Mixtures of stably coexisting species overyield

Diverse plant communities usually produce more biomass than monocultures, an advantage that strengthens over time and is attributed mainly to the complementarity effect - the extra biomass produced, relative to monocultures, when species exploit different resources, share fewer enemies or facilitate one another. Yet whether this advantage is a mere tendency of diverse communities, or something that every persistent community must have, has remained unknown. Here we show that stable coexistence requires a positive complementarity effect, with vanishingly rare exceptions, and that underyielding communities are significantly more likely to lose a species within two years or sampling steps, across four long-term biodiversity experiments, with odds of losing a species nearly three times higher than in other communities. In the twenty-five years since the complementarity effect was defined, the link between biodiversity effects and species coexistence had only been established theoretically for two species in competition or observed as a correlation; our theoretical result makes it a general property of multispecies communities, in which the complementarity effect scales with two established measures of how securely species coexist - local and structural stability. Our analyses are, to our knowledge, the first to test a coexistence prediction - impending species loss - prospectively in biodiversity experiments, from a functioning measure alone, turning a measure of what diversity does into a diagnostic of whether diversity can persist. Stable coexistence and higher productivity are thus intrinsically linked: biodiversity does not merely benefit ecosystem production on average; biodiversity that endures cannot but benefit it through complementarity. We anticipate that this diagnostic will turn existing biodiversity experiments, sown grasslands and intercrops into early-warning systems for species loss, since it requires only the biomass of each species in mixture and in monoculture - data these systems already collect, and that agronomists already combine into the land equivalent ratio - and that it will extend to forests, through the growing networks of tree diversity experiments and mixed-species plantations where the same measurements are made.