Summary: The relationship between species richness and ecosystem function, as measured by productivity or biomass, is of long‐standing theoretical and practical interest in ecology. This is especially true for forests, which represent a majority of global biomass, productivity and biodiversity. Here, we conduct an analysis of relationships between tree species richness, biomass and productivity in 25 forest plots of area 8–50 ha from across the world. The data were collected using standardized protocols, obviating the need to correct for methodological differences that plague many studies on this topic. We found that at very small spatial grains (0.04 ha) species richness was generally positively related to productivity and biomass within plots, with a doubling of species richness corresponding to an average 48% increase in productivity and 53% increase in biomass. At larger spatial grains (0.25 ha, 1 ha), results were mixed, with negative relationships becoming more common. The results were qualitatively similar but much weaker when we controlled for stem density: at the 0.04 ha spatial grain, a doubling of species richness corresponded to a 5% increase in productivity and 7% increase in biomass. Productivity and biomass were themselves almost always positively related at all spatial grains. Synthesis. This is the first cross‐site study of the effect of tree species richness on forest biomass and productivity that systematically varies spatial grain within a controlled methodology. The scale‐dependent results are consistent with theoretical models in which sampling effects and niche complementarity dominate at small scales, while environmental gradients drive patterns at large scales. Our study shows that the relationship of tree species richness with biomass and productivity changes qualitatively when moving from scales typical of forest surveys (0.04 ha) to slightly larger scales (0.25 and 1 ha). This needs to be recognized in forest conservation policy and management.

Habitat complexity has been considered a key driver of biodiversity and other ecological phenomena for nearly a century. However, there is still no consensus over the definition of complexity or how to measure it. Up‐to‐date and clear guidance on measuring complexity is urgently needed, particularly given the rise of remote sensing and advent of technologies that allow environments to be scanned at unprecedented spatial extents and resolutions. Here we review how complexity is measured in ecology. We provide a framework for metrics of habitat complexity, and for the related concept of spatial heterogeneity. We focus on the two most commonly used complexity metrics in ecology: fractal dimension and rugosity. We discuss the pros and cons of these metrics using practical examples from our own empirical data and from simulations. Fractal dimension is particularly widely used, and we provide a critical examination of it drawing on research from other scientific fields. We also discuss informational metrics of complexity and their potential benefits. We chart a path forward for research on measuring habitat complexity by presenting, as a guide, sets of essential and desirable criteria that a metric of complexity should possess. Lastly, we discuss the applied significance of our review.

To estimate species loss from habitat destruction, ecologists typically use species–area relationships, but this approach neglects the spatial pattern of habitat fragmentation. Here, we provide new, easily applied, analytical methods that place upper and lower bounds on immediate species loss at any spatial scale and for any spatial pattern of habitat loss. Our formulas are expressed in terms of what we name the ‘Preston function’, which describes triphasic species–area relationships for contiguous regions. We apply our method to case studies of deforestation and tropical tree species loss at three different scales: a 50 ha forest plot in Panama, the tropical city‐state of Singapore and the Brazilian Amazon. Our results show that immediate species loss is somewhat insensitive to fragmentation pattern at small scales but highly sensitive at larger scales: predicted species loss in the Amazon varies by a factor of 16 across different spatial structures of habitat loss.

MacArthur and Wilson's theory of island biogeography predicts that island species richness should increase with island area. This prediction generally holds among large islands, but among small islands species richness often varies independently of island area, producing the so-called ‘small-island effect’ and an overall biphasic species–area relationship (SAR). Here, we develop a unified theory that explains the biphasic island SAR. Our theory's key postulate is that as island area increases, the total number of immigrants increases faster than niche diversity. A parsimonious mechanistic model approximating these processes reproduces a biphasic SAR and provides excellent fits to 100 archipelago datasets. In the light of our theory, the biphasic island SAR can be interpreted as arising from a transition from a niche-structured regime on small islands to a colonization–extinction balance regime on large islands. The first regime is characteristic of classic deterministic niche theories; the second regime is characteristic of stochastic theories including the theory of island biogeography and neutral theory. The data furthermore confirm our theory's key prediction that the transition between the two SAR regimes should occur at smaller areas, where immigration is stronger (i.e. for taxa that are better dispersers and for archipelagos that are less isolated).