Comparing machine learning algorithms for simultaneous prediction of tree diameter distribution percentiles

Accurate predictions of tree diameter distributions are important for assessing forest structure, quantifying biodiversity, and estimating carbon sequestration. Percentile-based approaches are among the most effective methods for reconstructing diameter distributions from stand-level variables. In this study, we compared three modelling approaches, generalised least squares (GLS), Multi-Output Random Forest (MORF), and a multi-output deep learning-based model (MODL), across nine datasets representing different forest types and management regimes, aiming to predict simultaneously six diameter distribution percentiles. Our results show that MODL consistently outperformed both GLS and MORF in predictive accuracy across all nine training subsets and five out of nine test subsets, demonstrating strong generalisation across diverse forest types. MODL was particularly effective in achieving high accuracy while preserving the standard deviation of the response variables. While GLS performed slightly better in predicting the 100th percentile, MODL showed superior performance at the lower percentiles in most datasets. Interestingly, although MORF was generally the least accurate, it was the only method that consistently maintained the monotonicity of the predicted percentiles, a desirable property not inherently ensured by GLS or MODL, especially in the case of narrow diameter distributions. These findings underscore the strong potential of deep learning models for predicting diameter distribution percentiles and position MODL as a promising alternative to traditional parametric approaches.