Nonlinear Model Selection for Fruit and Kernel Development as a Function of Heat in Pistachio

Abstract

Knowing a tree crop’s seasonal growth and development as a function of heat accumulation can facilitate scheduling of irrigation, pesticide applications, and harvest. Our objective was to compare the goodness of fit of applied models and determine which provides the best description of pistachio nut growth as a function of thermal unit accumulation. Three fruit growth traits of pistachio—pericarp (hull) + endocarp (shell) size, endocarp thickening and hardening, and embryo (kernel) size—exhibited clear nonlinear dependence on heat accumulation. We tested three nonlinear models—Michaelis–Menten, three-parameter logistic, and Gompertz—fitted to fruit development data to create a tool to forecast pest susceptibility and harvest timing. Observation of development began at full bloom and ended at harvest. Data were collected from six pistachio cultivars in one experimental and eight commercial orchards over 3 years. Analyses of residual distribution, parameter standard errors, coefficient of determination (R2) and the Akaike information criterion (AIC) all demonstrated the Gompertz function was the best model. Cultivars differed significantly in all the three parameters (Asym, b, and c) for all three traits with the Gompertz model, demonstrating the Gompertz model can adjust to incorporate cultivar differences. The growth curve of the three traits together provided integrated information on nut biomass accumulation that facilitates predicting the critical timing for multiple orchard management practices.

Keywords

• embryo
• gompertz model
• nut growth
• pistacia vera