FISHERY BULLETIN: VOL. 84, NO. 2 



the population loses 52% of the age-1 fish and 35% 

 of the older fish to natural mortality. 



The short-term impact on the entire population 

 was determined by 1) calculating a mean F weighted 

 by the number of individuals taken by age for ages 

 1-3 and then estimating u by Equation (4) and 2) 

 directly comparing numbers landed with the recon- 

 structed population sizes. The average annual loss 

 of individuals from the population to the fishery was 

 about 40% by both methods. However, recruitment 

 is only partial at age 1, and u is much higher at older 

 ages. Natural mortality losses averaged about 

 47%/year for the overall population. In the absence 

 of fishing, annual losses to natural mortality would 

 be about 67% for all ages. 



A measure of how a unit of fishing effort affects 

 the population is commonly quantified through its 

 effect on F. Traditionally this effect, the catchabil- 

 ity coefficient (q), is assumed to be a constant. The 

 total fishing effort times this constant should equal 

 F for the year: 



F=qf 



(5) 



where / = a unit of fishing effort (here, a vessel- 

 ton-week). 



if the catchability coefficients were independent of 

 this variable (Fig. 4). An inverse relationship was 

 noted, a situation which also exists for the Atlantic 

 menhaden (Schaaf 1975b). The data were fitted to 

 the power function to demonstrate the curvilinear 

 inverse relationship. 



SPAWNER-RECRUIT RELATIONSHIP 



The cohort analysis provides estimates of popula- 

 tion size at ages 1-4 from 1964 to 1977. All fish 

 mature by the end of their second year, and spawn- 

 ing apparently reaches a peak in December and 

 January (Lewis and Roithmayr 1981). Therefore, 

 estimates of number-at-age in the population as of 

 1 January were used to provide estimates of spawn- 

 ing stock size and subsequent recruitment (Table 6). 

 Spawning stock was identified as all fish that had 

 reached at least their second birthday by 1 January. 

 Lewis and Roithmayr also showed that length ac- 

 counted for a greater porportion of the variance in 

 fecundity than either age or weight. Our fecundity 

 estimates, assuming a 1:1 sex ratio, were based on 

 Lewis and Roithmayr's relationship: 



log, E = -9.8719 + 3.8775 (log, I) 



(6) 



Estimates of q for the 1964-77 fishing years were 

 obtained by solving for q in the above equation for 

 the population F for ages 1-3 (i^.3) weighted by 

 number taken at age, and also for the population 

 total F (Table 5). The resultant g's are quite variable 

 (in excess of fourfold). Estimates of q were plotted 

 against corresponding population size to determine 



where E = fecundity in number of eggs and 

 I = fork length in millimeters. 



Because there was little variation in size at age 

 by year class, and the differences noted were not 

 related to population size, estimates of mean length- 

 at-age were obtained from the overall von Bertal- 



Table 5. — Estimated gulf menhaden population size as of April 4, number caught by 

 year, population exploitation rate (u), estimated population fishing mortality rate (F), 

 population catchability coefficient (q) x 10" 3 , weighted annual mean fishing mortal- 

 ity rate from cohort analysis (^.3), and the corresponding F v3 catchability coefficient 

 (q) x 10 " 3 calculated from vessel-ton-weeks (Table 1), 1964-77. 



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