Abstract
Many organisms are patchily distributed, with some patches occupied at high density, others at lower densities, and others not occupied. Estimation of overall abundance can be difficult and is inefficient via intensive approaches such as capture-mark-recapture (CMR) or distance sampling. We propose a two-phase sampling scheme and model in a Bayesian framework to estimate abundance for patchily distributed populations. In the first phase, occupancy is estimated by binomial detection samples taken on all selected sites, where selection may be of all sites available, or a random sample of sites. Detection can be by visual surveys, detection of sign, physical captures, or other approach. At the second phase, if a detection threshold is achieved, CMR or other intensive sampling is conducted via standard procedures (grids or webs) to estimate abundance. Detection and CMR data are then used in a joint likelihood to model probability of detection in the occupancy sample via an abundance detection model. CMR modeling is used to estimate abundance for the abundance-detection relationship, which in turn is used to predict abundance at the remaining sites, where only detection data are collected. We present a full Bayesian modeling treatment of this problem, in which posterior inference on abundance and other parameters (detection, capture probability) is obtained under a variety of assumptions about spatial and individual sources of heterogeneity. We apply the approach to abundance estimation for two species of voles (Microtus spp.) in Montana, USA. We also use a simulation study to evaluate the frequentist properties of our procedure given known patterns in abundance and detection among sites as well as design criteria. For most population characteristics and designs considered, bias and mean-square error (MSE) were low, and coverage of true parameter values by Bayesian credibility intervals was near nominal. Our two-phase, adaptive approach allows efficient estimation of abundance of rare and patchily distributed species and is particularly appropriate when sampling in all patches is impossible, but a global estimate of abundance is required.