Probabilistic Distributions for Acacia Mearnsii De Wild Total Height and the Influence of Environmental Factors

Abstract

This paper discusses the hypothesis of height distribution on a forest stand of Acacia mearnsii De Wild, known as black wattle. It remains constant at varied growing environments and, in addition, they are not influenced by age factor. The Wakeby equation was applied. The research was carried out in a black wattle stand at varied age levels and over two different agroecological regions where plantations are found: Serra do Sudeste and Encosta do Sudeste, Rio Grande do Sul State, Brazil. It was observed that as the age rises there is an increase in the stand total height; while the number of trees decreases for the lower classes, it increases for the upper ones. This resulted in lengthening of the curve tail to the left and mode shift to the right, generating negative asymmetrical curves. Two types of height distribution were found: the sharp increase of probability in a specific class and some similar probabilities in successive classes. The distribution curves between the cultivation areas were statistically different and therefore the height distribution was dependent of environment.

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Sanquetta, C. , Behling, A. , Pelissari, A. , Corte, A. , Netto, S. and Simon, A. (2014) Probabilistic Distributions for Acacia Mearnsii De Wild Total Height and the Influence of Environmental Factors. Journal of Applied Mathematics and Physics, 2, 1-10. doi: 10.4236/jamp.2014.23001.

Keywords:Wakeby Distribution; Forest Stand Age; Cultivation Area; Forest Structure

1. Introduction

The forestry production forecast, especially by wood volume, is an important problem in the Forestry Science and the lack of comprehensive studies, as the stem diameter and tree height are related to the volume, so these variables become the main elements to the forest structure assess.

The stem diameter and tree height distribution are particularly valuable to the estimation of the forest stand volume and necessary for the production planning. Even for those non-properly planned forest stands, the class distribution modeling for those variables promotes useful information as a comparison standard among various stands.

The probabilistic model may express the empirical distribution of various stand variables, since their parameters are properly estimated. Among the parameter estimation methods are highlighted the moments [1], maximum likehood [2] and percentile [3]. A great number of probability density functions (henceforth called PDF) have been applied in the Forest Science, and the studies in the most part are related to stem diameter.

The Weibull PDF is one of the functions of the best performing for modeling the diameter distribution. For this reason, it is used in many situations, mainly in the forest sector, such as [4-13]. Besides, it is also easy and correlated to the stand characteristics [4].

The authors [14,15] observed that other functions demonstrated superiority related to the Weibull. According to these researches, the Burr and Dagum were more flexible than Weibull as they covered an area of greater asymmetry and kurtosis. Others have also been widely used as: Beta [16-21], Gamma [22], Johnson’s SB [23-25] and Log-normal [26].

It is known that the growing and production levels of a certain species are considerably varied to the detriment of environment. The tree height, particularly the dominant one, is a variable strongly related to environmental factors and has little influence of silvicultural treatments and tree competition. For this reason, it is considerably applied to the growing and production models.

However, understanding the height behavior of the trees is relevant and allows the forester to have the knowledge of many factors related to the cultural treatments for decision making. However, there are few works that modeled the height distribution, even when related to the stem diameter. As examples: [27-33].

The height probabilistic distribution is a practical tool for the prediction of the section number in the stem wood with pre-established dimensions on the basis of mechanized harvest. The height growing assess is integrated to the cultivation environment, or the last soil use, as the cultural treatments and planting model. There is also the possibility to evaluate the pest, disease and others. Thus, the study hypothesis is based on the presupposition that tree height distribution and growth keep constant in varied environment conditions and stand age.

The black wattle species, which is used in this study, is one of the most important forest species in Brazil not only economically but also environmentally and socially. Besides, being the most cultivated genera in the country by small farmers, its cultivation generates thousands of direct or indirect jobs. The cultivation is performed in South of Rio Grande do Sul State especially in two agroecological regions: Serra do Sudeste e Encosta do Sudeste, so over different environmental conditions.

In this way, for the present research, it was aimed to verify whether the different cultivation environments influence in the stand height distribution of black wattle. Additionally, we studied the age effects on the height distribution.

2. Methodology

The data of 24 temporary plot were used for the present work. The plots were performed in commercial planting of black wattle in the agroecological regions of Serra do Sudeste and Encosta do Sudeste in the Rio Grande do Sul State. For each location it was performed studies for different stand age: one; three, five and seven years, in order to cover the crop cycle.

In the Encosta do Sudeste, the evaluated areas are located between 30˚54’ South and 50˚40’ West coordinates and in the Serra do Sudeste, are between 31˚25’ South and 52˚58’ West, all in the altitude of 320 to 370 meters above sea level.

For both regions, the plantings were made even for new areas (first rotation) and for areas under reformation (second rotation), according to Framework 1. For all cases, the soil preparation was performed on the crop row (minimal cultivation), the plots were subsoiled with three chisel plows in a 40 cm depth and harrowed twice. The crop spacing was of 3 × 1.75 m (1904 plant/ ha) for the first year treatment and 3 × 1.5 m (2222 plants/ ha) for the other ages and added 50 g of NPK (5-30-15) by plant.

For each stand was selected a northern exposure slope, where three plots were designated in the superior, medium and inferior one-third. The plot sizes were delimited in 9 × 16 m for the one year stands and 9 × 14 m for the others, in a total of 4 crop rows with 10 plants each.

The stem diameter was measured for the plots, in a height of 1.3 m from soil, using a dendrometrical tape measure and the height with an electronic clinometer (Haglöf), together with a digital tape measure (Sonin Multimeasure Combro-pró, 10300) in order to identify the distance to the tree.

Framework 1. List of the areas where stands were performed.

Conflicts of Interest

The authors declare no conflicts of interest.

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