A system-of-equations approach to modeling age structured fish populations: the case of Alaskan red king crab, Paralithodes camtschaticus

This paper presents a simultaneous system-of-equations approach to modeling age-structured populations using trawl survey age/size frequency data. The analysis builds upon a Ricker spawner-recruit structure and provides a cohort-based estimation method that retains the underlying dynamic properties of a delay-difference model. The framework shares a common spawner-recruit function across age-class equations. This exploits the commonality among cohort members and serves as an instrumental variable, lessening the effect of measurement errors in estimation. The dynamic features of the underlying age-structured population are retained through age-specific net survivability and growth parameters that link age-classes. The technique uses multiple observations on a cohort to further mitigate the effect of measurement error and improve overall estimation efficiency. A seemingly unrelated regression estimation method is required to address contemporaneous correlation of errors across age-classes. This framework is applied to trawl survey data for adult male Alaskan king crab, Paralithodes camtschaticus.