POPAN - fixing PENTs

[caspar]

Dear all,

I'm making an attempt to estimate abundance over multiple groups using the POPAN formulation. Not all groups were sampled at all occasions (specifically one group has not been sampled the first two occasions) so I am considering to fix group specific PENT and p parameters when no sampling took place.
On page 17 from chapter 14 I read "It is possible to specify that some of the PENTs are zero if, for example, the experimenter knew that no new animals entered the study population during this interval."
I would like for example to explain to MARK that it is not possible to obtain a probability of entrance for occasion 1 because i never sampled that particular group at that occasion. However "...MARK does not allow the user to specify the parameter b0 (the proportion of the population available just before the first sampling occasion) and so only presents 7 PENT parameters in the PIM..." (at page 16), and this counts also for the fixing part.

Does anyone have suggestions on how I would get around this one?

Thanks in advance
Caspar

[cschwarz@stat.sfu.ca]

Just because you didn't sample a group at occasion 1, doesn't mean that it didn't exist prior to occasion 1. Forcing $\beta_0$ to be 0 would imply that the population didn't exist in your study area prior to the first sampling occasion which likely isn't what you want.

It is true that if you don't sample at some occasions, that some parameters will become confounded. For example, if you don't sample at occasion 3, only the product of $\phi_2$ $\phi_3$ is estimable in a $\phi(t)$ model.

Similarly, if you don't sample at time 1, some combination of $\beta_0$, $p_1$, $\phi_1$, and $\beta_1$ is only estimable. [You would have to write out some capture histories to see which parameters can't be separated.] So I would force $\beta_1$ to be 0 for that group and then $\beta_0$ will likely pick up all of the confounded parameters as a single parameter.

Note that if you don't sample at time 1, then $N_2$ is likely not estimable for that group as well.

Carl Schwarz