Time varying M with starvation mortality in a state-space stock assessment model: Part 2: Atlantic cod (Gadus morhua) on the southern Grand Bank of Newfoundland

State-space models are now a common tool for modeling time-varying ecological phenomena. This extends to state-space stock assessment models (SSAMs), recognized as pivotal components within the evolving landscape of next-generation stock assessment methodologies. Though methods are rapidly evolving, the estimation of time-varying rates of natural mortality (M) remains a challenge, and the sensitivity of stock assessments and management advice to assumed M values underscores the pressing need for improved estimation methods. Using southern Grand Bank (SGB) Atlantic cod as a case study, we introduce a novel approach to estimate time-varying M. We first convert a length-based starvation M index into an age-based index, which we then include in an age-based SSAM to estimate two components of M: starvation M and a remainder component. This produces a new SGB cod SSAM with time-varying total stock M. This model produces a large decrease (68 %) in the size of the model process errors (i.e., their standard deviation) and better fit compared to a model that did not account for time-varying M, indicating that the starvation M index improves our model of stock productivity. By leveraging readily available information on fish body condition and the proportion of fish in really poor condition, the proposed methods offer a valuable solution to the challenges associated with estimating time-varying M. The proposed methods offer a tractable solution to the common struggles associated with quantifying changes in fish productivity, which is crucial for the management of dynamic systems.