Per Recruit Analyses

Recruitment in many fish stocks is highly stochastic. To evaluate fishery management measures in spite of this haracteristic, 'per-recruit' analyses were developed. By computing the utility (in some sense) expected from a typical fish from recruitment through death, such analyses sidestep the uncertainty associated with recruitment. Per-recruit analyses are widely used to model yield (catch in weight) and spawning contribution. However, other measures of utility, such as economic value, can be modeled equally well.

Yield per recruit (YPR) expresses yield as a function of overall fishing mortality rate, conditioned on the selectivity pattern (Figure 4). It is calculated as

where Ya is yield at age (eqn [28]), and R is an arbitrary recruitment used to initialize abundance at the first exploited age. If selectivity shifts to older fish, YPR increases due to somatic growth, but decreases due to the prolonged force ofnatural mortality.

As stocks have become more heavily exploited, focus has broadened from maximizing yield to maintaining stock viability through adequate spawning biomass. This is the motivation for analysis of spawning biomass per recruit (SPR or $F). Specifically, SPR quantifies the amount of reproductive output per recruit expected a a s a s a

Figure 4 Example of per-recruit analysis, based loosely on tilefish (Lopholatilus chamaeleonticeps) off the southeastern United States. Solid line represents yield per recruit (YPR; weight per fish); dashed line represents spawning potential ratio unitless).

Fishing mortality rate (yr1)

Figure 4 Example of per-recruit analysis, based loosely on tilefish (Lopholatilus chamaeleonticeps) off the southeastern United States. Solid line represents yield per recruit (YPR; weight per fish); dashed line represents spawning potential ratio unitless).

based on random sampling. In contrast, when abundance indices are developed from fishery-dependent data, removing variation in q (a step known as 'effort standardization') can be difficult. Catchability may vary for biological or nonbiological reasons. If fishing effort is mainly along the edge of a stock's range, U computed from fishery data may decline more quickly than abundance. Conversely, if catches saturate at some level due to finite fishing capacity, U may not increase when abundance does. Such hyperstability of U can occur also when abundance decreases, because skillful fishermen often maintain their catch rates at lower stock sizes. This phenomenon is especially pronounced in schooling species, where aggregations may be easy to locate. A related issue is the increase in q over time due to improvements in fishing gear, vessel efficiency, and navigation technology.

under different fishing regimes. Computation is similar to that of unfished SPR (eqn [11]), with the same assumptions and fishing mortality included:

It is often convenient to express SPR relative to that with no fishing ($0), a ratio known as spawning potential ratio (Figure 4). Here, we propose the notation = $F/ $0. This ratio scales SPR to a species' reproductive potential, which allows more meaningful comparison across stocks and species than does SPR alone. Unfortunately, the abbreviation SPR has been used by different authors to mean either $ or leading to considerable confusion.

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