  How do any of these measures of stability relate to diversity? The only honest answer is that no one is sure. If diversity is interpreted as richness, traditionally, it was commonly assumed that diversity is positively correlated with at least persistence. However, there was never much hard evidence supporting this assumption. If stability is interpreted as a return to equilibrium, mathematical models that should answer questions about stability are easy to construct but hard to analyze unless the system is already close to equilibrium. This is called local stability analysis. The most systematic analyses performed so far give no straightforward positive  correlation.[48]  It was once believed that natural ecosystems are usually at equilibrium (the “balance of  nature”).[49]  But ample empirical data now suggests that this assumption is almost never correct: natural ecosystems are usually far from  equilibrium.[50]  Moreover, if natural selection between species occurs during the transition to equilibrium, equilibrium communities will be less rich than those that are yet to reach equilibrium. On short time scales (short enough to make speciation unlikely), selection between species that utilize the same resources (that is, they occupy the same “niche”) will lead to the exclusion of the less fit by the more fit through “competitive  exclusion.”[51]  The eventual equilibrium community, one in which selection would no longer be acting, the (controversially) so-called “climax community,” is necessarily less rich than those that temporally preceded it.