After seeing the input data and models, I've figured out what is going on. All the animals were released on the first occasion, so that means there are 2^5 = 32 possible encounter histories. Only 10 of these were observed because p=1 for the first 2 occasions. And for most of the 4 groups, fewer were observed.

To keep this simple, consider just a single group with p=1 for each occasion. MARK computes the DF of the data by assuming a multinomial distribution for each cohort. Further assume p = 1, so only 6 histories are possible, giving 5 DF. The global model of {phi(t) p(t)} has 9 parameters if you let p be estimated. Thus, 5 - 9 = -4, and negative DF for the deviance. But this situation is more subtle than that given that we are interested in GOF. What you actually have are 5 binomial distributions, i.e., animals that are alive at each occasion either survive or not for 5 occasions. There is no GOF possible because you have fit a saturated model. All 5 DF in the data are estimated by the 5 parameters.

So for the actual data with all releases at occasion 1, there were 10 observed values over 4 groups. Given that the DF for the multinomial is 1 less than the number of cells in the multinomial distribution, there there are 9 DF for each group, except that not all groups had each of the 10 observed encounter histories. But to make this simple again, assume that each group contributes 9 DF, giving 36 DF from the data. Then when you fit the {phi(g*t) p(g*t)} global model, you have 36 parameters. So you would have 0 DF for GOF, again because of p=1 removes DF from the data.

The result is that you are not fitting a saturated model like described above for all occasions with p=1, but you are coming close. The negative DF is telling you that you have no DF for GOF. Were you to run the data one group at a time, you might have 1 or more of the groups with a GOF test, but the rest would be saturated models with no GOF possible.

In summary, if you really have data with p=1, then thinking about the data as a known fate model makes it clear that you are fitting a saturated model. For the actual data here, you have some hybrid between the CJS and known fate model.

Gary