“…It has been of interest for forest modelers to better understand this phenomenon, particularly on the basis of statistical modeling and analysis (Wang et al, 2017). The traditional crown profile modeling methods have been used to deal with the autocorrelation and heteroscedasticity in the crown profile equations, they are mainly direct variance-covariance modelling (Hann, 1999;Crecente-Campo et al, 2009;Crecente-Campo et al, 2013), mixed-effects modelling (Fu et al, 2013;Sharma et al, 2016;Fu et al, 2017;Sharma et al, 2017;Sun et al, 2017;Jia and Chen, 2019;Wang et al, 2019;Chen et al, 2021;Di Salvatore et al, 2021), and nonlinear marginal modeling (McCulloch and Searle, 2001;Lejeune et al, 2009;de-Miguel et al, 2012;Chen et al, 2022). With the rapid development of machine learning artificial intelligence, some machine learning algorithms have the characteristics of high accuracy and good robustness for the data with nonlinear features (Singh et al, 2016;Dong et al, 2021), which has subsequently been applied to crown profile modeling.…”