realized N with spatial variation in D

[howeer]

Thanks for the response to my last post, I'll model the sexes using sessions.

We seek a precise estimate of the number of animals (black bears) occupying a functional island that was sampled throughout exept for a couple of potential "holes". Inference is limited to the sampled population, so we wish to treat N as fixed and exclude process variation in N. Is it necessary to specify details$distribution when fitting the secr model, or can we use the poisson distribution when fitting models and still exclude process variation by reporting realized N?

Furthermore, we suspect that density varies spatially within B, and the number animals occupying a National Park at the north end of B is of interest, so we're interested in modeling the density surface with spatial covriates. If we include spatial variation in D in the secr model (for example D~y), is the sampling variance of realized N from region.N still comparable to the sampling variance of a conventional closed capture-recapture model?

Thanks in advance,
Eric

[murray.efford]

Is it necessary to specify details$distribution when fitting the secr model, or can we use the poisson distribution when fitting models and still exclude process variation by reporting realized N?

The latter, I think. You have a choice between estimating 'expected N' under the fixed-N model [details=list(distribution = 'binomial'] or 'realised N' under the Poisson-N model [the default]. The table in Efford & Fewster App 2 may help clarify my terms.

Furthermore, we suspect that density varies spatially within B, and the number animals occupying a National Park at the north end of B is of interest, so we're interested in modeling the density surface with spatial covriates. If we include spatial variation in D in the secr model (for example D~y), is the sampling variance of realized N from region.N still comparable to the sampling variance of a conventional closed capture-recapture model?

I can't give a definite answer on the effect of extra terms in the D model on the variance of the estimate of realised N. Probably it will depend on the data. E&F Fig 4 suggests for one dataset that the relative SE of realised N in region S from inhomogeneous density models was of similar magnitude to that from nonspatial estimators.

I think the bigger problem is that you are trying to get a variance for realised N in a subregion B of the 'functional island' which I assume is your area of integration (region S in E&F). That doesn't work because we cannot be sure which of the n detected animals belong to B, so we cannot strictly compute a variance for realised N (of course, expected N is fine). Or maybe I just misunderstand your scenario.

Murray

[howeer]

Thanks very much Murray,

Our main objective is estimating the population occupying the entire functional island, which was sampled throughout. All (or nearly all) individuals in the population of interest were at risk of capture, all of the detected animals belong to B, and S and B coincide, so I think realized N applies.

Of secondary interest is the population size occupying a National Park (a spatial subset of both S and B). Expected N within that region will certainly suffice for our purposes.

Have a good weekend,
Eric