Research Document - 2016/040

Testing estimators of walrus abundance: insights from simulations of haul-out behaviour

By T. Doniol-Valcroze, A. Mosnier and M.O. Hammill

Abstract

Walrus are a challenging species to enumerate owing to their clumped distribution and the highly variable proportion of animals hauled out at any one time. Previous attempts to describe this variability using a statistical framework assuming a uniform or a binomial distribution underestimate the uncertainty in haul-out proportions. Based on simulations, we determined that a more appropriate approach is to consider that counts follow a beta-binomial distribution which takes into account the overdispersion due to correlation among hauled-out walruses. Using this framework, four abundance estimators were examined for bias in estimating the size of a simulated population, with the number of animals hauled-out following a beta-binomial distribution with known parameters. The Minimum Counted Population (MCP) and Bounded Count (BC) methods were both likely to underestimate the true population size, even when corrected by an estimate of the maximum proportion of the population that can be hauled-out at any given time. The Simple Count (SC) method, using mean counts corrected by the average proportion of time hauled-out, provides a reliable and unbiased estimator.  Previous implementations of the MCP, BC and SC methods did not provide a realistic estimator of variance. Based on the beta-binomial framework, we propose a variance estimator for the SC method that takes into account the extra variance linked to the behavioural correlation among individual walrus. We also suggest a Bayesian estimator that provides a valid point estimate of the population size as well as a full and convenient description of the error distribution.

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