The relationship between biodiversity and ecosystem functions (BEFs) has attracted great interest. Studies on BEF have so far focused on the average trend of ecosystem function as species diversity increases. A tantalizing but rarely addressed question is why large variations in ecosystem functions are often observed across systems with similar species diversity, likely obscuring observed BEFs. Here we use a multi‐trophic food web model in combination with empirical data to examine the relationships between species richness and the variation in ecosystem functions (VEFs) including biomass, metabolism, decomposition, and primary and secondary production. We then probe the mechanisms underlying these relationships, focusing on the role of trophic interactions. While our results reinforce the previously documented positive BEF relationships, we found that ecosystem functions exhibit significant variation within each level of species richness and the magnitude of this variation displays a hump‐shaped relationship with species richness. Our analyses demonstrate that VEFs is reduced when consumer diversity increases through elevated nonlinearity in trophic interactions, and/or when the diversity of basal species such as producers and decomposers decreases. This explanation is supported by a 34‐year empirical food web time series from the Gulf of Riga ecosystem. Our work suggests that biodiversity loss may not only result in ecosystem function decline, but also reduce the predictability of functions by generating greater function variability among ecosystems. It thus helps to reconcile the debate on the generality of positive BEF relationships and to disentangle the drivers of ecosystem stability. The role of trophic interactions and the variation in their strengths mediated by functional responses in shaping ecosystem function variation warrants further investigations and better incorporation into biodiversity—ecosystem functioning research.

Large variations in crown shape are observed across the globe, from plants with wide and deep crowns to those with leaves clustered at the top. While there have been advances in the large‐scale monitoring of forests, little is known about factors driving variations in crown shape with environmental conditions. Previous theoretical research suggests a gradient in crown shape with latitude, due to the effects of sun angle. Yet, it remains unclear whether such changes are also predicted under competition. Using a size‐structured forest‐growth model that incorporates self‐shading from plants and competitive shading from their neighbors, we investigate how changes in site productivity and sun angle shape crown evolution. We consider evolution in two traits describing the top‐heaviness and width‐to‐height ratio of crowns, shaped by trade‐offs reflecting the costs and benefits of alternative architectures. In top‐heavy trees, most of the leaves are at the top half of the trunk. We show that, contrary to common belief, the angle of sun beams per se has only a weak influence on crown shapes, except at low site productivity. By contrast, reduced site productivity has a strong effect, with trees growing in less productive sites keeping their leaves closer to the ground. The crown width‐to‐height ratio is generally higher at a lower site productivity, but this trait is not strongly influenced by any environmental factor. This theoretical analysis brings into question established beliefs about the effects of latitude on crown shapes. By introducing geometry‐related growth constraints caused by shading from both the surrounding forest and the tree on itself, and costs for constructing and maintaining a three‐dimensional crown, our analysis suggests crown shapes may vary with latitude, mostly via effects on overall site productivity, and less because of the angle of the sun.

In this paper, we consider a free boundary problem describing the invasion of a generalist predator into a prey population. We analytically derive the conditions guaranteeing the existence and uniqueness of the classical solution by means of the Schauder fixed point theorem, and further study the long-time behaviours of these two species. Finally, we numerically investigate the dynamical behaviour during the early invasion stage. Numerical results show that generalist predators are more likely to succeed in alien invasion by reducing the threshold size of the spatial domain of initial invasion, below which invasion fails.

No abstract