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We modelled the population dynamics of porbeagle using two equations: a spawner-recruit relationship that expresses recruitment as a density dependent function of spawner biomass, and the replacement line, the slope of which is the inverse of the rate at which recruits produce replacement spawners. Here, an implicit assumption is made that all density-dependent processes occur between spawning and recruitment. The production model also includes a third component: a yield per recruit relationship. We used the selectivity curves for the Shelf-Edge fishery in the following analysis. All results are therefore specific to that fishery. Results would vary if other selectivity curves had been assumed.
The SR model was discussed in the previous section. We modelled the rate at which recruits produce spawners (the inverse of the slope of the replacement line) by calculating the number of spawners per recruit (SPRF) as a function of fishing mortality (Shepherd 1982; Mace and Sissenwine 1993, Mace 1994):
 ,
where  is the age and gear specific fishing mortality rate for females. Note that the resulting reference points are specific to the selectivity assumed in the calculation.
The yield per recruit for a given F (YPRF) is found similarly:
 .
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