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Modeling long-term tree growth curves indirectly with piecewise linear regression and explaining factors, when tree ages are unknown

Martin Ricker et al.

Environmental and Ecological Statistics2026https://doi.org/10.1007/s10651-025-00689-zarticle
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0.50

Abstract

The current lack of an easily applicable method to estimate the growth curves of tree species in the tropics, when annual tree rings are not formed, has far-reaching consequences for developing forest management. Often, the projection of the whole growth curve over decades is needed. We present in detail a method to estimate statistically the long-term growth curve of stem diameter (or radius) as a function of unknown tree age. Logarithmic relative growth is modeled with piecewise linear regression as a function of tree-stem quantity. This relationship can be measured during one or a few years in different-sized trees with unknown ages. Under the assumption that the climate of the measurement period is representative for the long term, the estimated regression equation is converted into the desired relationship of mean quantity as a function of time. To find the (usually 1–3) best knot points with connected segments, we developed a method of bounding the segments’ slopes. In order to avoid the dominance of large residuals, weighted least squares regression is employed. Manly’s exponential transformation of logarithmic relative growth is used. Our method is successfully applied with data from two tree species, one of which has known ages to verify the adequacy of the results. Based on multiple linear regression, linear and quadratic functions are included in the model to explain variation in growth rate, and confidence curves are calculated. Alternative approaches with the nonlinear Schnute function or a polynomial are tested. Piecewise linear regression resulted to be more flexible and more reliable.

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https://doi.org/https://doi.org/10.1007/s10651-025-00689-z

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@article{martin2026,
  title        = {{Modeling long-term tree growth curves indirectly with piecewise linear regression and explaining factors, when tree ages are unknown}},
  author       = {Martin Ricker et al.},
  journal      = {Environmental and Ecological Statistics},
  year         = {2026},
  doi          = {https://doi.org/https://doi.org/10.1007/s10651-025-00689-z},
}

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