Advantages:

• Focuses on estimating productivity and scale given catch and index data
• Efficient exploration of parameter space
• Explicitly incorporates biological uncertainty through priors
• Proven robust and effective for pelagic fish assessments

Trade-offs:

• Simplifies complex age-structured dynamics
• Assumes single well-mixed population
• Knife-edged selectivity assumption

Fletcher-Schaefer production model

Population dynamics: \[N_t = \left(N_{t-1} + \text{Production}_{t-1}\right) \times \text{Process error}_{t} \times \text{Fishing survival}_{t-1}\]

Fishing impact linked to effort: \[\text{Fishing survival}_{t} \text{ inversely proportional to } \text{Fishing mortality}_t\] \[\text{Fishing mortality}_{t} = \text{Catchability}_{t} \times \text{Fishing effort}_t\]

Key features:

• True population (numbers) is treated as an unobserved random variable
• Model only fits to observations of relative abundance and catch
• Catchability is allowed to vary temporally so fishing mortality can match catch
• Biology captured in Production as max rate of population growth \(R_{Max}\)

1. Develop priors:

• Use biological simulation framework to develop initial prior for \(R_{Max}\) and production function shape parameter \(n\)
• Develop priors for population scale and catchability based on maximum observed catch and early period CPUE

2. Prior pushforward:

• Pass random parameter combinations through the population dynamics model
• Filter parameter combinations for biological and fishery realism
• Develop a multivariate prior based on emergent parameter correlations

3. Fit models to data 🤩

• Evaluate model performance (fits & diagnostics)
• Draw inference from posterior updates
• Consider sensitivities to data inputs

• Fits to the DWFN index

• Uses a robust likelihood for fitting to catch data

• Estimates scale, \(R_{Max}\), production shape, annual catchability deviates, process error, and index observation error

• Posterior distributions of estimated quantities were derived from sample chains starting from 5 different starting points

• Standard Bayesian diagnostics indicated that all sample chains satisfactorily converged to a stable distribution without issue

Conclusion: Stock is overfished but not undergoing overfishing. Only 22.9% joint probability of being simultaneously overfished and undergoing overfishing.

Data representativeness:

• CPUE indices may not represent true stock trends
• Potential under-reporting of catches for bycatch stock
• Stock structure uncertainty (genetic evidence of SWPO fish in North Pacific catches)

Model simplifications:

• Single well-mixed population assumption
• Knife-edged selectivity
• No age structured dynamics
• Stationary productivity and carrying capacity over 70 years

Parameter uncertainty:

• Substantial uncertainty in absolute population scale
• Shape parameter \(n\) not estimable from data
• High uncertainty in key biological processes translates to uncertainty in \(R_{Max}\)

Environmental factors:

• Future variability in environmental and oceanographic conditions are not explicitly modeled
• Process error spikes suggests unmodeled dynamics

Stock structure research:

• Develop conceptual model for SWPO striped marlin
• Collaborate with ISC Billfish Working Group

Data and biological research:

• Reduce uncertainty in key biological processes where possible
• Investigate representativeness of abundance indices
• Address stock connectivity questions with genetic research

Future modeling approach:

• Progressive development within Bayesian framework
• Move toward Bayesian fully integrated age-structured models similar to WCPO oceanic whitetip shark

Collaborative Assessment Process

This assessment greatly benefited from collaboration with a broad group of interested parties and stock assessment experts where feedback was provided in an iterative manner throughout the model development process. Leveraging their diverse expertise helped produce a stronger scientific product.

Special thanks to:

K. Kim (SPC), N. Davies (Te Takina Ltd.), S. Hoyle (Hoyle Consulting), R. Ahrens (PIFSC), and M. Nadon (PIFSC)

for their insights and thoughtful discussion which improved the assessment!