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Environments change, for both natural and anthropogenic reasons, which can threaten species persistence. Evolutionary adaptation is a potentially powerful mechanism to allow species to persist in these changing environments. To determine the conditions under which adaptation will prevent extinction (evolutionary rescue), classic quantitative genetics models have assumed a constantly changing environment. They predict that species traits will track a moving environmental optimum with a lag that approaches a constant. If fitness is negative at this lag, the species will go extinct. There have been many elaborations of these models incorporating increased genetic realism. Here, we review and explore the consequences of four ecological complications: non-quadratic fitness functions, interacting density- and trait-dependence, species interactions and fundamental limits to adaptation. We show that non-quadratic fitness functions can result in evolutionary tipping points and existential crises, as can the interaction between density- and trait-dependent mortality. We then review the literature on how interspecific interactions affect adaptation and persistence. Finally, we suggest an alternative theoretical framework that considers bounded environmental change and fundamental limits to adaptation. A research programme that combines theory and experiments and integrates across organizational scales will be needed to predict whether adaptation will prevent species extinction in changing environments. This article is part of the theme issue ‘Integrative research perspectives on marine conservation’.

Numerous studies show that increasing species richness leads to higher ecosystem productivity. This effect is often attributed to more efficient portioning of multiple resources in communities with higher numbers of competing species, indicating the role of resource supply and stoichiometry for biodiversity–ecosystem functioning relationships. Here, we merged theory on ecological stoichiometry with a framework of biodiversity–ecosystem functioning to understand how resource use transfers into primary production. We applied a structural equation model to define patterns of diversity–productivity relationships with respect to available resources. Meta-analysis was used to summarize the findings across ecosystem types ranging from aquatic ecosystems to grasslands and forests. As hypothesized, resource supply increased realized productivity and richness, but we found significant differences between ecosystems and study types. Increased richness was associated with increased productivity, although this effect was not seen in experiments. More even communities had lower productivity, indicating that biomass production is often maintained by a few dominant species, and reduced dominance generally reduced ecosystem productivity. This synthesis, which integrates observational and experimental studies in a variety of ecosystems and geographical regions, exposes common patterns and differences in biodiversity–functioning relationships, and increases the mechanistic understanding of changes in ecosystems productivity.