Environmental heterogeneity is regarded as one of the most important factors governing species richness gradients. An increase in available niche space, provision of refuges and opportunities for isolation and divergent adaptation are thought to enhance species coexistence, persistence and diversification. However, the extent and generality of positive heterogeneity-richness relationships are still debated. Apart from widespread evidence supporting positive relationships, negative and hump-shaped relationships have also been reported. In a meta-analysis of 1148 data points from 192 studies worldwide, we examine the strength and direction of the relationship between spatial environmental heterogeneity and species richness of terrestrial plants and animals. We find that separate effects of heterogeneity in land cover, vegetation, climate, soil and topography are significantly positive, with vegetation and topographic heterogeneity showing particularly strong associations with species richness. The use of equal-area study units, spatial grain and spatial extent emerge as key factors influencing the strength of heterogeneity-richness relationships, highlighting the pervasive influence of spatial scale in heterogeneity-richness studies. We provide the first quantitative support for the generality of positive heterogeneity-richness relationships across heterogeneity components, habitat types, taxa and spatial scales from landscape to global extents, and identify specific needs for future comparative heterogeneity-richness research.

No abstract

In ecology, the true causal structure for a given problem is often not known, and several plausible models and thus model predictions exist. It has been claimed that using weighted averages of these models can reduce prediction error, as well as better reflect model selection uncertainty. These claims, however, are often demonstrated by isolated examples. Analysts must better understand under which conditions model averaging can improve predictions and their uncertainty estimates. Moreover, a large range of different model averaging methods exists, raising the question of how they differ in their behaviour and performance. Here, we review the mathematical foundations of model averaging along with the diversity of approaches available. We explain that the error in model‐averaged predictions depends on each model's predictive bias and variance, as well as the covariance in predictions between models, and uncertainty about model weights. We show that model averaging is particularly useful if the predictive error of contributing model predictions is dominated by variance, and if the covariance between models is low. For noisy data, which predominate in ecology, these conditions will often be met. Many different methods to derive averaging weights exist, from Bayesian over information‐theoretical to cross‐validation optimized and resampling approaches. A general recommendation is difficult, because the performance of methods is often context dependent. Importantly, estimating weights creates some additional uncertainty. As a result, estimated model weights may not always outperform arbitrary fixed weights, such as equal weights for all models. When averaging a set of models with many inadequate models, however, estimating model weights will typically be superior to equal weights. We also investigate the quality of the confidence intervals calculated for model‐averaged predictions, showing that they differ greatly in behaviour and seldom manage to achieve nominal coverage. Our overall recommendations stress the importance of non‐parametric methods such as cross‐validation for a reliable uncertainty quantification of model‐averaged predictions.

Most current research on land-use intensification addresses its potential to either threaten biodiversity or to boost agricultural production. However, little is known about the simultaneous effects of intensification on biodiversity and yield. To determine the responses of species richness and yield to conventional intensification, we conducted a global meta-analysis synthesizing 115 studies which collected data for both variables at the same locations. We extracted 449 cases that cover a variety of areas used for agricultural (crops, fodder) and silvicultural (wood) production. We found that, across all production systems and species groups, conventional intensification is successful in increasing yield (grand mean + 20.3%), but it also results in a loss of species richness (−8.9%). However, analysis of sub-groups revealed inconsistent results. For example, small intensification steps within low intensity systems did not affect yield or species richness. Within high-intensity systems species losses were non-significant but yield gains were substantial (+15.2%). Conventional intensification within medium intensity systems revealed the highest yield increase (+84.9%) and showed the largest loss in species richness (−22.9%). Production systems differed