Comparison of four light-response models using relative curvature measures of nonlinearity

Photosynthetic light response curves serve as powerful mathematical tools for quantitatively describing the rate of photosynthesis of plants in response to changes in irradiance. However, in practical applications, the daunting task of selecting an appropriate nonlinear model to accurately fit these curves persists as a significant challenge. Thus, there arises a need for a method to systematically evaluate the efficacy of such models. In the present study, four distinct nonlinear models, namely Exponential Model (EM), Rectangular Hyperbola Model (RHM), Nonrectangular Hyperbola Model (NHM), and Modified Rectangular Hyperbola Model (MRHM), were used to fit the relationship between light intensity and the rate of photosynthesis across 42 empirical datasets. The goodness of fit for each model was assessed using the root-mean-square error, and relative curvature measures of nonlinearity were employed to assess the nonlinear behavior of the models. In terms of goodness of fit, pairwise difference tests of the root-mean-square error revealed that there was little to choose among the four models, although RHM gave a marginally poorer fit. However, in terms of nonlinear behavior, EM not only provided the most favorable linear approximation performance at the global level, but also exhibited the best close-to-linear behavior at the individual parameter level among the four models across the 42 datasets. Consequently, the results strongly advocate for EM as the most suitable mathematical framework for fitting photosynthetic light response curves. These findings provide insights into the model assessment for nonlinear regression in describing the relationship between the photosynthetic rate and light intensity.