Application of functional analysis in dendrometry using five-year growth of selected dendrometric traits of scots pine ( <i>Pinus sylvestris</i> L.)

Abstract The differentiation between age classes of Scots pine ( Pinus sylvestris L.) was analyzed with regard to the five-year increment of seven traits: height growth (zh5), diameter growth at breast height (zd5), cross-sectional area growth at breast height (zg5), volume growth (zv5), volume growth intensity coefficient (i5), and slenderness (s). Measurements were made in five periods for 24-year-old trees and six periods for 33-year-old trees, all growing in fresh mixed coniferous forest sites. Repeated measures data analysis was conducted separately for all traits. Multivariable functional data analysis (FDA) was proposed to compare age classes of trees. The functional variables which resulted from this analysis can be used, as data, in many analyses (designate functions representing each of trees, FPCA – functional principal component analysis, FLDC – discriminant analysis, permutation analysis of variance). The results of the above analyses revealed significant differences between age groups. Furthermore the functions and FPCA were used to detect outliers. This procedure had not previously been used for such a purpose. FPCA explained 55% of the total variance, with the first two components clearly separating the groups. The study showed that 33-year-old trees exhibit stable growth, while 24-year-old trees show greater variability, highlighting the impact of age on growth dynamics. Permutation analysis of variance confirmed significant growth differences between the groups. The findings highlight the importance of age as a factor influencing tree growth and demonstrate the effectiveness of the multivariable FDA approach for analyzing such data.