Comparing hypotheses about missed burrows in gopher tortoise line transect surveys: Bayesian distance analysis with data augmentation
The gopher tortoise is a keystone species in fire-dependent pine forests of the southeastern USA, and a candidate for federal listing under the Endangered Species Act in the eastern part of its range. With the advent of scopes to check burrow occupancy, line transect distance sampling (LTDS) has become a standard method for assessing tortoise population sizes. However, mark-recapture studies and anecdotal evidence suggest that: 1) burrow detectability is size-dependent; and 2) LTDS burrow surveys may violate a key assumption of distance sampling, namely that all individuals are detected along the centerline. Burrows of juvenile tortoises --an important size class to investigations of demographics and movement-- are likely detected imperfectly along the survey transect under some conditions.
To accommodate these features of tortoise LTDS surveys, we constructed a Bayesian distance analysis model based on a data augmentation approach to population size estimation. Detection of occupied burrows was allowed to vary along the centerline, with burrow diameter. The model is hierarchical, with information about size-dependent detectability shared among survey sites. By specifying several different prior distributions for the diameters of unobserved (augmented) burrows, we compared the consequences of missing smaller burrows under different hypotheses regarding their detectability.
Many of the 68 tortoise surveys we considered showed a strong dependence of detection rate upon burrow diameter. The consequences of that dependence, however, were greatly influenced by our choice of prior for the diameters of unobserved burrows. Population size estimates and uncertainty ranges approximately matched those from program DISTANCE, when the diameter prior was uniform. When we used a beta prior with more density in the range of smaller burrows, point estimates nearly doubled in some cases.
Larger burrows were most influential in determining the shape of the distance function. In a model with uniform diameter prior, our estimate of the burrow diameter at which probability of detection along the centerline reaches 1 was precise across the set of surveys, 29.4 cm (CrI: [28.6, 30.4]). The estimated detection rate of the smallest burrows (~5cm) along the centerline was remarkably low (mean: 0.08, CrI: [0.06, 0.10]).
Uncertainty in population size estimates from distance sampling data can be extreme when systematic problems exist in detecting certain classes of objects along the centerline. To increase the value of gopher tortoise survey results, we recommend that the LTDS survey design be augmented to allow independent estimation of the detection rate of smaller burrows.