Geographic gradient interactions reveal non-additive organization of aboveground carbon density in mountain forests

Classical geographic zonality describes latitudinal, longitudinal, and elevational differentiation in forest vegetation, but these dimensions are commonly treated as separable gradients. In mountain regions, however, horizontal geographic position and elevation jointly define the environmental context in which forest carbon accumulates. Whether mountain forest aboveground carbon density (AGCD) follows uniform geographic belts or exhibits context-dependent three-dimensional organization remains unresolved. Here, we evaluated whether mountain forest AGCD is better represented by additive geographic effects or by interactions among longitude, latitude, and elevation. Using an inventory-derived AGCD dataset for Yunnan, southwestern China, we fitted nested generalized additive models (GAMs) with additive effects (M1), additive and pairwise terms (M2), and additive, pairwise, and three-way terms (M3). The same model hierarchy was fitted separately in six global mountain systems for independent regional replication. In Yunnan, full-data deviance explained increased from 10.80% (M1) to 13.94% (M2) and 14.18% (M3). Full-data RMSE declined from 23.71 to 23.00 and 22.86 Mg/ha, respectively. Pairwise interactions accounted for approximately 93% of the interaction-related improvement. The three-way interaction provided only a small additional refinement in full-data fit. M3 had the lowest full-data AIC, but this reflects in-sample fit rather than spatial predictive performance. Five-fold spatial block cross-validation showed low predictive R 2 and no consistent predictive advantage of M2 or M3 over M1. High AGCD in the fitted response surface was concentrated within restricted longitude–latitude–elevation combinations rather than continuous single-axis geographic belts. Across the six mountain systems, marginal geographic responses differed substantially, yet interaction models generally improved full-data fit, with pairwise interactions accounting for most of the improvement beyond additive effects. These results suggest a recurrent non-additive geographic organization of mountain forest AGCD, in which AGCD associations along each geographic axis depend on the broader geographic context. These descriptive associations provide a framework for comparing mountain forest carbon patterns but do not establish causal ecological mechanisms. A major limitation is that uncertainty in inventory measurements and conversion parameters was not propagated through the AGCD estimation chain and geographic modeling.