Occupancy Estimation Robust Design

The robust design occupancy estimation model (McKenzie et al. 2003) provides a method to estimate the rate (epsilon) at which occupied sites (plots) go extinct, or vice versa, the rate (gamma) at which unoccupied sites are occupied. The parameters of the models implemented in MARK are psi (proportion of sites occupied), epsilon (probability of an occupied site becoming unoccupied), gamma (probability of an unoccupied site becoming occupied), and p (detection probability on a visit to the site). Three implementations of the model are present in MARK. The default, which is the parameterization used when the "Robust Design Occupancy Estimation" button is clicked in initiating a new analysis, is {psi(1), epsilon(t), gamma(t), p(session, t)}. The time intervals specifed when the data are first read into MARK determine determine the number of intervals where epsilon applies, and the number of primary sessions that psi applies. The time intervals are specified the same as for the robust design data type.

The default parameterization {psi(1), epsilon(t), gamma(t), p(session, t)} does not currently generate any derived parameters. The main advantage of this parameterization is that gamma and epsilon can be constrained to the [0, 1] interval with the link function, and not affect convergence properties of the optimization. The {psi(t} epsilon{t} p(session, t)} produces derived parameters of gamma(t) and lambda(t), the ratios of consecutive occupancy rates. However, gamma is constrained to the [0, 1] interval through the penalty function approach, and for some problems, numerical convergence may be problematic. The {psi(t} gamma{t} p(session, t)} produces derived parameters of epsilon(t) and lambda(t), the ratios of consecutive occupancy rates. Here, epsilon is constrained to the [0, 1] interval through the penalty function approach, and for some problems, numerical convergence may be problematic.

To build models for the {psi(t} epsilon{t} p(session, t)} and {psi(t} gamma{t} p(session, t)} parameterizations, you change the data type from the PIM main menu. All three of these models have the same likelihood, so AICc values are comparable between them. In additiona, the Pledger mixture models have been added for all 3 of the the robust design occupancy models, and are also available with the change data type menu choice from the PIM main menu.

The usual occupancy model can also be used with robust design data by treating the primary sessions as different attribute groups, and psi estimated for each group. However, this approach to the analysis would not provide estimates of the extinction (epsilon) and recolonization (gamma) rates.