The equilibrium catch (C*) is R* multiplied by the yield per recruit for the given value of F:
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Reference points from the spawning biomass per recruit and yield per recruit analyses were found using a grid search across a set of F's {0 to 2.0; increment of 0.0025}. We calculated YPRF and SPRF for each value of F, and reference points were then estimated by selected the fishing mortality rate corresponding to the appropriate reference point criterion. The SPRx% reference points were found by selecting the fishing mortality rate where the SPRF was x% that of SPRF=0.
We estimated five reference points from the production model. The equilibrium spawning biomass in the absence of fishing, SSNeq, was estimated directly from the production model. A spawning biomass of 20% SSNeq is sometimes used as a minimum threshold population size (Beddington and Cooke 1983, Goodyear 1993). SSN20% was calculated as 20% the equilibrium female spawner abundance in the absence of fishing:
The grid searches were used to find the fishing mortality rate that produces maximum sustainable yield (Fmsy), the corresponding spawner biomass that produces maximum sustainable yield (SSNmsy) and the fishing mortality rate that drives the population to extinction (Fcol). We estimated Fmsyby calculating C* for each value of F, and selecting the value of F where C* was maximized. SSBmsy, the spawning biomass at MSY, was found similarly. The equilibrium fishing mortality rate at which the population goes extinct, Fcol, is determined by the slope of the SR relationship at the origin , and is the value of F where .
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, and is the value of F where 
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