I am trying to find one p estimate for each grid sampled
Understood
The probability of catching an animal at least once is 1 minus the probability of missing it on every day, which is the product of t daily values (1-p_t), hence 1 - prod(1-p_t). For the Huggins model I think you would compute this for each individual (p_i, using the predicted p_ti for individual i) and then compute the harmonic mean of these (1 / mean(1/p_i)), but this is getting technical and I'm sorry I can't give you the MARK-specific advice you need
Murray