So I'm trying to run an NMDS (using the vegan package in R) for a species X site matrix. Unfortunately the abundances of species are not inherently equal (If you can use that word) meaning that not all the sites had equal sampling efforts for this data. Therefore I standardized the abundances of everything by dividing the abundance by the number of months that were actively sampled per site. For example, if site A only sampled 5 out of 12 months and had an abundance of 30 for species B, then the new standardized value would be 30/5 or 6. I realized that when I run the NMDS, the default method in vegan is to utilize bray-curtis distances to calculate distances between sites in terms of dissimilarity or turnover. My question is: Can we use that measure of beta diversity for data that has now been altered and don't reflect true abundances but rather abundances per sampling effort? Maybe the better question is: Is it right to do so? If not then what other sort of measure should I be using.
You can use "abundances per sampling effort" to calculate Bray-Curtis distances. However, it does not account for the fact that you are more likely to have higher species richness in the more intensively sampled sites. Whenever you sample a site, there will be species you don't detect - at sites where you have sampled 12 months you are more likely to have found rare species than sites that you have only sampled for 5 months. When you turn each count into a proportion there is still a difference between zero and non-zero proportions for those rare species.
Instead of normalizing through proportions, you can use rarefaction. This works by randomly removing sampling from your more intensively sampled sites until all sites have the same (lowest) sampling effort. The downside of this is that you lose a fair bit of your data, and so lose some power for distinguishing differences between sites. There are papers recommending alternatives to rarefying if you're interested, but the methods are often quite complex and less intuitive.