Keystoneness, centrality, and the structural controllability of ecological networks

An important dimension of a species' role is its ability to alter the state and maintain the diversity of its community. Centrality metrics have often been used to identify these species, which are sometimes referred as “keystone” species. However, the relationship between centrality and keystoneness is largely phenomenological and based mostly on our intuition regarding what constitutes an important species. While centrality is useful when predicting which species' extinctions could cause the largest change in a community, it says little about how these species could be used to attain or preserve a particular community state. Here we introduce structural controllability, an approach that allows us to quantify the extent to which network topology can be harnessed to achieve a desired state. It also allows us to quantify a species' control capacity—its relative importance—and identify the set of species that are critical in this context because they have the largest possible control capacity. We illustrate the application of structural controllability with ten pairs of uninvaded and invaded plant‐pollinator communities. We found that the controllability of a community is not dependent on its invasion status, but on the asymmetric nature of its mutual dependences. While central species were also likely to have a large control capacity, centrality fails to identify species that, despite being less connected, were critical in their communities. Interestingly, this set of critical species was mostly composed of plants and included every invasive species in our dataset. We also found that species with high control capacity, and in particular critical species, contribute the most to the stable coexistence of their community. This result was true, even when controlling for the species' degree, abundance/interaction strength, and the relative dependence of their partners. Synthesis. Structural controllability is strongly related to the stability of a network and measures the difficulty of managing an ecological community. It also identifies species that are critical to sustain biodiversity and to change or maintain the state of their community and are therefore likely to be very relevant for management and conservation. Structural controllability is strongly related to the stability of a network and measures the difficulty of managing an ecological community. It also identifies species that are critical to sustain biodiversity and to change or maintain the state of