Integrative Biology Journals

JOURNAL OF FORESTRY RESEARCH ›› 2026, Vol. 37 ›› Issue (1): 1-.DOI: 10.1007/s11676-026-01985-5

• Original Paper •    

Modeling Pinus tree taper data using mixed‑effects models

Breno Gabriel da Silva1, Clarice Garcia Borges Demétrio1,  Alexandre Behling2, Geert Molenberghs3, Renata Alcarde Sermarini1, Geert Verbeke4, Eduardo Resende Girardi Marques5,  Yuri Accioly5, Marco Aurélio Figura5   

  1. 1Department of Exact Sciences, Luiz de Queiroz College of Agriculture, University of São Paulo (ESALQ/USP), Piracicaba, SP 13418-900, Brazil 

    2Federal University of Paraná, Curitiba 80060-000, Brazil 

    3I-BioStat, Universiteit Hasselt, 3500 Hasselt, Belgium 

    4I-BioStat, KU Leuven, B-3000 Louvain, Belgium 

    5Forestry Department, Klabin S.A, Telêmaco Borba, PR 84275-000, Brazil

  • Received:2025-07-19 Accepted:2025-10-14 Online:2026-02-21 Published:2026-01-01
  • Supported by:
    This study was supported by the Coordena??o de Aperfei?oamento de Pessoal de Nível Superior - CAPES and Conselho Nacional de Desenvolvimento Científico e Tecnológico – CNPq (No. 141409/2020-7) and CNPq Project: 312645/2021 0, Brazil for Clarice G. B. Demétrio.

Abstract: Taper models are widely used to estimate log assortments and, consequently, forest yield from inventory data. However, for Pinus taeda, few studies have employed mixed-effects taper models that explicitly account for the hierarchical structure of forestry data and heterogeneity of variances. This study addresses this gap by developing and evaluating mixed-effects taper models based on modified versions of Kozak’s (1969) equation. The models incorporate random effects at the farm/forest region, stand, and tree levels and allow for different variance structures, enabling them to capture the heterogeneity commonly observed in P. taeda stands. Diagnostic procedures using least confounded residuals were applied to assess model adequacy. Compared with traditional fixed-effects taper models, the selected mixed-effects model achieved superior performance, including reduced bias, improved fit across stem sections, and better predictive accuracy. Additionally, in Appendices, we provide a tutorial outlining the computational procedures in R software for statistical modeling of data related to this species within the mixed-effects model framework.

Key words: Taper modeling, Pinus taeda L., Mixed effects models, Least confounded residuals, Sustainable forest practices