Apologies, I know this is not the most appropriate forum to post this as it's a community ecology question more than anything else, but I'm having trouble even coming up with the right keywords to search for this. 

I have a microbial community dataset that I'm analyzing in phyloseq. I want to see if there are any pairs of OTUs that tend NOT to be found in the same sample or whose relative abundance in a sample is negatively correlated (leading to the hypothesis that one OTU competitively excludes the other). I imagine this would require calculating a matrix in which, for each pair of OTUs, there is a value reflecting the number of samples that contain both species and/or the two species' evenness in that sample, and a statistical test to calculate if this value is unusually low for a given pair. 

So basically rather than calculating the number of jointly-occuring species for each pair of samples, I want to calculate the probability of being found in the same sample for each pair of species. I know I've read about similar tests, but I'm failing to find anything. Is there a way to do something similar in vegan/phyloseq?