AHRENHOLZ: RECRUITMENT AND EXPLOITATION OF GULF MENHADEN 



Table 7. — Estimates from scaled data of total annual instan- 

 taneous mortality rate (Z2), rate of exploitation ( Ui), instantane- 

 ous fishing mortality iFih instantaneous natural mortality (M), 

 and their approximate 95% confidence intervals (C.I.), for Gulf 

 menhaden tagged as adults in the Gulf of Mexico. 



Parameter 



Estimate High 95% C.I. limit 



Low 95% C.I. limit 



M 



2 2241 

 0.4692 

 1.1701 

 1.0540 



2.4356 

 0.5041 

 1 .3456 

 1 .0900 



2.0126 

 0.4307 

 1 .0005 

 1,0121 



1969 and 1971 releases, no Type C correction, and 

 an unweighted predictive regression estimate for 

 Z. The resulting mean estimate for M, 1.0852, is 

 very similar to the estimate of M, 1.0935, obtained 

 from the more refined analysis. Inclusion of the 



1970 release-recovery data in this analysis re- 

 sulted in a somewhat lower mean estimate of M, 

 1.0089. The lower M estimates for the 1970 re- 

 leases probably resulted from a lower rate of tag- 

 ger induced mortality than for the 1969 and 1971 

 release groups, as the 1970 tagged fish were larger 

 than the fish tagged during the other 2 release 

 years. 



As evidenced by the similarity of results from 

 the two modified analyses and the results depicted 

 in Table 6, the estimate of M is apparently more 

 sensitive to the correction factor for tagging mor- 

 tality loss than the estimates of other parameters 

 used in its estimation. Unfortunately, data on the 

 nature of the statistical distribution on which to 

 base variance estimates and hence approximate 

 95% C.I. are lacking. Based on the current knowl- 

 edge of tagging mortality for menhaden, the esti- 

 mates obtained for a 20% tagging loss and the 

 weighted regression technique (M = 1.0935 and u 

 = 0.456) are the best estimates currently avail- 

 able. 



AREA-SPECIFIC AND AGE-SPECIFIC 

 EXPLOITATION RATES 



To estimate area-specific and age-specific 

 exploitation rates from recoveries of tagged 

 juveniles, it is necessary to estimate the number of 

 tagged fish alive at the beginning of each fishing 

 season. These numbers can be estimated from the 

 number of recoveries by sequential analysis 

 (Ricker 1975). The data and parameters needed 

 are the number of recoveries (Rn) by age in), an 

 estimate of M, and an estimate of u for a given 

 cohort during its last year in the fishery. 



The numbers of tags recovered in all years for 

 fish released in specific areas were pooled by age of 



capture and, with one exception, were unweighted 

 (Table 8). For three estuaries, which constituted 

 the southeast Texas area, the recoveries were 

 weighted so that each estuary contributed equally 

 to the totals. 



Table 8. — Area-specific annual exploitation and fishing mor- 

 tality rates estimated by sequential analysis of recoveries of 

 tagged juvenile Gulf menhaden in the Gulf of Mexico. Numbers 

 in parentheses are initial rates of exploitation obtained from the 

 analysis of adult-tagged fish. 



'Weighted recoveries for this subarea only. 

 ^Pooled age-3 and age-4 recoveries. 

 ^Estimates are unrealistic: see Table 9 and text. 



The number of tagged fish alive (Nn) in their 

 last representative year in the fishery at the be- 

 ginning of a fishing season was estimated by: 



u 



(7) 



where u = 0.456 from the adult tagging analysis. 



An estimate of Sn -1 was required to estimate the 

 number of 2-yr-old tagged fish alive (Nn-i) at the 

 beginning of a fishing season from the equation: 



K-i = 



N. 



'n-l 



(8) 



Sn-i was estimated by substituting trial mortal- 

 ity estimates (assuming M = 1.0935) into the fol- 

 lowing equation until the right side equaled the 

 number of recoveries at age n-l (Ricker 1975): 



333 



