Surplus Production

A surplus production model (SPM) is one of the most basic population dynamics models. SPMs view the population as a single unit of biomass, with all individuals (i.e., all age classes) having the same growth and mortality rates. They rely on relatively basic ideas of growth and death and sustainable exploitation. Variation in the population size results from both increases due to growth and reproduction (i.e., production) and decreases due to natural mortality (M) and fishing mortality (F). This method estimates stock biomass and fishing mortality using catch, effort, and any available indices of relative abundance. Estimated biomass and fishing mortality can be examined relative to reference points to determine stock status.

The SPM model we provide in the downloadable Workbook, and linked here, is for the Schaefer model, which assumes the population is at equilibrium. Other SPM models exist, some which do not depend on this assumption (which may be preferable, especially as climate change impacts increase), but these methods generally require more data.

Note: Surplus production models are sometimes called "biomass dynamic models."

Inputs:

• Total catch (if discards are low, then can be just landings), stock biomass estimate
• Preferably more than 10 years of catch and abundance data
• Catchability
• Effort
• Index of relative abundance, such as CPUE, depletion or biomass estimate (optional)

Outputs:

• Estimate of MSY
• Time series of biomass, which can be used to estimate B/B_MSY
• Time series of fishing mortality, which can be used to estimate F/F_MSY

Input Sensitivities, Assumptions and Caveats:

• Sensitive to life history phenomena not incorporated (e.g., age of recruitment);
• Sensitive to survival and growth rate inaccuracies or fluctuations
• Assumes population is at equilibrium
• Assumes the stock has been at both high and low abundance levels
• Assumes catch is known without error
• Assumes stock is undifferentiated (no age, size, or gender differences)
• Assumes catch and/or index is linearly related to the stock abundance
• Assumes entire population covered by catch and index

Reference points:

• F_MSY
• F10%B
• F40%B
• B_MSY

Recommendations:

• Fishing mortality is adjusted through harvest control methods (e.g. catch limits, seasons, or spatial closures) based on how far apart these values are from TRP & LRP.
• Surplus production models produce relative estimates of MSY and F_MSY, and estimates of q (catchability: the parameter that scales abundance indices into biomass estimates), which can be scaled to steepness of the recruitment curve to increase the certainty.