Allometric models for non-destructive estimation of the leaflet area in acai (Euterpe oleracea Mart.)

The leaflet area of acai (Euterpe oleracea) can be estimated by an exponential regression model adjusted by the relationship of leaflet maximum length and width.

This work was carried out aiming to fit linear regression models for the non-invasive estimation of leaflet area (LA) in acai (Euterpe oleracea Mart.). Thus, 5010 leaflets were sampled from 403 fronds sampled on 100 acai seedlings. Maximum length (LL) and width (LW) of each leaflet were measured with a ruler and LA was determined using a leaf area meter. Half of the data set was used to adjust the models and the other half was used for model validation. The Jackknife re-sampling method was applied to reduce model bias. Two double-entry models (models A and B) were fitted using LL and LW simultaneously, while these linear dimensions of the leaves were separately considered in single-entry models (models C to F). The adjusted coefficients of determination varied between 0.9075 and 0.9785, with the highest values observed in models A and B, which also showed the lowest standard error of the estimate and Akaike's information criterion (AIC) score. All models were highly accurate in estimating LA, with values above 0.9156; however, the double-entry models A and B showed the best performance regarding the relationship between estimated and observed LA. Comparing the double-entry models, the lowest AIC score in model B indicates that this model is the most parsimonious for non-invasive estimation of acai leaflet area in relation to model A. Therefore, the equation \({\text{LA}} = 1.0147 \left[{{\text{e}}}^{0.3685 + 0.8165 {\text{ln}}\left({\text{LL}} \times {\text{LW}}\right)}\right]\) $\text{LA}=1.0147\left[{\text{e}}^{0.3685+0.8165\text{ln}\left(\text{LL},\times ,\text{LW}\right)}\right]$ , deduced from model B, is the more precise model for the non-invasive determination of leaflet area in acai seedlings.