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Fishery Bulletin 100(2) 



partial recruitment based on average F at age, these refer- 

 ence points were estimated for the recent time period from 

 the primary and alternate catch matrices as F^^.^^ = 0.5/yr 

 and 0.7/yr, respectively; and F,, j = 0.23/yr and 0.25/yr, re- 

 spectively (Table 7). 



Spawning potential ratio, spawning-stock biomass, 

 and stock-recruitment model 



Estimates of static SPR were calculated by catch matrix, 

 time period, and assumed value of M and for four mea- 

 sures of spawning biomass (total mature biomass, mature 

 female biomass, mature male biomass, and egg produc- 

 tion) (Table 6; Fig. 7). Static SPR based on mature female 

 biomass was less affected by increases in F than static 

 SPR based on mature male biomass because younger fish 

 are predominantly female and older fish, male. For exam- 

 ple, full F that produced 59% SPR in mature female bio- 

 mass produced 49% SPR in egg production, 42% SPR in 

 total mature biomass, and 27% SPR in mature male bio- 

 mass (Table 6). 



Corresponding estimates were made of reduction in the 

 proportion of males due to fishing in the three periods. 

 For example, a value of 69% in the last column of Table 

 6 means that if the proportion of males in the mature un- 

 fished population had been 50'/( , introduction of fishing 

 mortality would reduce this proportion to 34.5% of the 

 population (69% x 50%). These estimates were made on 

 the basis of observed sex ratios at size and assuming that 

 the rate of transformation from female to male does not 

 increase as the population is fished down. 



Total spawning stock biomass (SSB) was estimated from 

 the primary catch matrix to have reached its peak in about 

 1979 at 3530 t, dechning to 397 t in 1997 (Fig. 8A). When 

 missing values were substituted for zeroes in computing 

 the CPE index, estimates of SSB near the end of the se- 

 ries were slightly higher (Fig. 8A). Estimates from the al- 

 ternate matrix were similar, with the largest differences 

 occurring before 1983 (Fig. 8A). 



Static SPR estimated from the primary catch matrix 

 was high during the 1970s, reached 67% in 1975, and de- 

 clined to a minimum of 33% in 1982, increased again to 

 55% in 1993, and declined to about 18% in 1997 (Fig. 8B). 

 Estimates from the alternate catch matrix were similar, 

 but markedly lower from 1983 to 1994 (Fig. 8B). Values of 

 full F providing spe cified values of static SPR (based on 

 female egg production and total spawning stock biomass) 

 are summarized in Table 7, along with values of full F av- 

 eraged by period, for comparative purposes. 



The recent management definition of overfishing is stat- 

 ic SPR <35% (amendment 12 ISAFMC'*]). Our primary es- 

 timates are of static SPR >35'7f from 1972 to 1994 (except 

 for 1982), lower thereafter Estimates from the alternate 

 catch matrix show static SPR >35% from 1972 to 1980, 

 lower thereafter 



During the early to mid 1970s, a large spawning stock 

 produced high recruitment. Despite a high spawning- 

 stock size estimated through about 1983, SPR and re- 

 cruitment declined, and the unsustainable landings of the 

 late 1970s and 1980s reduced the spawning stock to levels 



not expected (under the stock-recruitment model) to pro- 

 vide good recruitment. Similar patterns were apparent in 

 stock-recruitment cui-ves derived from both catch matri- 

 ces (Fig. 9). 



Estimates of benchmarks from simulations 



Estimates of MSY, Bmsy s^^ F^igy were made from the 

 stock-recruitment model and age-structured simulations 

 (Table 8; Fig. 10). In addition, minimum stock size thresh- 

 old (MSST), a benchmark recently introduced into U.S. 

 Federal fishery management, was calculated from B-^^^y as 

 suggested in Restrepo et al. (1998). namely as MSST = 

 (1-M) S[^,t;Y' with M = 0.28/yr Although benchmarks are 

 somewhat sensitive to assumptions examined, sensitivity 

 was small compared with the difference between estimated 

 benchmarks and current status of the stock and fishery 

 (Table 8). For example, estimates of MSY obtained in this 

 way (240-280 t/yr) were similar to recent landings (about 



