Correlations of estimates in bipartite dataset

[AlexaBennett]

This is more of a feature request than an issue.

What is the correct method, statistically speaking, for testing for correlations between estimates in bipartite datasets? What if the data is non-normally distributed and requires a non-parametric test?

For example, I have data for a taxonomic marker gene and two functional potential marker genes. I want to see if the diversity overall or within covariate groups correlates with each combination of marker genes. An additional caveat is that the diversity estimates for the functional genes are commonly non-normally distributed.