Optimal allocation of point-count sampling effort

Both unlimited and fixed-radius point counts only provide indices to population size. Because longer count durations lead to counting a higher proportion of individuals at the point, proper design of these surveys must incorporate both count duration and sampling characteristics of population size. Using information about the relationship between proportion of individuals detected at a point and count duration, we present a method of optimizing a point-count survey given a fixed total time for surveying and travelling between count points. The optimization can be based on several quantities that measure precision, accuracy, or power of tests based on counts, including (1) mean-square error of estimated population change; (2) mean-square error of average count; (3) maximum expected total count; or (4) power of a test for differences in average counts. Optimal solutions depend on a function that relates count duration at a point to the proportion of animals detected. We model this function using exponential and Weibull distributions, and use numerical techniques to conduct the optimization. We provide an example of the procedure in which the function is estimated from data of cumulative number of individual birds seen for different count durations for three species of Hawaiian forest birds. In the example, optimal count duration at a point can differ greatly depending on the quantities that are optimized. Optimization of the mean-square error or of tests based on average counts generally requires longer count durations than does estimation of population change. A clear formulation of the goals of the study is a critical step in the optimization process.