Capture-recapture estimation of bowhead whale population size using photo-identification data

Abstract

Statistical models andmaximumlikelihood methods are developed for estimating bowhead whale population size from photo-identification data. These are tested on both simulated data and actual data from 1985 and 1986 photographic studies. Initially a multinomial model that accounts for unmarked whales is used. Variance is estimated using the parametric bootstrap. In the cases considered, the variance estimators perform similarly to previously used delta method based estimators in terms of confidence interval coverage, as long as log-normal rather than symmetric confidence intervals are used for the latter. Further models are developed to account for heterogeneity in capture probabilities (highly marked whales are more likely to be captured than moderately marked) and non-random sampling caused by age segregation. These models, particularly the latter, perform better than the multinomial model on simulated data that incorporate these violations of standard capture-recapture assumptions. All three models are applied to actual bowhead whale data. The resulting estimates of the 1+ population size (animals 1 year old or older) in 1985-86 range from 4,719 (using the non-random sampling model on the small dataset in which lengths are available for all whales so that age class can be determined) to 7,331 (using the heterogeneity model on the full dataset). Standard errors are comparable to those obtained from the ice-based census in years with sub-optimal environmental conditions. All confidence intervals include the ice-based census estimates for 1985 and 1986, as well as the corresponding values of 1+ population size in the most likely trajectory from a Bayesian synthesis analysis. These most likely values – 6,649 and 6,820 – incorporate the ice-based census estimates and additional data on bowhead whale population dynamics.