Model residuals elucidate spatial effects on biomass of individual trees and their components in Pinus kesiya var. langbianensis forests from different origins

• Model residuals reveal the spatial effects for biomass distribution. • Bark, branches, and foliage are main components affecting tree biomass model accuracy. • Plantation tree biomass shows higher spatial autocorrelation but lower heterogeneity than natural forest. • Residuals of spatial regression models effectively explain the spatial structure of biomass. Understanding the spatial effects of biomass for individual tree and its components is essential for revealing stand spatial patterns and improving model accuracy. Yet using model residuals to reveal such effects has rarely been reported. This study aimed to i) evaluate the performance of biomass models for different biomass components across forest stands of different origins, and comparing the spatial autocorrelation and spatial heterogeneity of the model residuals. ii) compare the spatial patterns of the biomass itself with those of the corresponding model residuals. In this study, the ordinary least squares (OLS), spatial lag model (SLM), spatial error model (SEM), spatial Durbin model (SDM), and geographically weighted regression model (GWR) were applied to fit the biomass of individual tree components (wood, bark, branches, foliage) and AGB of Pinus kesiya var. langbianensis plantation and natural forest in Pu’er, Yunnan, China. Then, Moran’s I and the intra-group variance were calculated for biomass and model residuals to reflect the spatial autocorrelation and the spatial heterogeneity. Results indicated that the disparity in biomass fitting accuracy between the two origins was primarily contributed to by the bark, branches, and foliage. Biomass in the plantation exhibited stronger spatial autocorrelation than in the natural forest, while the residuals from the SEM and SDM showed relatively weaker spatial autocorrelation compared to other models. In contrast, biomass in natural forests showed higher spatial heterogeneity, which increased with lag distance and eventually stabilized. This pattern was better captured by the GWR. The results indicated that the residuals of biomass models effectively reflected the spatial structure of biomass, and that spatial regression models were able to accurately capture and explain this spatial structure. These findings enhance the understanding of spatial patterns in individual tree biomass and provide insights for improving biomass modeling and forest management.