Natura non facit saltus: biological realism, interpolation, and extrapolation in machine-learning-based allometric models

Abstract

Allometric models are fundamental components of forest growth and yield systems used to project tree and stand development. Machine learning (ML) approaches are increasingly applied in their development because they can learn complex functional relationships directly from data without requiring the explicit specification of a functional form. However, despite their growing use, the ability of these algorithms to interpolate across data gaps and extrapolate beyond observed ranges, while maintaining biological realism in both contexts, has received limited evaluation. Using a controlled simulation framework, we evaluated the ability of six widely used machine learning algorithms to reproduce established allometric relationships. We further examined their capacity to generalize across data gaps and beyond the observed data domain, quantifying performance under different missing-data mechanisms. Our results show that, given complete and representative training data, most algorithms can successfully reproduce the underlying functional relationships. However, extrapolation performance was generally poor, with predictions frequently exhibiting biologically unrealistic behavior. Some tree-based regression algorithms also failed to interpolate smoothly across data gaps, producing piecewise-constant predictions that are inconsistent with the continuous nature of biological growth. While ensemble effects and stochastic variation in empirical data may partially obscure these discontinuities, the underlying algorithmic limitations remain. These findings suggest that predictive accuracy within the observed data domain alone may be insufficient for evaluating the suitability of machine learning models in ecological applications. When models are expected to generalize beyond this domain, validation should explicitly assess reliability under both interpolation and extrapolation, as well as consistency with established forest growth principles.

Keywords

 Forest growth /  Algorithmic models / Tree-based models / Model evaluation / Biological constraints / Inductive bias

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