Growth and yield models for eucalyptus stands obtained by differential equations

Adriano Ribeiro De Mendonça,Natalino Calegario,Gilson Fernandes Da Silva,Samuel De Pádua Chaves E Carvalho

doi:10.1590/1678-992x-2016-0035

Adriano Ribeiro De Mendonça, Natalino Calegario + Show 2 more

Open Access

https://doi.org/10.1590/1678-992x-2016-0035

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Abstract

The main purpose of this study was to assess nonlinear models generated by integrating the basal area growth rate to estimate the growth and yield of forest stands. The database was collected from permanent sample units, in Paraopeba county, in the state of Minas Gerais, Brazil. The stands were represented by Eucalyptus camaldulensis × Eucalyptus urophylla hybrid trees, with 3 × 3 meters of spacing. The data were divided into two groups: fitting and validating databases. Two nonlinear models (Strategy A and Strategy B) were developed using differential equations to estimate the basal area growth and yield of the sample units. The logistic model was fitted to estimate the volumetric yield as a function of age, site index and basal area. The efficiency of the systems generated by logistic model and models obtained by differential equations (Strategy A and Strategy B) was also compared to the efficiency of the system estimated by the Clutter model (Strategy C). The projection models used to estimate basal area obtained by differential equations were compatible with forest growth and yield, and the logistic model with covariates was compatible with volumetric growth and yield. Strategy A and Strategy B generated different thinning and harvesting options for different site indices, which is biologically consistent.

Highlights

An accurate estimation of forest growth and yield is fundamental to the achievement of forestry planning objectives
The main purpose of this study was to assess nonlinear models generated by integrating the basal area growth rate to estimate the growth and yield of forest stands
The efficiency of the systems generated by logistic model and models obtained by differential equations (Strategy A and Strategy B) was compared to the efficiency of the system estimated by the Clutter model (Strategy C)

Summary

Introduction

An accurate estimation of forest growth and yield is fundamental to the achievement of forestry planning objectives. The stand growth and yield volume, both present and future, are the most important items of information if forestry planning is to be successful. Growth models represent the relationship between the quantity of yield and growth and the various factors that explain or allow for the estimation of this growth (Davis et al, 2000) and several studies on forest growth and yield have been completed in the past including the following: Bonet et al (2012), Burkhart (1971), Clutter (1963), Pienaar (1979), Pienaar and Turnbull (1973), Schumacher (1939) and Sullivan and Clutter (1972). The sampling process for estimating the present yield of forest stands and their dynamics has led to the continued improvement of techniques used to construct growth and yield models. Garcia (1980) developed a stochastic differential equation model for the height growth of even-aged stands in which the deterministic part is equivalent to the Bertalanffy-Richards model

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