Estimation of the Basic Wood Density of Native Species Using Mixed Linear Models

Abstract

This paper aimed to estimate the basic density (DB) of the wood of Cerrado species using mixed linear models. For performing the DBH measurement, the sampling of 334 individuals was carried out. By keeping the Pilodyn apparatus in the DBH position, two measurements were made on opposite sides. Further, for determining DB, the trees were knocked down, followed by removal of five wood discs at different height of stem positions. For this purpose, two sets of modeling alternatives were proposed, which take into account with and without random effects, employing species as a random effect grouping variable. Thus, it was elucidated that, for the estimation of DB, the mixed model that considered the random effects performed better as compared to the alternative model without random effects. The inclusion of random effects leads to the estimation of DB with high accuracy.

Influence of growth parameters on wood density of Acacia auriculiformis

“…The random effects were: plots nested within zone of data collection and the fixed effect was tree diameter. Based on the inspection of the scatterplots and models previously used for explaining the relation between tree diameter or tree age and wood density, a linear (Silva et al 2019) and four nonlinear functions (Table 3) were assumed to potentially fit well the data. The nonlinear functions include the second-degree polynomial function (Githiomi and Kariuki 2010), the first exponential function (Oddi et al 2019), the Michaelis-Menten asymptotic function (Oddi et al 2019) and the second exponential function (Oddi et al 2019).…”

“…For example, an estimation of the wood density of Cerrado species (e.g. Luehea paniculata, Terminalia fagifolia) was obtained in Brazil with a lineal mixed model (Silva et al 2019) and for several species in Madagascar (Ramananantoandro et al 2016). Similarly, a linear mixed-effect model was used to estimate the wood density of Quercus petraea as a function of growth parameters and site quality (Guilley et al 2004).…”

“…Tree growth is usually expressed in several ways, including height increment, and diameter growth (DeBell et al 1994, Silva et al 2019. Tree growth influence several characteristics of wood such as wood density.…”

A Formalism of the General Mathematical Expression of Multilayer Perceptron Neural Networks

“…with b i0 = w i0 called bias and x 0 ≡ 1. The activation function or transfer function, f is a real value function, continuous, not necessarily non-linear and class C ∞ defined from R to R and applied to equation (5) gives:…”

“…W D = aD + b [5]; polynomial of the second degree : W D = aD 2 + bD + c [6]; exponential : W D = aD exp(−bD) [7]; asymptotic by Michaelis-Menten : W D = aD 1+bD [7] and again exponential : W D = a exp(bD) [7] where a, b and c are the parameters of the models. The appropriate model that best fits this data was selected based on the performance of criteria such as the Akaike Information Criterion (AIC) [8], the coefficient of determination and the overall significance of the model coefficients.…”