A Bayesian birth distribution model for grey seals and an evaluation of timing of the harvest

Abstract

Aerial surveys were completed to estimate northwest Atlantic grey seal (Halichoerus grypus) pup production in eastern Canada during December 2020 to February 2021. These surveys underestimate pup production if animals are born after the surveys are flown or if pups leave the breeding site before it is surveyed. Past assessments have modelled the distribution of births to correct this bias by fitting the proportion of animals in different morphometrically defined stages of fixed duration to a gamma or Weibull distribution (Myers Birth Distribution [MBD] Model). A new Bayesian modelling approach was developed and compared with the MBD model to examine how this approach impacts our understanding of the timing of births. Assuming that animals are weaned at 20 days of age, the model was also applied to determine the proportion of animals that were weaned and thus available to harvesters at different colonies. The MBD and Bayesian models showed similar estimates when applied to the data rich dataset acquired on Sable Island. At other breeding sites, the Bayesian model tended to estimate a slightly shorter period of births compared to the MBD model, resulting in a higher estimated proportion of animals born on the aerial survey date, and thus a smaller adjustment of counts. The weaning date estimated with the Bayesian model showed a general trend starting off the Nova Scotia coast then moving into the Gulf of St. Lawrence. The model estimated that 50% of the grey seal pups were weaned by January 6, 2021 on the southwestern Nova Scotia Islands, and on January 24 in the southern Gulf. Application of the Bayesian model to staging data acquired at several colonies in previous years showed that the date when 50% of the pups are weaned has advanced by approximately one day each year since the early 2000s in the Gulf. This trend was less clear outside the Gulf, but the timing of births in 2021 was also estimated to be earlier than in previous years. The Bayesian model provides an approach to consider several sources of uncertainty not previously taken into account. These include uncertainty associated with the date of first birth, the development stage duration, and variability in classification of stages by the various observers. By updating priors, the model can make use of new information as it is collected. The use of the Bayesian model should lead to improved estimates of population size.