Fig. 1: The stability framework.

Panels illustrate the different components of stability and asynchrony obtained from reef fish abundance data at the community (a) and metacommunity (b–f) levels of organization. Two sites, each including one population of two species, are used throughout to illustrate the derivation of stability and asynchrony measures from timeseries of fish abundance. Stability is indicated as the ratio between the temporal mean and standard deviation of fish abundance (µ/σ), whereas η indicates asynchrony. a Alpha stability, species stability and species asynchrony; \({\mu }_{i,j}\) and \({\sigma }_{i,j}\) are the temporal mean and standard deviation of species j at site i, respectively. b Average alpha stability (AAS) and spatial community asynchrony (SCA) calculated from total fish abundance between two sites. c Average species stability (ASS) and average species asynchrony (ASA) calculated from the two populations of each species and then averaged between species. d Spatial species asynchrony (SSA) quantified as the average dissimilarity of temporal fluctuations between populations. e Metapopulation stability (MPS) and metapopulation asynchrony (MPAS), calculated from total population abundance and averaged across species. f Gamma stability (GAS) obtained by dividing the temporal mean of total metacommunity abundance by its standard deviation. Arrows pointing to this panel indicate the positive contribution of stability and asynchrony at lower organizational levels to gamma stability. Pink and green ovals indicate whether timeseries were aggregated among species within sites (b, c), among populations in the metacommunity (d) or among metapopulations (e) to derive stability and asynchrony measures. Panels indicate the equations (Eq) used to calculate the various stability and asynchrony measures, which are described in full in Methods.