How collectively integrated are ecological communities?
Beyond abiotic conditions, do population dynamics mostly depend on the species direct predators, preys and conspecifics? Or can indirect feedbacks that ripple across the whole community be equally important? Here we show that the spectral radius of a communitys interaction matrix controls the length of indirect interaction pathways that actually contribute to community-level dynamical patterns, such as the depth of a perturbations reach, or the contribution of biotic processes to realized species niches. The spectral radius is a measure of collectivity that integrates existing approaches to complexity, interaction structure and indirect interactions, while also being accessible from imperfect knowledge of biotic interactions. Our work provides an original perspective on the question of to what degree communities are more than loose collections of species or simple interaction motifs; and explains when reductionist approaches focusing on particular species and small interaction motifs, ought to suffice or fail when applied to ecological communities.