Mathematical system based on taper functions for distribution by structural product of culms in three giant bamboo taxa

Abstract

Aim of study: To generate a mathematical system to distribute structural products of bamboo culms. Study area: Northeastern region of the state of Puebla, Mexico. Materials and methods: Eighty-seven culms of Bambusa oldhamii Munro, Guadua aculeata Rupr. and Guadua angustifolia Kunth were collected in Puebla, Mexico. Four taper functions were evaluated, the one with the best predictive capacity was fitted to model the diameter over and under wall together with a wall thickness model. The fitting strategy consisted of a system of additive equations using Weighted-Nonlinear Seemingly Unrelated Regression (WNSUR) procedure with autocorrelation correction, in combination with the Dummy Variable technique. Main results: The Fang & Bailey case 1-a model was selected to describe the diameter over and under wall; the Cao and Papper model was used to model the wall thickness. The R2adj of the system fitted were 0.977, 0.944 and 0.918, and RMSE values 0.186 cm, 0.200 cm and 0.134 cm, for diameter over wall, diameter under wall, and wall thickness, respectively. G. angustifolia had the greatest taper and wall thickness, followed by G. aculeata. The highest proportion of primary product was presented by G. angustifolia. The system generated had parameters specific for each bamboo taxon. Research highlights: The diameter profile of bamboo culms can be modeled by taper functions. A mathematical system for distribution by structural product type was developed consisting of: (1) a taper model for the diameter over wall and, (2) a function to estimate the commercial height.