Occupancy Estimation
Occupancy Estimation
Estimation of the percent occupancy of a species at a set of sites (plots) is complicated by probability of detection < 1. To estimate the percent occupancy, a set of sites (plots) are surveyed for t occasions to determine if a plot is occupied by the species of interest. This model has real parameters of the detection probability [p(i)] for each i =1, …, t occasions, and the proportion of the plots occupied (psi). The model is most easily understood with an example for t = 2 occasions. The cell probabilities for each of the 4 possible encounter histories are:
11 psi*p(1)*p(2)
10 psi*p(1)*[1 – p(2)]
01 psi*[1 – p(1)]*p(2)
00 psi*[1 – p(1)]*[1 – p(2)] + (1 – psi)
Thus, as shown for the “00” encounter history, a site may contain the species but not be detected with probability [1 – p(1)]*[1 – p(2)], or the site may not be occupied with probability 1 – psi. Note that sites must be resurveyed even after a positive detection in made in order to estimate the probability of detection. Otherwise, the probability of detection and the occupancy rate are confounded.
This model is particularly useful with individual covariates, because the probability of occupancy (psi) can likely be explained by site-specific covariates. However, site-specific covariates may also be useful for modeling the detection probability.
Missing observations are allowed in this model, specified by a period (.).. For example, suppose for t = 4 occasions, that the survey on occasion 3 was not conducted because of a truck breakdown. Then the encounter history 10.1 would mean that the species was detected on occasions 1 and 4, not detected on occasion 2, and was not surveyed for on occasion 3.
Details of the formulation of this model and some simulation results are published by MacKenzie et al. (2002). MacKenzie et al. (2003) have also extended the model to a robust design occupancy model.
Individual Heterogeneity for p
The Pledger mixture model has been added to MARK to model individual heterogeneity around the p values, and this model is available with the Change Data Type option under the PIM menu choice. Typically 5 or more occasions would be needed to detect this sort of individual heterogeneity.
Another approach to handling individual heterogeneity of p is the incorporation of a normally distributed random error on the logit scale, and then numerically integrating out this random error using Gauss-Hermite numerical quadrature (McClintock and White 2009, Gimenez and Choquet 2010). This estimator has also been added to MARK. As with the Pledger mixture models, 5 or more occasions would typically be required to detect this sort of individual heterogeneity.
The Royle and Nichols (2003) model is also available with the Change Data Type option under the PIM menu choice. Two flavors of this model are provided: Poisson and negative binomial. This model also is modeling individual heterogeneity in p by assuming p changes with the number of animals available on a site. That is, the more animals available to detect and demonstrate occupancy, the higher the value of p should be.
The Royle (2004) Poisson and Negative Binomial models are also available, but are not compatible with the other occupancy models because the encounter histories are entered as the count of animals observed on each occasion.
The Kendall et al. (2013) occupancy model with relaxed closure assumption is also available.
Multiple Scale Occupancy
The multi-scale occupancy estimator is implemented in MARK (Nichols et al. 2008). To use this data type, select it from the list that comes up when the occupancy button is clicked on the list of data types. Although this model includes both “1” and “2” values to identify states of occupancy, the other occupancy models treat the “2” state as if it were a “1”, so the user is not required to reformat their data to run any of these models.
2 Species Models
The 2-species occupancy data type is available in 2 different parameterizations. Select these data types from the full list on the initial values for a new analysis.
False Positive Models
The false-positive models of Miller et al. (2011), both single and multi-season, are implemented