Selecting non-linear mixed effect model for growth and development of pecan nut

Abstract

Pecan is the only commercial tree nut native to the United States. The optimal times for orchard irrigation, pesticide sprays, and harvest are difficult to identify. Growth and development of the nut as a function of heat unit accumulation is a potential tool predicting different nut growth stages. Growth models utilizing heat unit accumulation are useful decision making tools for growers to fine tune inputs. The objective of this research was to compare different non-linear growth models and determine which best fits the growth and development of the pecan nut components i.e., embryo, shell, and shuck. The sampled nuts were collected in two different years (2019 and 2020). In 2019, three varieties of nuts were sampled from five different locations. In 2020, samples of two varieties were collected from one location. Separate models were fitted for (1) the 2019 data to capture the variation among different locations and varieties and (2) the 2019 and 2020 data within one location that also considered the random effect between years for the two cultivars. A comparison of the coefficient of determination (R2) and Akaike information criteria (AIC) among the fitted models, demonstrated the Gompertz model best fit the embryo development for both datasets. It also best described the shuck growth in the 2019 data. The Logistic model performed slightly better than Gompertz for modeling shell growth for both datasets and the shuck for the two-year data. In both years, slow initial growth of fruit was observed until the beginning of the water stage, followed by an increase in size until the gel stage through nut filling in the dough stage. Our findings suggest that irrigation is more crucial during the water stage of pecan, whereas thinning should be done at the late water stage prior to the nut filling stage. Similarly, pesticide use can be minimized by determining when the pecan shell lignifies and is not susceptible to piercing sucking insect mouthparts. These results can guide pecan growers in fine tuning irrigation, thinning, and pest management based on an integrated growth model of the three phenotypic traits, shuck, shell, and embryo, as a function of accumulated heat units.