R/E-25

Impact/Outcome:

The goals of this project were to 1) evaluate the performance of a spatially explicit stock assessment modeling approaches for striped bass (Morone saxatilis) and to understand how performance of spatially explicit models changes with data availability; and 2) determine how the performance of spatially explicit stock assessment models change as a result of changes in population dynamics (such as natural mortality) as a result of climate change and other processes.

Objective 1 - Evaluate the performance of spatially explicit models for striped bass

To evaluate the performance of spatially explicit models for striped bass, a simulation model was developed to better understand how spatial assumptions affect model output. Additionally, we considered how data inputs, such as assuming age data has ageing error, may affect estimates of abundance and fishing mortality rates from the model. Striped bass data primarily relies on age data that is informed by scale ages, rather than otoliths. However, scales can commonly overestimate younger striped bass and underestimate older striped bass compared to otolith which are less biased (Liao et al. 2013). For this simulation we developed an operating model (OM) to simulate a ‘true’ population and dynamics of striped bass. The OM developed was spatially explicit with two stocks (Chesapeake Bay and Atlantic coast), two areas (Chesapeake Bay and Ocean), and movement during two subannual 6-month time-steps. Additionally, the OM incorporated life history assumptions based on striped bass biology-based model outputs (e.g., recruitment estimates, movement rates, etc.) from a spatially explicit model developed in Nehemiah (2024). 

Five stock assessment, or estimation models, with different spatial considerations and data inputs were developed to understand model performance. The first estimation model (FAA1) was a spatially implicit statistical catch-at-age model that does not explicitly consider spatial dynamics in population structure (e.g., recruitment, migration) but does assume that there are spatial differences in the fishery characteristics. This model does not address potential ageing biases in data sets. This model closely resembles the current assessment model used for management of striped bass. The second estimation model (FAA2) was a spatially implicit statistical catch-at-age model that addresses potential ageing biases using an aging error matrix. The third estimation model (SE1) was a spatially explicit, two-stock statistical catch-at-age model that does not address potential ageing biases in the data sets. The fourth estimation model (SE2) was a spatially explicit, two-stock statistical catch-at-age model that addresses ageing error in the data sets using an ageing error matrix. The fifth estimation model (SE3) was a spatially explicit, two-stock statistical catch-at-age model that included data sets with increased quality that includes stock composition for the fisheries independent and dependent datasets. The fifth model also accounts for ageing error in data sets using an aging error matrix. 

Figure 1. Boxplots of the distribution of relative errors, which describe accuracy and bias, in the last year of the simulation. Relative error is provided for the total abundance over stocks and regions (N), annual fishing mortality at age-8 (F-8), and fishing mortality that achieves a 40% spawning potential ratio (F40) for the entire population. The dashed red line represents when relative error is equal to 0, representing when the estimates are unbiased. The lower and upper hinge of the box represents the 25th and 75th percentiles. The middle line represents the median. The whiskers extend to the minimum and maximum values of relative error.

The results suggest model estimates were approximately unbiased when they closely matched the assumptions of the data generating model (Figure 1). Spatially-explicit model estimates were approximately unbiased likely because they closely matched the assumptions of the data generating model. Spatially implicit models resulted in unbiased estimates of total abundance, but overestimate estimates of fishing mortality. Additionally, models that did not correct for ageing error in data sources using an ageing error matrix provided severely biased and inaccurate estimates of fishing mortality, compared to models that appropriately corrected for ageing bias. 

https://github.com/snehemiah/SE-model-performance

Objective 2 – Evaluate the impact of population changes over time

A simulation study was conducted to understand how spatially explicit model performance changes when populations are undergoing changes to their dynamics (e.g., changes in movement over time). For this study, five OMs were developed to represent potential “true” population dynamics for striped bass over time based on observed changes in the population. Each operating model included similar age-specific processes as the OM used for Objective 1. All OMs assumed two stocks, two regions, and that biological processes occurred during six sub-annual, two-month time-steps (e.g., Jan.-Feb., Mar.-Apr., etc.). The first OM (OM-B) resembled the OM developed for objective 1. The second OM (OM-M) assumed that striped bass natural mortality varied for each region and increased over time in the Chesapeake Bay. The third OM (OM-P) assumed migration of striped bass changed over time to reflect less time spent in the Chesapeake Bay. The fourth OM (OM-R) assumed striped bass recruitment in the Chesapeake Bay declined over time, on average. The fifth OM (OM-MPR) combined the assumptions from OMs 2-4 to assume time-varying natural mortality, movement, and recruitment.

Three estimation models were developed to evaluate how incorrect assumptions on natural mortality, movement, and recruitment, resulting from potential climate change affects (e.g., temperature increases), affected bias and accuracy of various assessment models. Estimation models were similar to those tested for objective 1 but did not include ageing error. The first estimation model (FAA) was a spatially implicit statistical catch-at-age model. The second estimation model (SE) was a spatially explicit, two-stock statistical catch-at-age model. The third estimation model (SE-S) was a spatially explicit, two-stock statistical catch-at-age model that includes data sets with increased quality that includes stock composition for the fishery independent and dependent datasets.

Our results suggest that spatially explicit models were better able to account for changes in recruitment and movement over time with relatively unbiased estimates of abundance (N) and fishing mortality (F; Figure 2). However, when true natural mortality changed over time but were not accounted for in the estimation models, all models yielded substantially biased estimates of abundance, spawning stock biomass (SSB), and fishing mortality. Ignoring time-varying natural mortality and migration can lead to the overestimation of striped bass abundance, potentially providing incorrect management advice.

Code for the simulation for objective 2 can be found at:  https://github.com/snehemiah/Simulation_SEmismatch

Figure 2. Boxplots of the distribution of relative errors of annual abundance over stocks and regions (N), spawning stock biomass on January 1 (SSB), and fishing mortality at age 8 in the last year of all operating model simulations for the three estimation models. The titles above each box indicate the operating models.  The dashed red line represents when relative error is equal to 0, representing when the estimates are unbiased. Box and whisker definitions are in Figure 1.