Climate reverses directionality in the richness–abundance relationship across the World’s main forest biomes

More tree species can increase the carbon storage capacity of forests (here referred to as the more species hypothesis) through increased tree productivity and tree abundance resulting from complementarity, but they can also be the consequence of increased tree abundance through increased available energy (more individuals hypothesis). To test these two contrasting hypotheses, we analyse the most plausible pathways in the richness-abundance relationship and its stability along global climatic gradients. We show that positive effect of species richness on tree abundance only prevails in eight of the twenty-three forest regions considered in this study. In the other forest regions, any benefit from having more species is just as likely (9 regions) or even less likely (6 regions) than the effects of having more individuals. We demonstrate that diversity effects prevail in the most productive environments, and abundance effects become dominant towards the most limiting conditions. These findings can contribute to refining cost-effective mitigation strategies based on fostering carbon storage through increased tree diversity. Specifically, in less productive environments, mitigation measures should promote abundance of locally adapted and stress tolerant tree species instead of increasing species richness.

The piecewiseSEM package includes both indices BIC and CIC and so it is worth testing the sensitivity of our results to using one or the other criterion for model selection.
To formally test this, we computed both BIC and CIC and analysed the relationship between them using a correlation test based on the Pearson moment correlation index.
Supplementary Figure S1 shows that both indices yielded almost identical results. Supplementary Material S3. Sensitivity analysis to data harmonization.
Original data used in this research come from different sources: i.e. National Forest Inventories and previous research projects. This introduces uncertainties associated to the number of trees accounted for at the plot level if disparate protocols are applied to gather the different realities in the different regions. In particular, while some of the regional datasets consider trees with DBH higher than 5 cm, other set the threshold in 10 cm DBH. By analyzing each regional dataset independently, the issues related to this uncertainty should be largely alleviated. Yet, it is worth questioning whether these differences can affect the final outcomes of our research. To answer this question, we firstly harmonized the general dataset by including only trees with a DBH higher that 10 cm in each regional dataset. Then, we compared BIC (MSH vs MIH) according to the SEM model described above for every regional dataset in its original and harmonized versions separately.
To formally evaluate whether original or harmonized data introduce any discrepancy on the model outputs regarding the latitudinal patterns in ∆BIC, we fitted a linear model in which the ∆BIC is expressed as linear function of the interactive effects of latitude and the type of data (original/harmonized). This interaction implies that latitudinal patterns in ∆BIC varies depending on the type of data considered (i.e. the slope of the relationship change significantly between the original and harmonized data).
Moreover, and even if influences of latitude on ∆BIC are assumed to remain constant, the ∆BIC could be comparatively higher or lower depending on the type of data (i.e. the main effects associated to the type of data influence the intercept in the linear model). To unveil this, we evaluated whether the type of data has a significant contribution to the ∆BIC     Supplementary Material S6. Influence of the sampling size on the ∆BIC.
The number of plots varies from one dataset to another (see Supplementary Table S1) and 11. We gathered 48 plots of 400 m 2 located in the south-western of Ecuador nearby the border with Peru. This area has been heavily militarized due to recent border conflicts, which has allowed an almost pristine status of the forests.
12. 44 plots of 900 m 2 were retrieved from the Australian national forest inventory.
We selected those plots that has not experienced a fire in at least the last 150 years and that were placed within Parks/Reserves or State Forests.
13. 61 plots of 706 m 2 and located in the Mercantour Nationa Park (France) were obtained from the France national forest inventory.
14. We retrieved 109 plots of 500 m 2 from the Chilean national forest inventory. Plots were classified as autochthonous mature forest (bosque autóctono maduro) and were located within a series of proximate national parks (del Alerce Andino,  22. We used 44 plots of 1000 m 2 located in the Madidi National Park (Bolivia) 23. 96 plots of 1000 m 2 were collected from the Costa Rica national forest inventory.
Plots classified as autochthonous mature forest and secondary forest were used.

Data representativeness
Following our search criteria, we gathered a total of 23 datasets distributed around the world. Using this sample of forests, we detected a clear pattern where the diversity effects hypothesis is supported toward more productive regions. Yet, it is worth questioning whether the sample of forest used is enough to robustly estimate the relationship between productivity and the support of the diversity effects hypothesis.
To evaluated this, we conducted a bootstrap analysis over the linear regression of ΔBIC supporting the diversity effect hypothesis as a function of NPP. Bootstrap analysis is intended to estimate population parameters (in our case all world forests matching our search criteria) based on a given sample (i.e. the forests for which we found plot data) 25 . We resampled with replacement the forest datasets 10,000 times.
In each bootstrap replicate, we computed a linear model of ΔBIC as a function of NPP, focusing on the statistical significance of the model, the coefficient of determination and the standardized regression coefficient. Bootstrap results strongly support the negative relationship between NPP and the diversity effect hypothesis. A total of 99.95% of bootstrapped replicates showed a significant negative relationship between NPP and ΔBIC (Supp. Fig. S6a). Moreover, we found a median R 2 = 0.43 (5 th and 95 th percentiles = 0.17 and 0.69; respectively, Supp. Fig. S6b) and a median standardized regression coefficient= -4.32 (5 th and 95 th percentiles = -6.71 and -2.09; respectively Supp. Fig. S6c). Therefore, these results show that the used sample of Madrigal González et al. Climate reverses the causal direction in the richness-abundance relationship across the main world's forest biomes.
forests provided robust results, confirming that the diversity forest hypothesis is supported toward the most productive regions on Earth.
Supplementary Figure