (732.78 and 1 200.34 μmol·mol^-1, respectively). Consequently, the g_s-C_a model developed in this paper can be used as an effective mathematical tool to quantitatively study the effect of stomatal conductance on CO₂ concentration.