Sex as session or group for region.N

[howeer]

Good day,

We're trying to estimate the number of black bears occupying a functional island from hair snag data. We expect sigma, and possibly also Density, to vary with sex. We tried fitting secr models and estimating N with sexes modeled as different sessions, and by defining the sex of each animal using individual covariates and then grouping animals by sex using make.capthist and secr.fit. Results of secr.fit were identical regardless of how we define the sexes, but differences arose when we try to estimate N from the associated secr objects.

For example, when D~1, expected N is the same with either method, but region.N reports N as session-specific when sexes are modeled as different sessions, but N is not group-specific when sexes are modeled as groups, leaving me unsure whether total or sex-specific expected N is being reported. Furthermore, Realized N differs considerably from Expected N when sexes were defined using groups.

When D~sex and sexes are defined as sessions, results of region.N are similar to those with D~1, but when sexes are defined using groups, I get the following error message whey I try to estimate N from the secr object
Error in pmax(temp, 0) : cannot mix 0-length vectors with others

My questions are:

Is there any reason to use sessions over groups to define sexes when estimating population size, other than the apparent "problems" we encountered? I.e. should both methods give the same results if models are defined properly?

Does region.N report session-specific N when D is session-specific? What about when D is group-specific?

Thanks very much,

Eric

[murray.efford]

Hi Eric

The help for region.N says "Group-specific N has yet to be implemented", at least in the version in front of me (2.4.0). I can't remember why, but there was some subtlety my brain couldn't handle at the time.

The good news is that for mask area A, N-hat (realised or expected) is D-hat x A, and the SE of expected N also follows by multiplication (at least we claimed so in our 2012 Oikos paper). If you want the SE of realised N in the area of your mask then likewise you can just set distribution = 'binomial' and multiply SE(D-hat) by A.

Both sessions and groups are partitions of the data into independent subsets, and there should be no difference in the MLE (the maths are the same, it's just a matter of convenience). The likelihoods reported by secr may differ because of the way the constant (multinomial coefficient) is calculated (see ?logmultinom and not-quite-relevant example below), but this should not affect the estimates.

I hope this solves your immediate issue; I'm reminded this bit of region.N needs more work.
Murray

sidebar:

Code: Select all

# no groups
> sapply(ovenCH, logmultinom)
    2005     2006     2007     2008     2009
41.64247 48.47118 61.26170 38.64674 30.67186
# groups
> mapply(logmultinom, ovenCH, lapply(ovenCH, function(x) covariates(x)$Sex))
    2005     2006     2007     2008     2009
31.07733 35.09163 45.10433 28.10691 21.32699