I have occupancy data for two vole species, in 347 habitat patches. We only made one survey per patch, but we recorded time to first detection for presence signs of both species and stopped the survey once both species were detected (or continued to a maximum amount of time if at least one of the species was not detected). The maximum survey time was variable and dependent on the patch size.
Since the information that we have is the time to first detection, we opted to apply a removal sampling design to our data, by dividing the total survey time in each patch in equal intervals and consider each interval a different survey. Since the time to first detection for both species is different, we also have two distinct detection histories for each vole species. For example, in a single patch, if species A was detected in the first time interval, we have a history 1----- ; and if species B was not detected we can have a history 00000.
I tried to run a two-species, single-season model with this data. The input data was formatted by doubling the number of sites, with 694 records, where the first 347 were from species A and records 348-694 were from species B. With this input data, the resulting models (and different parameterizations) do not converge and give pretty strange results (in comparison with the single-species models, and even the naive occupancy estimates are wrong).
I tried a different approach, where I coded the data as 0 = no detection of either species, 1 = detection of species A only, 2 = detection of species B only, 3 = detection of both species. However, in this case, whenever I had a patch where both species were not detected in the same timey interval, I had to “force” false detections after the first detection of the first species to be detected, until the first detection of the second species. The results of this model were much better (and agree with single-species model results), but, as expected, the detection probability was overestimated (around 0.96 for both species, where the detectability in the single-species models was 0.79 and 0.82).
So my question is:
Is there any problem in applying removal sampling with two species models, or the problem is specifically with my dataset (too much variability in the number of time intervals between both species, maybe?)? How can I get around this?
Any advice will be greatly appreciated.
Helena Sabino-Marques