GoKawiilStudy sites and census data
Our study was based on multiple censuses of 32 large permanent forest dynamic plots, with an average plot size of 24.5 ha (range: 9–50 ha). Data were sourced from the Forest Global Earth Observatory (http://www.forestgeo.si.edu) and Chinese Forest Biodiversity Monitoring Network (http://www.cfbiodiv.org) (Fig. 2a and Supplementary Table 1). Plots span tropical to boreal terrestrial biomes with latitude ranging from 1.92° S to 61.30° N. All plots were established and censused several times following a standardized protocol41. In each census, all free-standing woody stems with a diameter at breast height (DBH) greater than 1 cm were tagged (unique ID), mapped (coordinates), identified (species identity), measured (DBH) and recorded (alive, dead or recruit). The census was repeated every 5 years to monitor forest dynamics (for instance, survival, growth and recruitment). Most plots were only censused twice. For a few plots with three or more censuses, we selected two consecutive censuses between 1998 and 2022 for analysis (Supplementary Table 1). Overall, we compiled data for more than 3 million trees of 5,000 species across the 32 study plots.
Growth and survival models with HOIs
We estimated species interactions from demographic growth and survival models using the compiled dynamic forest census data3,27. For trees with more than one stem (that is, with multiple branches at height less than 1.3 m), we considered the survival and growth of the main stem. The growth of a focal tree f of a species i (\({{\rm{Growth}}}_{{i}_{f}}\)) was modelled as a function of its potential growth rate in the absence of neighbours (\({G}_{i}\)), size (\({{\rm{DBH}}}_{{i}_{f}}\)), and neighbourhood pairwise (\({\mathrm{Pair}}_{{i}_{f}}\)) and higher-order effects (\({{\rm{HOI}}}_{{i}_{f}}\))27,42:
$${{\rm{G}}{\rm{r}}{\rm{o}}{\rm{w}}{\rm{t}}{\rm{h}}}_{{i}_{f}}={G}_{i}\,\times {{\rm{D}}{\rm{B}}{\rm{H}}}_{{i}_{f}}^{\gamma }\,\times {{\rm{e}}}^{{{\rm{P}}{\rm{a}}{\rm{i}}{\rm{r}}}_{{i}_{f}}}\,\times {{\rm{e}}}^{{{\rm{H}}{\rm{O}}{\rm{I}}}_{{i}_{f}}}.$$ (1)
Similarly, the survival probability of a focal tree f of a species i (\({{\rm{Survival}}}_{{i}_{f}}\)) is modelled as27:
$${{\rm{S}}{\rm{u}}{\rm{r}}{\rm{v}}{\rm{i}}{\rm{v}}{\rm{a}}{\rm{l}}}_{{i}_{f}}=\frac{1}{1+{{\rm{e}}}^{{\lambda }_{i}+{\gamma }_{1}\times {{\rm{D}}{\rm{B}}{\rm{H}}}_{{i}_{f}}^{-1}+{\gamma }_{2}\times {{\rm{D}}{\rm{B}}{\rm{H}}}_{{i}_{f}}+{\gamma }_{3}\times {{\rm{D}}{\rm{B}}{\rm{H}}}_{{i}_{f}}^{2}+{{\rm{P}}{\rm{a}}{\rm{i}}{\rm{r}}}_{{i}_{f}}+{{\rm{H}}{\rm{O}}{\rm{I}}}_{{i}_{f}}}},$$ (2)
where \({\lambda }_{i}\) is the intrinsic survival probability in the absence of neighbours. The inverse of diameter (\({{\rm{DBH}}}_{{i}_{f}}^{-1}\)) is included to model rapid decline in mortality rate with increasing diameter, whereas the terms \({{\rm{DBH}}}_{{i}_{f}}\) and \({{\rm{DBH}}}_{{i}_{f}}^{2}\) model the U-shaped senescence effect43.
The pairwise effects of all neighbours on the focal tree \({i}_{f}\) (\({\mathrm{Pair}}_{{i}_{f}}\)) can be decomposed into conspecific and heterospecific effects:
$${{\rm{P}}{\rm{a}}{\rm{i}}{\rm{r}}}_{{i}_{f}}={\alpha }_{ii}\,\times \,{n}_{i,{i}_{f}}+{\alpha }_{ih}\,\times \,{n}_{h,{i}_{f}},$$ (3)
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