A length-based extension to the Brownie-Peterson model and its performance

Abstract

The Brownie model is an effective statistical method that can be used to estimate age-related fishing and natural mortality from multi-year tag recapture programs. The extension of the Brownie model by Polacheck et al. (2006) to include a Peterson estimator on catch-at-age data enables the estimation of abundance at the same time and improves the prediction of mortality rates. Since its development, the Brownie-Peterson (BP) model has had many applications in large-scale regional tuna tagging programs. The cohort-structured BP model assumes the age of tagged fish is known and, in most applications, requires the age of the fish to be presumed or directly derived from the fish length, constituting a potential source of bias. In this paper, the BP model is extended based on the length of fish at the time of release by integrating the recapture probability of tagged fish over the distribution of age at the length by combining catch-at-length data, length distribution-at-release observations, and growth information. The length-based model extension differs to other full-length structured models in that it is still based on age-structured dynamics, allowing it to provide age-dependent mortality rates while integrating the uncertainty in the age-length relationship. The analytic framework of the length-based model extension is described, and validated using observations simulated from a simple population and tag dynamic model. When parameterized with the correct parameters, the length-based BP model that integrated the catch-at-length data produced relatively accurate estimates of mortality and abundance, and compared to models where the age is assumed to be known, the confidence bounds of estimated parameters are wider. The Brownie model with conditional age at length estimated externally also performed well. The length-based BP model can provide a very useful extension to the existing BP model for analysing large-scale tuna tagging programs where the age data is scarce, but length composition data of sufficient quality can usually be obtained.