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The future trajectory of global forests is closely intertwined with tree demography, and a major fundamental goal in ecology is to understand the key mechanisms governing spatio‐temporal patterns in tree population dynamics. While previous research has made substantial progress in identifying the mechanisms individually, their relative importance among forests remains unclear mainly due to practical limitations. One approach to overcome these limitations is to group mechanisms according to their shared effects on the variability of tree vital rates and quantify patterns therein. We developed a conceptual and statistical framework (variance partitioning of Bayesian multilevel models) that attributes the variability in tree growth, mortality, and recruitment to variation in species, space, and time, and their interactions – categories we refer to as organising principles (OPs). We applied the framework to data from 21 forest plots covering more than 2.9 million trees of approximately 6500 species. We found that differences among species, the species OP, proved a major source of variability in tree vital rates, explaining 28–33% of demographic variance alone, and 14–17% in interaction with space, totalling 40–43%. Our results support the hypothesis that the range of vital rates is similar across global forests. However, the average variability among species declined with species richness, indicating that diverse forests featured smaller interspecific differences in vital rates. Moreover, decomposing the variance in vital rates into the proposed OPs showed the importance of unexplained variability, which includes individual variation, in tree demography. A focus on how demographic variance is organized in forests can facilitate the construction of more targeted models with clearer expectations of which covariates might drive a vital rate. This study therefore highlights the most promising avenues for future research, both in terms of understanding the relative contributions of groups of mechanisms to forest demography and diversity, and for improving projections of forest ecosystems. [ABSTRACT FROM AUTHOR]