Per-recruit analysis & spawning potential ratio
Overview
Per-recruit analysis is used to calculate metrics of yield-per-recruit (YPR) and spawning potential ratio (SPR) based on inputs of life history characteristics, selectivity, and retention (e.g., minimum size limits or slot limits), and fishing mortality rate. Per-recruit analysis and the related quantity of spawning potential ratio (SPR) are outputs of analyses in the Size Limit Builder and Stock Health Tracker. Per-recruit analysis was originally developed analytically by Beverton and Holt (Beverton and Holt 1957), whereas the more complex population dynamics models utilized in the Size Limit Builder are based on a numerical approach contained in the R package FishSimGTG (Harford 2024).
The quantity yield-per-recruit (YPR) is the expected lifetime yield per fish by weight. YPR is typically used in fisheries decision-support to ensure high yields are likely to occur. When lower-than-optimal yields occur, this problem is known as growth overfishing (Beverton and Holt 1957). Growth overfishing occurs when too many fish are harvested at small sizes, resulting in lower YPR. The quantity spawning potential ratio (SPR) is the ratio of spawning biomass per recruit (SBPR) in a fished stock to SBPR in an unfished stock, with a maximum value of 1.0 (or 100% if expressed as a percentage) and declining toward 0.0 as fishing mortality increases (Goodyear 1993). Thus, SPR is a measure of reproductive output of a fished cohort during its lifetime relative to an unfished cohort during its lifetime. SPR is typically used in fisheries decision-support to avoid recruitment failure under high fishing mortality; a problem that is known as recruitment overfishing. Recruitment overfishing occurs when spawning is depleted to levels that could jeopardize replenishment.
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Reference points
In fisheries management, reference points are benchmarks used to compare the current status of a fishery management system against a desirable (or undesirable) state. FishKit users should develop reference points to support decision-making that are specific to their intended application. Below is a non-exhaustive summary of some research that has been carried out on the topic. Previous research exploring suitable SPR reference points as proxies for the fishing mortality rate that produces maximum sustainable yield (FMSY) and corresponding biomass, have suggested targets no less than 30% SPR for the most resilient fish stocks (Brooks et al. 2010; Harford et al. 2019). But where resilience is unknown (including the possibility of low steepness of the stock-recruitment relationship) or where life histories suggest lower productivity, like long-lived species, proxies for FMSY of no less than 35% to 40% SPR have been suggested (Clark 1991, 2002; Mace 1994; Brodziak 2002; NEFSC 2008; Harford et al. 2019). Studies also caution that 40% SPR may still be too low for certain life histories (e.g., protogynous hermaphroditism, forage species), when accounting for environmental variability, or where there is considerable uncertainty in growth parameters and the rate of natural mortality (Restrepo et al. 1998; Brodziak 2002; Dorn 2002; Cadrin 2012; Harford et al. 2019). As it relates to yield or YPR, a pragmatic approach that acknowledges limitations in achieving maximum yield and instead targets a satisfactory level is known as ‘pretty good yield’ (Hilborn 2010).
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