Single vs multi-season occupancy models

[ekalies]

I have 3 years of data, 3 surveys per year, for a bunch of bird species. I can't quite understand what the difference is if I run, per species:

a single-season occupancy model where I stack the data, so that there is a total of 3 visits and year is a covariate (so the 3 years are stacked)

or

A multi-season occupancy model where I display the data as 3 seasons, 3 visits each, for a total of 9 surveys.

For the single-season model I ran it with year as a covariate (detection constant), and for the multi-season model I used the parametrization that derives yearly occupancy and colonization, and applied a year effect to occupancy (colonization and detection constant).

In running the two models, I got very similar estimates of occupancy for each of the three years (.87, .97, .99 versus .86, .99, .97). The confidence intervals were tighter using the single season model.

All I want out of this is estimates of occupancy; I'm not particularly interested in year effects (although obviously I want to account for yearly changes) or colonization/extinction rates; rather, the habitat covariates are my primary interest and they don't change over time (aka, no treatment was applied during the 3 years or other major changes- I would only expect weather-related impacts).

I realize there is pseudo-replication with including the same sites over and over again as separate observations in the single-season model, but I can deal with that by using UTMs (transformed) as a covariate, I didn't mention it above for simplicity. Otherwise, my basic question remains- what is the difference, exactly? thanks for any help, this has been troubling me for a while now!

[darryl]

By stacking your years you're essentially assuming changes in the presence/absence of the species occur at random, ie all units have the same probability of being occupied regardless of their occupancy state in the previous season. Even if not true, this model may give you reasonable estimates of occupancy each year, but not about underlying processes, or factors that actually are driving occupancy in the longer term; you're only able to determine what factors correlate with presence/absence of the species in each year.

Now the multi-season model was developed so you can start thinking more about processes rather than patterns. If you don't want to think about them as colonization and persistence (the complement of extinction), you can just think of them as 2 different types of occupancy, 1 for units that were unoccupied last season and 1 for units that were occupied. So now you can consider questions like, does the probability of a unit currently being occupied depend upon whether the unit was occupied in the previous season or not. Or, are the factors (eg habitat) that drive occupancy the same for units that were occupied or not in the previous season.

Cheers
Darryl