Occupancy Estimation with Relaxed Closure Assumption
Occupancy Estimation with Relaxed Closure Assumption
Single Season
The usual single-season occupancy model (data type 27) requires closure over the t sampling occasions. That is, the site is either occupied for the entire time, or is not occupied. The model of Kendall et al. (2013) allows the site to become occupied and then to become unoccupied later. The model has 4 parameters:
psi — probability the site is occupied. Because this is a single-season model, the psi PIM has just a single entry.
pent — given that the site is occupied during the season, the probability that the species enters the site between occasions j and j + 1. This parameter is the beta of the Kendall et al. (2013) paper. The PIM is a single row with t – 1 entries, with the last (tth) value obtained by subtraction because the sum of the pent values must be <= 1. Hence, the mlogit link is usually used the pent parameter.
d — given that the species is available for detection at the site on sampling occasion j, is the probability that it will depart the site (and therefore unavailable for detection) before sampling occasion j + 1. The PIM is a single row with t – 1 entries, as there are only t – 1 parameters.
p — the probability that the species is detected on the site, given that it is available for detection. The PIM is a single row with t entries for the t occasions.
This data type is compatible with the single-season occupancy model, so that you can run both the usual model and the relaxed closure model in the same Results Browser. To jump between these data types, use the Change Data Type menu choice under the PIM menu entry. Other single season occupancy models are also available with Change Data Type.
The addition of parameters to allow entry and departure of the species from the site means that a number of the parameters are not identifiable with a fully time-specific model. One reasonable approach is to fit the time-specific pent parameters with a quadratic function in the design matrix. Otherwise, constant d or constant p models might be considered.
Also, this model is a mixture model built on top of another mixture model, so you should be careful to check for multiple optima. The Simulated Annealing optimization method should be used routinely to check your results.
Four derived parameters are provided: residence time, probability of presence (alpha) for each occasion, and the mean arrival time and the mean departure time.
Multiple Seasons
The multiple-season occupancy model (Chambert et al. 2015) extends the psi, epsilon, and gamma (data type 30) multiple-season occupancy model for each primary occasion as described above for the single season occupancy model with relaxed closure. The pent parameter should normally have the mlogit link function.
The same 3 derived parameters as the multi-season models are included as well as the probability of presence (alpha) for each secondary occasion, mean arrival time for each primary occasion, and mean departure time for each primary occasion.