Remarks

The relevance of the buffer S around the sampled region X is apparent from Eq. (7.3.2). In order for this integral to be unaffected by the size of S, it must be large enough so that Pr(x G X|s) is negligible for any s G S. As we have noted, S is, in effect, a prior distribution on s - the potential origin of captureable individuals. Thus S must be sufficiently large so as to contain all potentially captureable individuals. Prescribing a particular S can be thought of as truncating the prior distribution on s, which should not be too detrimental provided that S is large relative to a. As S becomes large relative to a, there will be no effect on estimates of N(X) and other parameters due to this truncation of the prior. This concept also applies to the data augmentation idea, where we impose a uniform [0, M] prior on N.

Under the spatial capture-recapture model described here, effective sample area Ae is a by-product of the model. That is, it is a function of the canonical model parameters. This is one nice feature of the model-based formulation - it produces a = 0.15 Ae= 12.03 a = 0.3 ;4e=15.34

Figure 7.5. Effective sample area (Ae) of a 9 ha plot for various values of a. Units of Ae are hectares (ha). The grayscale scheme in all cases is about 1.0 for the completely white and 0.0 for the completely black.

Figure 7.5. Effective sample area (Ae) of a 9 ha plot for various values of a. Units of Ae are hectares (ha). The grayscale scheme in all cases is about 1.0 for the completely white and 0.0 for the completely black.

estimates of abundance, density, and effective sample area that are equivalent representations of the information in the data, under the prescribed model.

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