Document: MAR-3-20-6

The estimation of sightability error in replicated counts.

TAPER, M.L.*

Dept. of Biology, Montana State University/Bozeman ¹

Abstract:
For many organisms, population sizes are estimated by simple counts of observed individuals. This process is statistically problematic because the population size estimates are biased and have no associated estimates of error. Multiple counts have sometimes been used to reduce bias, with the population estimate being taken as the highest count. However, multiple counts contain information not only about population size, but about sightability. I discuss two cases. In the first, sightability is assumed constant over all observations. Counts are replicate observation from a binomial distribution. The second case allows sightability itself to be a random variable. I model sightability with a beta distribution. It can be shown that counts will follow the compound distribution known as a beta-binomial. For neither process can the parameters of interest, population size, and sightability, be successfully estimated using maximum likelihood methods. This is because true population size is an upper boundary for the observed counts. Maximum likelihood asymptotic theory does not apply to boundary parameters. In this problem ML estimates tend to either approach infinity or the observed counts. I employ a technique known as the maximum spacing product to estimate the parameters of interest. I develop estimates and confidence intervals. The utility of the method is demonstrated using estimates of bison abundance from Yellowstone National Park..

Keywords: measurement error, observer error, population estimate, bison, Yellowstone National Park, replicated counts, sightability

This abstract is being presented at: 10:15 AM in session:
Symposium # 15: Measurement Error in Ecological Data.