Intensified exploitation of natural populations and habitats has led to increased mortality rates and decreased abundances of many species. There is a growing concern that this might cause critical abundance thresholds of species to be crossed, with extinction cascades and state shifts in ecosystems as a consequence. When increased mortality rate and decreased abundance of a given species lead to extinction of other species, this species can be characterized as functionally extinct even though it still exists. Although such functional extinctions have been observed in some ecosystems, their frequency is largely unknown. Here we use a new modelling approach to explore the frequency and pattern of functional extinctions in ecological networks. Specifically, we analytically derive critical abundance thresholds of species by increasing their mortality rates until an extinction occurs in the network. Applying this approach on natural and theoretical food webs, we show that the species most likely to go extinct first is not the one whose mortality rate is increased but instead another species. Indeed, up to 80% of all first extinctions are of another species, suggesting that a species' ecological functionality is often lost before its own existence is threatened. Furthermore, we find that large-bodied species at the top of the food chains can only be exposed to small increases in mortality rate and small decreases in abundance before going functionally extinct compared to small-bodied species lower in the food chains. These results illustrate the potential importance of functional extinctions in ecological networks and lend strong support to arguments advocating a more community-oriented approach in conservation biology, with target levels for populations based on ecological functionality rather than on mere persistence.

Global warming leads to increased intensity and frequency of weather extremes. Such increased environmental variability might in turn result in increased variation in the demographic rates of interacting species with potentially important consequences for the dynamics of food webs. Using a theoretical approach, we here explore the response of food webs to a highly variable environment. We investigate how species richness and correlation in the responses of species to environmental fluctuations affect the risk of extinction cascades. We find that the risk of extinction cascades increases with increasing species richness, especially when correlation among species is low. Initial extinctions of primary producer species unleash bottom-up extinction cascades, especially in webs with specialist consumers. In this sense, species-rich ecosystems are less robust to increasing levels of environmental variability than species-poor ones. Our study thus suggests that highly species-rich ecosystems such as coral reefs and tropical rainforests might be particularly vulnerable to increased climate variability.

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The ecological importance of common species for many ecosystem processes and functions is unquestionably due to their high abundance. Yet, the importance of rare species is much less understood. Here we take a theoretical approach, exposing dynamical models of ecological networks to small perturbations, to explore the dynamical importance of rare and common species. We find that both species types contribute to the recovery of communities following generic perturbations (i.e. perturbations affecting all species). Yet, when perturbations are selective (i.e. affects only one species), perturbations to rare species have the most pronounced effect on community stability. We show that this is due to the strong indirect effects induced by perturbations to rare species. Because indirect effects typically set in at longer timescales, our results indicate that the importance of rare species may be easily overlooked and thus underrated. Hence, our study provides a potential ecological motive for the management and protection of rare species.