Table 1 Estimates from the meta-regressions testing the first and second hypothesized latitudinal patterns in stabilizing CNDD in tree mortality

Model	Characteristic	Beta	95% CI	P value
(a) Average species CNDD σ_r = 0.0018 σ_s = 0.0054	Intercept	0.004087	0.003072, 0.005102	2.9 × 10⁻¹⁵
(a) Average species CNDD σ_r = 0.0018 σ_s = 0.0054	tLatitude	−0.000044	−0.000107, 0.000019	0.17
(b) Abundance-mediated CNDD σ_r = 0.0018 σ_s = 0.0053	Intercept	0.007527	0.005870, 0.009183	5.3 × 10⁻¹⁹
	tLatitude	−0.000172	−0.000315, −0.000030	0.018
	tAbundance	−0.000990	−0.001353, −0.000626	9.5 × 10⁻⁸
	tLatitude:tAbundance	0.000035	0.000006, 0.000064	0.017

We fitted two models for the species-site-specific CNDD estimates (n = 2,534 species or species groups from 23 forest sites): (a) absolute latitude as a predictor (‘average species CNDD’ model); and (b) absolute latitude, species abundance and their interaction as predictors (‘abundance-mediated CNDD’ model). Species abundance was measured by log-transformed number of trees with DBH ≥1 cm per hectare. Predictors were transformed (t), that is, centred at abundance = 1 tree per hectare and absolute latitude = 11.75°, so that main effects for abundance and latitude assess slopes and respective significance tests for rare, tropical species. Stabilizing CNDD is defined as in Fig. 1. For the models, CNDD estimates (rAMEs) were log-transformed after adding 1 to improve normality assumptions, so that CNDD as the relative change in annual mortality probability in per cent induced by one additional conspecific neighbour can be calculated from the model coefficients as \(100\times ({e}^{{\beta }_{0}+{\beta }_{1}x\ldots }-1)\). Predictions of the models are shown in Figs. 2 and 3. σ_r and σ_s are the estimated standard deviations of random intercepts for CNDD among sites and species in sites, respectively. Bold P values are statistically significant at a significance level of 0.05.

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