CMSY

The CMSY method implements a stock-reduction analysis with Schaefer biomass dynamics similar to the original Catch-MSY method. It requires a prior distribution on population growth (r) and carrying capacity (K) as well as priors on the relative proportion of biomass at the beginning and end of the time series compared to unfished biomass (depletion). The method assumes r and K do not change over time. CMSY was modified from the original Catch-MSY method to generate biomass trends, in addition to Maximum Sustainable Yield (MSY), from all viable r-K pairs and produce an estimate of B/BMSY from the median trend. This was done by running the Schaefer model repeatedly using the catch time series and each viable r-K pair, and computing the arithmetic mean biomass ratio in each year along with upper and lower quartiles.

Inputs:

• Catch time series (including discards)
• Estimated ranges of stock size in the first and final years of catch data (B_initial and B_final)
• Life history information (i.e. r and K growth rates)

Outputs:

• Maximum Sustainable Yield (MSY)
• A time series of biomass
• A time series of B/B_MSY

Input Sensitivities, Assumptions and Caveats:

• Population growth and carrying capacity (r and K) are assumed to be constant
• Biomass assumed to be a fraction of the carrying capacity at both the beginning and end of the time series of catch data and the growth rate
• Based on Schaefer surplus production model, the overall effects of recruitment, growth, and mortality are pooled into a single production function
• Stock depletion is extremely difficult to estimate, particularly with limited data. Methods have been developed, such as the use of boosted regression tree models that correlate depletion with a range of predictors calculated from catch data, which can improve depletion estimates.
• Assumes catch is known without error
• Assumes stock is undifferentiated (no age, size, or gender differences)
• Assumes only a narrow range of r-K combinations can maintain the population
• Assumes population does not collapse or exceed the carrying capacity
• Ignores the age structure of the stock and does not consider individual growth, recruitment, or the vulnerability of the fish to the fishing gear
• Produces imprecise and biased estimates of B/B_MSY, especially for lightly exploited stocks
• They are also poor classifiers of stock status, but do a lot better in superensembles (combining models to emphasize their particular strengths and downplay their weaknesses)

Reference points:

• B/B_MSY: derived from the modeling approach as described above
• Stock status-based reference point to estimate sustainable yield, as a reference value to control F: F_MSY =r/2
• MSY calculated as: MSY=r*k/4

Recommendations:

Adjust fishing mortality through harvest control methods (e.g. catch limits, seasons, or spatial closures) based on how far apart these values are from TRP & LRP for OFL.