Latitudinal patterns in stabilizing density dependence of forest communities.

Numerous studies have shown reduced performance in plants that are surrounded by neighbours of the same species1,2, a phenomenon known as conspecific negative density dependence (CNDD)3. A long-held ecological hypothesis posits that CNDD is more pronounced in tropical than in temperate forests4,5, which increases community stabilization, species coexistence and the diversity of local tree species6,7. Previous analyses supporting such a latitudinal gradient in CNDD8,9 have suffered from methodological limitations related to the use of static data10-12. Here we present a comprehensive assessment of latitudinal CNDD patterns using dynamic mortality data to estimate species-site-specific CNDD across 23 sites. Averaged across species, we found that stabilizing CNDD was present at all except one site, but that average stabilizing CNDD was not stronger toward the tropics. However, in tropical tree communities, rare and intermediate abundant species experienced stronger stabilizing CNDD than did common species. This pattern was absent in temperate forests, which suggests that CNDD influences species abundances more strongly in tropical forests than it does in temperate ones13. We also found that interspecific variation in CNDD, which might attenuate its stabilizing effect on species diversity14,15, was high but not significantly different across latitudes. Although the consequences of these patterns for latitudinal diversity gradients are difficult to evaluate, we speculate that a more effective regulation of population abundances could translate into greater stabilization of tropical tree communities and thus contribute to the high local diversity of tropical forests.

Fixed or random? On the reliability of mixed-effects models for a small number of levels in grouping variables.

Biological data are often intrinsically hierarchical (e.g., species from different genera, plants within different mountain regions), which made mixed-effects models a common analysis tool in ecology and evolution because they can account for the non-independence. Many questions around their practical applications are solved but one is still debated: Should we treat a grouping variable with a low number of levels as a random or fixed effect? In such situations, the variance estimate of the random effect can be imprecise, but it is unknown if this affects statistical power and type I error rates of the fixed effects of interest. Here, we analyzed the consequences of treating a grouping variable with 2-8 levels as fixed or random effect in correctly specified and alternative models (under- or overparametrized models). We calculated type I error rates and statistical power for all-model specifications and quantified the influences of study design on these quantities. We found no influence of model choice on type I error rate and power on the population-level effect (slope) for random intercept-only models. However, with varying intercepts and slopes in the data-generating process, using a random slope and intercept model, and switching to a fixed-effects model, in case of a singular fit, avoids overconfidence in the results. Additionally, the number and difference between levels strongly influences power and type I error. We conclude that inferring the correct random-effect structure is of great importance to obtain correct type I error rates. We encourage to start with a mixed-effects model independent of the number of levels in the grouping variable and switch to a fixed-effects model only in case of a singular fit. With these recommendations, we allow for more informative choices about study design and data analysis and make ecological inference with mixed-effects models more robust for small number of levels.