Estimating Density From Locationofcapture Information

In this section, we consider a design that is not widely used, but one that provides a nice transition from the distance sampling model toward what proves to be a

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very broad and useful class of problems (namely, trapping arrays; Section 7.4). The situation we consider here is an 'area search' type of protocol wherein some prescribed area a quadrat or other areal unit - is subjected to a uniform search intensity such that individuals contained in the unit have constant detection probability. The quadrat is searched multiple times (i.e., J > 1), generating a spatial capture-history on n individuals. The lizard data that were introduced in Chapter 5 are of this type. The data are shown in Figure 7.1. A 9 ha plot 300 m on a side was searched on 14 (almost consecutive) days (see Royle and Young, 2008, for details). While the basic protocol does not appear to be widely used, we suppose that it could be generally applicable to other reptile and amphibian species that are easily captured by hand.

The main issue in dealing with this problem, as we have noted previously, is that there is movement of individuals onto and off of the plot between samples. Thus, non-capture of an individual could be either because the individual was present on the quadrat but not encountered, or because the individual had moved off of the quadrat. The effect of this is to yield under-estimates of p, and the estimated N is an estimate of some superpopulation of individuals that is ever exposed to capture (Kendall et al., 1997). Equivalently, N applies to some effective sample area of the quadrat - the area over which individuals have been exposed to sampling, which is unknown. Spatial capture-recapture information allows us to resolve this issue. We can model the movement process explicitly and obtain estimates of absolute density that, in effect, are adjusted (by a model) for movement bias.

We present a spatially explicit, capture-recapture model for estimating density from area-search sampling under a conventional multiple sample capture-recapture study design. The development here follows Royle and Young (2008), who specified a hierarchical model in terms of individual activity centers (described subsequently) and a model of individual movement conditional on the activity centers. This movement model is, essentially, an explicit model of temporary emigration. We elaborate on this shortly. The hierarchical model is completed by specifying a model for the observations conditional on the location of individuals during each sample occasion. The modeling objective is to estimate the absolute density of individuals in the survey plot. Under the proposed model, this objective is accomplished by estimating the number of activity centers contained within the delineated sample unit. We emphasize Bayesian analysis by data augmentation to carry out analyses.

Before proceeding, we note that the basic hierarchical model structure of this 'area search' problem is similar to that considered in the distance sampling with measurement error problem. Conceptually, the distance sampling model was based on the joint specification [y|x][u|x][x] for encounter data y, distance measurements u and actual distance x. In the present case the analogous model is [y|u][u|x][x] for encounter data y, observed location u and 'activity center' x (we will depart from use of x to represent a two-dimensional vector but use it here to clarify the analogy between models). The main technical distinctions are that the latent variable here is bivariate (but related to distance by a transformation), and the model of encounter y is conditional on observations u and not x. The model has other structural similarities. For example, we adopt the use of a bivariate normal 'movement kernel' to relate u to x in this model, just as we did in the distance sampling model (where it was used as a model for the detection function). An important distinction is that, here, [u|x] is a biological process related to movement, whereas in the distance sampling model it was purely an observation process (measurement error).

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