Estimation of tiger densities in India using photographic captures and recaptures

Ecology, Dec, 1998 by K. Ullas Karanth, James D. Nichols

Program CAPTURE computes several goodness-of-fit and between-model test statistics providing information about the appropriateness of the different capture-recapture models. We computed and examined these individual tests for all data sets. CAPTURE also includes a model selection algorithm that uses a discriminant function to provide an objective criterion for selecting the most appropriate model (Otis et al. 1978, Rexstad and Burnham 1991). Our a priori expectation was that model [M.sub.h] would provide a reasonable model for tiger capture probability. We expected variation among individuals in capture probability, and we hoped that the field sampling methods would reduce the likelihood of temporal variation and behavioral response to "capture." We computed the [M.sub.0] vs. [M.sub.0] vs. [M.sub.h], [M.sub.0] vs. [M.sub.b] and [M.sub.0] vs. [M.sub.t] test statistics to test for heterogeneity, behavioral response, and temporal variation, respectively. In addition to expecting heterogencity of capture probabilities, we also favored [M.sub.h] because the jackknife estimator (Burnham and Overton 1978) for this model is robust to deviations from underlying model assumptions and has performed well in simulation studies (Otis et al. 1978, Burnham and Overton 1979).

These models were developed for closed populations and assume that the sampled population does not change during the course of the study. The camera-trap sampling was restricted to periods of time that were sufficiently short that mortality and permanent movement in and out of the study areas were not anticipated. CAPTURE computes a closure test statistic from the capture history data, and we used this statistic to test the closure assumption for each data set. A specific kind of closure violation that we considered was the existence of animals briefly passing through the study area en route to locations outside the study area (e.g., see Pradel et al. 1997). These animals would not have an opportunity to be caught on multiple occasions, and their capture histories would lend the appearance of a trap-shy response. In addition to the closure test, the [M.sub.0] vs. [M.sub.b] test provides information about the existence of this type of capture history.

We report the estimates computed by CAPTURE for capture probability, abundance ([Mathematical Expression Omitted]), and estimated standard error of abundance ([Mathematical Expression Omitted]) for appropriate models. The capture probability estimates correspond to individual sampling occasions. It is also of interest to consider the probability that a tiger present in the sampled area is captured at least once during the sampling. This quantity can be estimated as [Mathematical Expression Omitted], where [M.sub.t 1] is the total number of individual tigers caught during all sampling occasions.

Finally, we were interested in using these abundance estimates to estimate tiger density in the different study areas. Density is defined as D = N/A, where N is animal abundance and A is the area on which the animals are found. In trapping-grid studies, trap spacing is usually established such that all animals moving in the grid interior are exposed to traps, and we believe that this was the case with camera-trapping (see Field methods). However, in trapping-grid studies, it is also recognized that the area from which animals are trapped is not equal to the area defined by assuming that the perimeter traps represent the outer boundary of the area (Dice 1938, Otis et al. 1978, White et al. 1982). Instead, it is typical to add a boundary strip to the area defined by the perimeter traps in order to account for the additional area from which trapped animals are taken (Dice 1938, Otis et al. 1978, White et al. 1982). Several approaches have been suggested for estimating the boundary strip width, and we used an ad hoc approach that has performed well in simulation studies (Wilson and Anderson 1985).