@rachel_haupt if I had 10 cents for every diversity metric I’ve stumbled across, I’d have … a lot of dimes. While I found the link that @jwdebelius recommended very useful, that post doesn’t illustrate all the different equations each metric is using in one place. When I was getting started with diversity measures this made it challenging to understand which metrics are more similar to each other, and what assumptions I was making in adopting that metric.
For instance, the Jaccard index is not unweighted, nor is the Bray-Curtis metric, so both can be used with abundance data. They are similar in spirit but differ in that one index (Bray-Curtis) weights the abundances of shared species more. To complicate things, both can work on (unweighted) presence-absence data. And if you want to run the Bray-Curtis values on unweighted data, you’re technically running a Dice-Sorenesen index.
I’ve found Anne Choa’s writings really clear - this paper helped me a lot in thinking about the appropriateness of a range of beta diversity metrics. You might also find this article helpful insofar as it is quite comprehensive in thinking about all the ways you could evaluate how any two metrics are similar or different from one another.