Comparison of three sigmoidal functions describing the leaf growth of Camptotheca acuminata Decne

Abstract

Leaf ontogeny and maturation are attended by a transition from importing to exporting photosynthates, which has important implications to plant growth and reproductive success. However, the influence of leaf age on leaf size has been seldom studied, although ontogenetic growth trajectories plotted against time typically exhibit sigmoidal curves, which can be approximated by corresponding sigmoidal functions. The three-parameter logistic equation (LE) is a classical sigmoidal function that assumes a symmetrical growth rate curve (i.e., the derivative of the LE) when plotted against time. LE has been verified as a general tool for describing ontogenetic growth such as seen in leaf maturation. However, there are other sigmoidal functions that assume that growth rate curves are skewed bell-shaped. Whether leaf ontogeny follows the LE, or some other sigmoidal functions is unknown. To explore the relationship between leaf area and leaf age, we recorded the leaf length and width of 61 leaves of Camptotheca acuminata Decne at 21 time-points during leaf expansion, and used three sigmoidal functions to fit leaf area (represented by 2/3 × leaf length × leaf width) when plotted against leaf age, i.e., the LE, the beta sigmoidal equation (BSE), and the Lobry-Rosso-Flandrois sigmoidal equation (LRFSE). LE had the best close-to-linear behavior and the lowest Akaike information criterion (AIC) among the three sigmoidal functions for the pooled data of 61 leaves. For 49 of the 61 leaves (80.3 %), the AICs of the LE were smaller than those of the BSE, and for 52 out of 61 leaves (85.2 %), the AICs of the LE were smaller than those of the LRFSE. In addition, the BSE provided incorrect predictions for the starting time of leaf growth. Thus, the data indicate that (1) the LE is the best sigmoidal function for describing ontogeny at the individual leaf level and for the combined data, and (2) the growth rate of C. acuminata leaves tends to be a symmetrical function rather than an asymmetrical function of leaf age. These findings provide insights into the ontogenetic importing-exporting transition attending leaf maturation.