Abstract Exploration of the relationship between species diversity and ecological stability has occupied a prominent place in ecological research for decades. Yet, a key component of this puzzle—the contributions of individual species to the overall stability of ecosystems—remains largely unknown. Here, we show that individual species simultaneously stabilize and destabilize ecosystems along different dimensions of stability, and also that their contributions to functional (biomass) and compositional stability are largely independent. By simulating experimentally the extinction of consumer species from a coastal rocky shore, we found that the capacity to predict the combined contribution of species to stability from the sum of their individual contributions varied among stability dimensions. This implies that the nature of the diversity-stability relationship depends upon the dimension of stability under consideration, and may be additive, synergistic or antagonistic. We conclude that, though the profoundly multifaceted and context-dependent consequences of species loss pose a significant challenge, the predictability of cumulative species contributions to some dimensions of stability provide a way forward for ecologists trying to conserve ecosystems and manage their stability under global change. Methods This dataset contains species abundance matrices for monthly suveys of experimental plots at Glashagh bay, Fanad, Co. Donegal, Ireland (55°26’5’’N, 7°67’5’’W) over 15 months from May 2016. We measured the percent cover of macroalgae monthly using a 25 x 25 cm quadrat with 64 intersections, positioned centrally within cages to avoid sampling edge effects. Species present within the quadrat but not occurring underneath any of the intersections were assigned a cover value of 1%. We used the data set to quantify six components of ecological stability, separately for both total algal cover (as a proxy for total algal biomass) and assemblage structure as measures of, respectively, functional and compositional stability. Please see Table 1 and methods section in the associated manuscript for details on calculating stability measures. Usage Notes Please see readme in the datafile for explanations of experimental treatments, survey methods and species abreviations.