One paper used 39 biodiversity experiments to test the relationship between diversity and stability across scales. In particular, we tested and verified one key prediction by Wang & Loreau (2016 Ecology Letters), namely beta diversity can lead to a higher spatial asynchrony and thus stabilize ecosystems at large scales. This finding provides insights for understanding the implications of ongoing biotic homogenization.
The other paper used Lotka-Volterra model to understand how complementarity and selection - the two major processes underlying biodiversity effects on ecosystem functioning - affect ecosystem stability as measured by invariability, resistance and resilience. Theory predicts that complementarity promote stability, whereas selection impairs it. Thus, ecosystem functioning and stability can exhibit either a synergy or a trade-off, depending on the dominating processes.