Bottom‐Up Interactions in State‐Space Age‐Structured Models Using Mass‐Balance Dynamics

Abstract

Age‐structured models are used worldwide to regulate fisheries. These models typically ignore top‐down interactions (predation affecting natural mortality) and bottom‐up interactions (consumption affecting individual growth, reproduction, or survival), whereas multispecies catch‐at‐age models often incorporate top‐down but not bottom‐up interactions. While Ecopath‐with‐Ecosim (EwE) incorporates both top‐down and bottom‐up interactions along with age‐structured dynamics, it is not typically fitted to age‐composition data. We extend Ecostate (a state‐space version of EwE) to incorporate age‐structured dynamics while fitting to age‐structured data and use this to illustrate how to add bottom‐up interactions to age‐structured models. Specifically, we add age‐structured dynamics and likelihood components for age‐composition and weight‐at‐age data while estimating residual variation in larval survival (recruitment deviations) and consumption (weight‐at‐age deviations). As a demonstration, we fit the model to biomass and age‐composition data for two commercial species (Alaska pollock and sablefish) in the Gulf of Alaska, including population dynamics for their major prey, while not fitting weight‐at‐age data so that it can be used for out‐of‐sample evaluation of model performance. The model can be viewed as a multispecies age‐structured model (e.g., estimating adult mortality rates, survey catchability and selectivity, and recruitment variation) and as a mass‐balance ecosystem model (e.g., estimating trophic position and weight‐at‐age based on forage consumption). The predicted weight‐at‐age is weakly correlated with independent measurements for pollock and sablefish but was improved when we incorporated forage biomass indices. We recommend that age‐structured models routinely explore the link between prey consumption and resulting size‐at‐age, whether using coupled predator–prey dynamics or simplifications that treat prey abundance as fixed data.

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