Accounting for 0 observations in presence/absence community data, PCoA/PCA: is this idea credible? I have a solution in mind for this problem, but I'm not sure if it is defensible (which is why I'm asking you all!). I have a data frame where each row represents an individual site, each column represents an individual species, and the data in each column is 0 or 1 for absence or presence of the species. For example:




Species 1
Species 2
Species 3




1
0
0


0
0
0


1
1
1




I am working on creating a PCoA figure showing the different community structures in each row. From what I see online, the best way to do this is to use the vegan package, first calculating the dissimilarity indices using the Jaccard index (because of the presence/absence) in the dist() function, followed by the actual PCoA calculation.
Here's the issue: my data frame has some rows where no species was observed, and dissimilarity indices are not equipped to handle sites where everything is 0. Recommendations from what I've seen online say to exclude these rows, but I'd like to keep these in (I'd lose a lot of information, otherwise). The solution I thought of is to include a new "dummy species," (a.k.a Species 4), that doesn't actually exist in real life but has a presence of 1 when every other species is absent and has a presence of 0 when at least 1 other species is present.  This would allow me to calculate dissimilarity indices while including all my data, and the rows of complete absence would still be "different" enough to be accounted for in the PCoA.
Is this actually a good idea? I haven't found any papers that I can cite to defend this thought, but I also can't think of any reason why it wouldn't work. If I'm making some hideous statistic mistake that I'm unaware of, do you have any other ideas on how to account for the 0 rows?
Thank you all!

The direct answer to your question: the idea is not credible.
Jaccard – as most other indices of compositional community dissimilarity – cannot be assessed if there is no community. You do not have information of non-existent communities and you will lose nothing if you remove the information you do not have.
There are several indices that are not based on composition, but on absolute abundances. These treat all non-existing communities (all zeros) as identical (which is non-sense) and presence of any species as indication of difference to empty. Usually this makes little ecological sense.
Things change in constrained (a.k.a canonical) analysis where you "explain" community with external variables (constraints, covariates). With these you can also explain "emptiness" or missing species.
There may be papers that defend your suggested approach, but I hope you do not find and use them: I think your approach cannot be defended.
