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I don’t think there’s an easy way to do that, but there are a few somewhat complicated ways you could try.
This search will show observations in Big Cypress National Preserve that are unique: https://jumear.github.io/stirfry/iNatAPIv1_observations_species_counts.html?order=asc&place_id=95106&rank=species (just scroll down until taxon obs count changes to 2)
So there are currently 450 species only observed once, but you’ll have to do more to filter it by user. You can copy/paste the text off that page, process the json from the API yourself, or maybe if we ask nicely, @pisum will add an export tool.
Once you have the list of 450 unique species, I would import that back into iNat as a list, and then use the list_id as a search parameter. Since each species is unique, every observation returned shows the only user to have seen that species at that location. If you add yourself as a search parameter, it should return only species in Big Cypress that you (and no one else) have seen.
It’s not ideal if you want to be able to do it repeatedly, but I think it should get the job done.
Edit: I realized that it won’t find species that no one else has observed, but that you have observed more than once. I’ll have to think about that…