The inherent multidimensionality of temporal variability: How common and rare species shape stability patterns

Empirical knowledge of ecosystem stability and diversity-stability relationships is mostly based on the analysis of temporal variability of population and ecosystem properties. Variability, however, often depends on external factors that act as disturbances, making it difficult to compare its value across systems and relate it to other stability concepts. Here we show how variability, when viewed as a response to stochastic perturbations, can reveal inherent stability properties of ecological communities, with clear connections with other stability notions. This requires abandoning one-dimensional representations, in which a single variability measurement is taken as a proxy for how stable a system is, and instead consider the whole set of variability values associated to a given community, reflecting the whole set of perturbations that can generate variability. Against the vertiginous dimensionality of the perturbation set, we show that a generic variability-abundance pattern emerges from community assembly, which relates variability to the abundance of perturbed species. As a consequence, the response to stochastic immigration is governed by rare species while common species drive the response to environmental perturbations. In particular, the contrasting contributions of different species abundance classes can lead to opposite diversity-stability patterns, which can be understood from basic statistics of the abundance distribution. Our work shows that a multidimensional perspective on variability allows one to better appreciate the dynamical richness of ecological systems and the underlying meaning of their stability patterns.