Aridity index and quantile regression influences on the maximum size-density relationship for coniferous and broad-leaved mixed forests

Abstract

The maximum size-density relationship (MSDR) of mixed stands is of great significance for optimizing stand structural components and increasing stand productivity. However, model structure, climatic factors and parameter estimation methods affect the prediction accuracy of MSDR for multi-species mixed stands with complex structures, emphasizing the need to improve MSDR prediction methods. This study applied likelihood analysis to 333 sample plots of larch (Larix principis-rupprechtii Mayr.) and birch (Betula platyphylla Suk.) coniferous and broad-leaved mixed forests in Saihanba, Hebei Province, China to determine the structure of MSDR. Nonlinear least squares and nonlinear quantile regression were used to construct the MSDR of mixed stands, including the Martonne aridity index (M) which is a composite index that responds to temperature and precipitation. The results indicate that the optimal model form for predicting the MSDR of mixed stands is a nonlinear additive error structure. When considering M and using a quantile q = 0.95, the MSDR can accurately describe the variation in stand density of mixed larch-birch coniferous and broad-leaved forests.