Hi Emily,
Thanks for the kind words about the package! Your interpretation is close, but it is not completely correct. The community-level occupancy mean parameters in an occupancy model are best interpreted as the
average effect of the covariate across the community. So, if there is a significant negative effect of a covariate at the community-level, I would interpret this as something along the lines of "on average across all species in the community, it is less-likely for a species to be present at high values of the covariate and more likely for it to be present at low values of the covariate." So, it is not so much the presence/absence of the entire community of species, but rather looking at the average patterns across the community. However, even with a significant community-level average effect, there can still be species that don't show that same pattern, in which case you could look at the species-specific effects. The community-level variance parameters give an indication as to how much variation there is the relationship among the species in the community from the overall mean. The higher the variances are, the more variation there is across species in the community. The smaller the variance, the less variation there is across species (and thus they would all be very close to the community-level mean). Figure 1 in our
manuscript on spAbundance tries to show this idea. That figure is for a multi-species distance sampling model, but the concept is analogous to the case with multi-species occupancy models.
Kind regards,
Jeff