Analysis of the Tiger Camera Trapping Data

Camera trapping is now widely used to study carnivore populations that can be distinguished by stripe or spotting patterns (O'Brien et al., 2003; Trolle and Kery, 2003; Wallace et al., 2003; Karanth et al., 2004; Kawanishi and Sunquist, 2004; Silver et al., 2004; Wegge et al., 2004; Trolle and Kery, 2005; Soisalo and Cavalcanti, 2006). We provide an analysis of the tiger camera trapping data that was introduced in Chapter 5. The analysis used here follows closely to that presented in Royle et al. (2008). These data are from surveys of tigers in the Nagarahole reserve in the state of Karnataka, southwestern India. Tiger stripe patterns are unique, and individuals are readily identified from photographs. This population has been studied via camera trap methods by Karanth and associates since 1991 (e.g., Karanth (1995); Karanth and Nichols (1998); Karanth et al. (2006)). The data used here were collected from 24 January to 16 March 2006 from sampling at 120 trap stations (see Figure 7.8). In this figure, the minimum area rectangle that encloses the array is shown. We will denote this polygon by X and provide an estimate of N(X) and the density, D over X.

We provide here an analysis of the model using the native R implementation (Royle et al., 2008) based on approximating S with a fine grid of approximately 10000 potential activity centers having spacing of approximately one-third of a km. The analysis by data augmentation used 800 augmented encounter histories, and thus M = 855. The minimum area rectangle containing the 120 camera trap locations was 679.4 km2. For comparison, the convex hull around the trap array has area approximately 462.5 km2. The estimates are summarized in Table 7.4.

model {

psi~dunif(C,1)

sigma~dunif(C,S)

for(i in 1:(nind+nz)){ xCg[i]~dunif(Xl,Xu) yCg[i]~dunif(Yl,Yu) w[i]~dbern(psi)

capprob[i]<- pC*total.exposure[i]/emax mu[i]<-w[i]*capprob[i]

dist2[i,j]<- ( pow(xCg[i]-grid[j,1],2) + pow(yCg[i]-grid[j,2],2) ) exposureC[i,j]<- exp(-dist2[i,j]/sigma) condlp[i,j]<- exposureC[i,j]/total.exposure[i]

total.exposure[i]<-sum(exposureC[i,1:ngrid]) }

Panel 7.3. WinBUGS model specification for the trapping grid model fit to the tiger data. The model is based on a conditional factorization of the multinomial cell probabilities in which the number of detections for each individual is a binomial random variable, and the trap of capture is a conditional multinomial as described in the text. In this specification, emax is supplied as data and must be greater than the maximum total exposure at any location in S.

Easting

Figure 7.8. Tiger camera trapping array, composed of 120 traps in the Nagarahole reserve in the state of Karnataka, southwestern India. A unit of distance on this map is 5 km. The minimum area rectangle is shown enclosing the trap array.

Table 7.4. Posterior summaries of model parameters for the tiger camera trapping data. Here, Ae is the area exposed to trapping (in J =12 samples) - or the effective sample area of the 120 trap array. It is a derived parameter under the model. N(X) is the number of activity centers located within the minimum area rectangle having area 679.4 km2, and D is the density per 100 km2. The number of unique individuals observed was 45. 0 is the zero-inflation parameter introduced by data augmentation.

Table 7.4. Posterior summaries of model parameters for the tiger camera trapping data. Here, Ae is the area exposed to trapping (in J =12 samples) - or the effective sample area of the 120 trap array. It is a derived parameter under the model. N(X) is the number of activity centers located within the minimum area rectangle having area 679.4 km2, and D is the density per 100 km2. The number of unique individuals observed was 45. 0 is the zero-inflation parameter introduced by data augmentation.

parameter

mean

sd

2.5%

median

97.5%

^

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