Journal of Agricultural Science; Vol. 10, No. 5; 2018 ISSN 1916-9752 E-ISSN 1916-9760 Published by Canadian Center of Science and Education 198 Competition Indices and Their Relationship With Basal Area Increment of Araucaria Emanuel Arnoni Costa 1 , César Augusto Guimarães Finger 1 & André Felipe Hess 2 1 Forest Science, Federal University of Santa Maria, Brazil 2 Forest Science, State University of Santa Catarina, Brazil Correspondece: Emanuel Arnoni Costa, Forest Science, Federal University of Santa Maria, Brazil. E-mail: emanuelarnonicost@hotmail.com Received: January 17, 2018 Accepted: March 8, 2018 Online Published: April 15, 2018 doi:10.5539/jas.v10n5p198 URL: https://doi.org/10.5539/jas.v10n5p198 Abstract Models that report the effect of competition are important for forest management since forests with higher levels of competition have lower increment rates, and their use is necessary to plan forest interventions. Thus, this study aimed to assess the effect of competition in the basal area increment of individual trees of Araucaria angustifolia (Bertol.) Kuntze in a natural forest. A total of 397 subject trees were measured, covering the diametric range. The dendrometric and morphometric characteristics of subject trees and their competitors were obtained, and 22 distance-dependent and distance-independent competition indices were calculated, in addition to increment cores extracted radially from the trunk at diameter at breast height. The relationship between models of periodic annual increment in basal area based on competition indices has allowed to obtain R 2 values of 0.425 and Syx% ≥ 50.2. The multivariate technique of principal component analysis has shown that three principal components explain 78.43% of total variation. The first component was responsible for explaining 52.95%, with similar eigenvector for 11 competition indices, evidencing that these models can be used to describe especies competition, although they show different variables and mathematical equations in calculations. Results show the importance of competition to predict increment of Araucaria in individual trees. Keywords: quantification, tree growth, mixed ombrophilous forest 1. Introduction One of the most important facts to simulate tree growth is to assess the effects of competition, i.e., the influence of characteristics of the population where the tree is found. These characteristics can be measured through competition indices, which are algebraic relationships used to quantify the effect of higher or lower resource availability for a subject tree in relation to other competitor trees. The use of these competition indices has become an important tool for forest management worldwide (Pedersen et al., 2013). It is possible to find in the literature competition indices with various complex ways of calculation, mainly the ones described by Gerrard (1969), Bella (1971), Arney (1973), Hegyi (1974), Ek and Monserud (1974), Glover and Hool (1979), Lorimer (1983), Corona and Ferrara (1989), Mugasha (1989), Rouvinen and Kuuluvainen (1997), Castagneri et al. (2008), among others. These competition indices can be divided into two classes: (a) distance-independent indices that use non spatial measurements, based on tree size distribution in a given area; (b) distance-dependent indices, in which competitors are identified based on their size and the distance in relation to the subject tree (Wimberly & Bare, 1996). Index assessment and its influence on tree growth have been investigated by several authors (Daniels et al., 1986; Pukkala & Kolström, 1987; Holmes & Reed, 1991; Biging & Dobbertin, 1995; Álvarez Taboada et al., 2003; Corral Rivas et al., 2005; Castagneri et al., 2008; Contreras et al., 2011). Some studies report diameter increment modelling and basal area of individual trees of Araucaria angustifolia (Bertol.) Kuntze (Zanon, 2007; Chassot, 2009). In some cases, when regression models are used, with a great variety of explanatory variables, multivaried statistics may be useful to reduce the number of variables without loss of understanding of the observed phenomenom. In this context, the Principal Components Analysis (PCA) aims at gathering most of the original information (variation) in a minimum number of factors for prediction purposes (Hair et al., 2009), and this