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.

Bowhead whale (Balaena mysticetus) census data obtained during the northward spring migration are summarized for 1978–1983. Population size estimates are derived from counts made by observers standing on the seaward edge of shorefast ice in the vicinity of Point Barrow, Alaska, from mid‐April to early June. The research design utilized two counting stations: South Perch, the primary counting station, and North Perch, used to determine the number of whales missed by South Perch observers. The percentage missed is estimated for each visibility category and used here to correct the census counts. Each season's population estimate is calculated as the sum of the number of trials of several independent multinomial distributions representing different visibility conditions. Corrections are applied for unwatched hours and hours with inferior visibility. A mean estimate of the number of whales passing within view of the census station was computed as 3,674 ± 299. This estimate was based on data collected in 1978, 1981, 1982, and 1983, years with the least apparent biases. Aerial survey data provide estimates of the proportion of whales passing at various distances seaward of the census sites as follows: 0.58 from the ice edge to 2 km, 0.76 to 3 km, and 0.80 to 4 km. Correcting for whales too far offshore to be seen by the ice‐based observers results in a population estimate of over 4,200 bowheads.

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