Fingerprints of High-Dimensional Coexistence in Complex Ecosystems

The coexistence of many competing species in an ecological community is a long-standing theoretical and empirical puzzle. Classic approaches in ecology assume that species fitness and interactions in a given environment are mainly driven by a few essential species traits, and coexistence can be explained by trade-offs between these traits. The apparent diversity of species is then summarized by their positions (“ecological niches”) in a low-dimensional trait space. Yet, in a complex community, any particular set of traits and trade-offs is unlikely to encompass the full organization of the community. A diametrically opposite approach assumes that species interactions are disordered, i.e., essentially random, as might arise when many species traits combine in complex ways. This approach is appealing theoretically, and can lead to novel emergent phenomena, fundamentally different from the picture painted by low-dimensional theories. Nonetheless, fully disordered interactions are incompatible with many-species coexistence, and neither disorder nor its dynamical consequences have received direct empirical support so far. Here we ask what happens when random species interactions are minimally constrained by coexistence. We show theoretically that this leads to testable predictions. Species interactions remain highly disordered, yet with a “diffuse” statistical structure: interaction strengths are biased so that successful competitors subtly favor each other, and correlated so that competitors partition their impacts on other species. We provide strong empirical evidence for this pattern, in data from grassland biodiversity experiments that match our predictions quantitatively. This is a first-of-a-kind test of disorder on empirically measured interactions, and unique evidence that species interactions and coexistence emerge from an underlying high-dimensional space of ecological traits. Our findings provide a new null model for inferring interaction networks with minimal prior information and a set of empirical fingerprints that support a statistical physics-inspired approach of complex ecosystems.

Abstract licence: CC BY

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