I believe that many researchers use closed models when populations are not geographically closed, and then innappropriately use individual covariates of capture probability for such characteristics as sex and age, when in fact apparent differences in capture probability are due to temporary emigration, i.e. the animals of different sexes/ages may have similar probabilities of capture, but due to differences in home range dynamics/mobility, spend different amounts of time on the sampling grid.
For example, bear populations are often enumerated by hair-snagging and closed population modeling. Densities are then calculated by estimating the area trapped using FEMALE home range data, and dividing the total abundance estimate (both sexes) by that area.

Male bears might commonly traverse the entire "area trapped", leaving and reentering it frequently, because they have much larger home ranges.
What are the implications for population size estimates of assuming all animals remain on the sampling grid but have different probabilities of capture, when in fact they have different probabilities of remaining on the grid? Is there any way to detect the difference using closed models and remotely sampled data?