Hayes: A biological reference point based on the Leslie matnx 



79 



spanning a trend in environmental conditions, the 

 estimate of future FJ/SSB may be biased. For this 

 stock, mean R/SSB for periods of 5 to 15 years appear 

 relatively stable. Over longer periods of time, mean 

 R/SSB shows an upward trend, punctuated by sharp 

 increases corresponding to the 1963 and 1975 year 

 classes when R/SSB ratios were much higher than in 

 any other years. Because of the trends observed over 

 longer periods of time, I chose the time period from 

 1976 to 1994 as representative of "current" conditions 

 for R/SSB, or equivalently, age-0 survival. For this 

 time period, R/SSB averaged 0.4092, and had a me- 

 dian of 0.1493. 



Based on the mean R/SSB for 1976 to 1994, the had- 

 dock population would be expected to grow at a rate 



of 18.0% per year with no exploitation (i.e. A,^=1.180). 

 For knife-edge recioiitment, I computed A^, for fishing 

 mortality rates ranging from to 2.0 (Fig. 1) and for 

 ages at entry (t^) from 1 to 5 years and for the commer- 

 cial fishery age selectivity observed in 199li^-94 (Table 

 2). Additionally, I determined F^, and ^MSP (following 

 the methods of Gabriel et al., 1989) for each age at entry 

 (Table 4). It is apparent ft-om this analysis that as age 

 at entry is delayed, the impact of fishing on the popula- 

 tion is decreased (Fig. 1). Thus, higher fishing mortality 

 rates can be sustained when recruitment to the fishery 

 is delayed (Table 4). In fact, when the age at entry is 5 or 

 greater, any level of fishing mortality is sustainable. 



These conclusions are not new; analysis of SSB/R 

 yields similar insights into the response of populations 



