A Hierarchical Distance Sampling Approach to Estimating Mortality Rates from Opportunistic Carcass Surveillance Data

Abstract

Distance sampling is widely used to estimate the abundance or density of wildlife populations. Methods to estimate wildlife mortality rates have developed largely independently from distance sampling, despite the conceptual similarities between estimation of cumulative mortality and the population density of living animals. Conventional distance sampling analyses rely on the assumption that animals are distributed uniformly with respect to transects and thus require randomized placement of transects during survey design. Because mortality events are rare, however, it is often not possible to obtain precise estimates in this way without infeasible levels of effort. A great deal of wildlife data, including mortality data, is available via road-based surveys. Interpreting these data in a distance sampling framework requires accounting for the non-uniformity sampling. Additionally, analyses of opportunistic mortality data must account for the decline in carcass detectability through time. We develop several extensions to distance sampling theory to address these problems.We build mortality estimators in a hierarchical framework that integrates animal movement data, surveillance effort data, and motion-sensor camera trap data, respectively, to relax the uniformity assumption, account for spatiotemporal variation in surveillance effort, and explicitly model carcass detection and disappearance as competing ongoing processes.Analysis of simulated data showed that our estimators were unbiased and that their confidence intervals had good coverage.We also illustrate our approach on opportunistic carcass surveillance data acquired in 2010 during an anthrax outbreak in the plains zebra of Etosha National Park, Namibia.The methods developed here will allow researchers and managers to infer mortality rates from opportunistic surveillance data.

Keywords: Carcass; Cue; Disease; Distance sampling; Hierarchical model; Mortality; Opportunistic surveillance.

Figure 1

Map of the central region of ENP showing plains zebra carcasses (squares) detected by passive surveillance in Feb-May 2010. Road (gray lines) width scales with the square root of the number of trips made on that road during the study period.

Figure 2

Distribution of perpendicular distance from road from 52,745 GPS fixes collected from 27 collared plains zebra in the Okaukuejo region of Etosha National Park during the late wet season (Feb-May). The black line shows the fitted truncated gamma distribution used as π(y) to fit the detectability functions. Data are only showed up to the maximum strip width of 800m for which the distance sampling analysis is conducted.

Figure 3

Proportion of time a sighting cue is the dominant cue at a carcass as a function of day since death as estimated from camera traps placed at fresh zebra carcasses.

Figure 4

Distribution of perpendicular distances between sighted carcasses and roads for zebra carcasses detected during passive surveillance in Feb-May 2010 by sighting cue type. Maximum likelihood fitted detectability functions, as estimated with the estimated distribution of π(y) modeled as a truncated gamma distribution from GPS movement data from live zebra (Fig. 2), are displayed as a black line, with lines normalized so that the area under the curve matches the area of the histogram bars.