As we have noted previously, one benefit of a well-defined probability model for spatial capture-recapture is that it produces a cohesive summary of abundance and effective sample area. The latter is a derived parameter, being equal to the probability that an individual at s is exposed to sampling during the J samples, integrated over s. This is calculated at each iteration of the MCMC algorithm by evaluating the bivariate normal pdf describing movements at every point on the grid, and then calculating the exposure of each 'grid cell' to the trap array, and then summing over s. For the tiger data, the probability of exposure as a function

Figure 7.9. Probability of exposure to trapping in a J =12 sample camera trapping study. The color of each pixel is the Pr(exposure to sampling) of a tiger with activity center at that pixel. Only pixels judged to be suitable habitat are included. The sum of all pixels is the effective sample area of the trapping array. Reproduced from Royle et al. (2008).

Figure 7.9. Probability of exposure to trapping in a J =12 sample camera trapping study. The color of each pixel is the Pr(exposure to sampling) of a tiger with activity center at that pixel. Only pixels judged to be suitable habitat are included. The sum of all pixels is the effective sample area of the trapping array. Reproduced from Royle et al. (2008).

of location is shown in Figure 7.9 (taken from Royle et al. (2008)). The sum of these exposure probabilities is 704.847.

The posterior mean of a is 0.586 - the typical distance moved, from center of range, between samples, is about 2.5 km and 95 percent of the movements are less than about 5 km from the center of activity. The estimated density is about 13.5 tigers per 100 km2. For comparison, if we use the estimate of N from model Mh reported in Chapter 6, which was 111.7, along with the estimated effective area, the computation yields a density estimate of 10.04 tigers per 100 km2. As we noted previously (in the lizard example), the relationship between N under the heterogeneity model and effective area is only heuristic, and not precise mathematically. Thus, we should not expect equivalence of the two estimates.

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