A Multinomial Model for Estimating the Size of a Whale Population from Incomplete Census Data

Abstract

This paper adapts the removal method of population size estimation to the problem of estimating the size of the western Arctic stock of bowhead whales. The whales are counted during their spring migration as they pass two census camps located near Point Barrow, Alaska. Whales seen at the first camp are "removed" from the population of concern to the second camp, where only whales missed by the first camp are counted. If both camps were in operation throughout the migration and if the probability of missing a whale were constant, the removal method would provide a population size estimate based on a trinomial model in which the size of the population would be the number of trials, whales counted by each camp would provide the observed cell totals, and whales missed by both camps would represent an unobserved cell total. Since the probability of missing a whale depends on visibility, we model the population size as the sum of the number of trials of several independent trinomial distributions, each of which represents a particular visibility condition occurring during the census. To account for the fact that watch cannot be maintained at both camps throughout the migration, we derive a confidence interval estimate of the number of trials under a more general model allowing for incomplete observation of totals within particular cells as well as for completely unobserved cells.