The Bounded-Count Method for Analysis of Lek Counts

Counts of displaying males at leks are the traditional method used to monitor populations of greater sage-grouse (Centrocercus urophasianus). Often, multiple daily counts are made during a single breeding season, and the maximum of those counts is used as an index to the population size. That maximum value clearly is a biased (low) estimate of the number of males because, as indicated by studies of radio-marked birds, some males in the population that use the lek may be either absent or present but not detected during the lek count. Here we consider an alternative, the Bounded-count (or jackknife) Estimator, which is always at least as large as the largest count. It is simple to compute, being twice the largest count minus the second-largest count, and allows confidence limits to be computed. We discuss the rationale for the estimator and apply it to simulated and actual data sets. When the recorded counts, or even a portion of them, are distributed uniformly between zero and the true population size, the Bounded-count Estimator performs well. In somewhat more realistic simulations with varying but low rates of occupancy and detection, the Bounded-count Estimator reduced the bias but did not result in values more closely correlated with the true population size.