Growth Rates of Morphometric Variables in Approximately Linear Sections Using Lines in R3

Abstract

Morphometric analyses have great potential for application in fruit crops, especially in the construction of indices that can be linked to biophysical and/or biochemical quantities of a physiological nature. For example, in peaches, it is convenient to establish quality attributes for harvest or postharvest, where usually the sigmoidal or double sigmoidal models describe the growth of some indicators. The nonlinear nature of this and other associated models sometimes makes it difficult to construct approximate growth rates, so instantaneous rates are used instead. The calculation of approximate rates in nonlinear models may be inappropriate due to aspects related to the phrase known as the “average fallacy.” In this research, different classification algorithms are applied to select the approximately linear phase present in various nonlinear models of variables or parameters used in the modeling of the growth of a crop. A 3D line model was fitted in the extracted section using the decomposition of singular values to generate a simple form of the growth rate. The application was illustrated with growth data of the equatorial and longitudinal diameters of peach fruits measured on different days after defoliation, using data from different elevations above sea level. The proposal simplifies obtaining some growth rates using nonconventional methods; in addition, it allows the comparison and adjustment of the model for the different elevations considered, which provides a novel way for the teaching of certain areas of applied mathematics in plant physiology.