Capture the time when plants reach their maximum body size by using the beta sigmoid growth equation

Of the many mathematical models proposed for capturing the dynamics of plant growth, the beta sigmoid function (BSF) is the newest and consequently is not well known to ecologists. A recent software package based on the Microsoft Excel macro, LEAF-E, was designed to promote the use of BSF, even though the performance of BSF and other growth models had not been compared. We developed R functions for fitting the BSF with a freer option for choosing the parametric number, and illustrated their performance using simulated data generated by four equations (the exponential, logistic, Gompertz, and von Bertalanffy equations), as well as dry weights of six crop species measured in growing seasons. Compared to other growth models, the BSF allowed for both symmetric and asymmetric growth curves, and thus the simulated data modeled the actual data quite well. It was demonstrated that the BSF was better than the above four traditional growth equations. In addition, the R functions developed here can facilitate future data fitting and model comparison for capturing plant growth dynamics. And the time when plants reach their maximum body size can be accurately obtained by using the BSF.