An ecosystem's stability is postulated to increase as its number of species goes up, owing to the increased number of interactions between those species and the subsequent robustness of the ecological network.
Carl Simpson and Wolfgang Kiessling of the Berlin Museum of Natural History propose an explanation for this relationship on evolutionary timescales. They say the 'diversity–stability' relationship can be explained solely by the extinction of species: high species turnover needs to be buffered by higher species numbers.
If this is true, then the diversity–stability relationship should be strongest when the extinction rate is high. Looking at historical coral reef data, they found that the relationship was historically strong during periods of high extinction, and weak during low-extinction periods.