Determination of the most effective design for the measurement of photosynthetic light-response curves for planted Larix olgensis trees

A photosynthetic light-response (PLR) curve is a mathematical description of a single biochemical process and has been widely applied in many eco-physiological models. To date, many PLR measurement designs have been suggested, although their differences have rarely been explored, and the most effective design has not been determined. In this study, we measured three types of PLR curves (High, Middle and Low) from planted Larix olgensis trees by setting 31 photosynthetically active radiation (PAR) gradients. More than 530 million designs with different combinations of PAR gradients from 5 to 30 measured points were conducted to fit each of the three types of PLR curves. The influence of different PLR measurement designs on the goodness of fit of the PLR curves and the accuracy of the estimated photosynthetic indicators were analysed, and the optimal design was determined. The results showed that the measurement designs with fewer PAR gradients generally resulted in worse predicted accuracy for the photosynthetic indicators. However, the accuracy increased and remained stable when more than ten measurement points were used for the PAR gradients. The mean percent error (M%E) of the estimated maximum net photosynthetic rate (P(max)) and dark respiratory rate (R(d)) for the designs with less than ten measurement points were, on average, 16.4 times and 20.1 times greater than those for the designs with more than ten measurement points. For a single tree, a unique PLR curve design generally reduced the accuracy of the predicted photosynthetic indicators. Thus, three optimal measurement designs were provided for the three PLR curve types, in which the root mean square error (RMSE) values reduced by an average of 8.3% and the coefficient of determination (R(2)) values increased by 0.3%. The optimal design for the High PLR curve type should shift more towards high-intensity PAR values, which is in contrast to the optimal design for the Low PLR curve type, which should shift more towards low-intensity PAR values.