AHRENHOLZ ET AL.: ATLANTIC MENHADEN POPULATION AND FISHERY 



Table 4. — Weight-length regression parameters for Atlantic menhaden, by quarter and year, 1970-81 seasons 



(\n W = a + b\r\ L). 



marily in discussions of the impact of nominal 

 effort and for modification of input variables for 

 surplus production analysis. 



The second series, with shorter time intervals, 

 permitted a more precise apportioning of fishing 

 mortality between fishing areas within a fishing 

 season and provided within season estimates of 

 numbers at age present in the population. This 

 series was conducted on a quarterly basis and 

 included the 1965-78 year classes. These esti- 

 mates permitted a reconstruction of the fishery 

 for the 1970-78 seasons which forms the basis of 

 the subsequent yield-per-recruit analyses. The 

 quarterly estimates of numbers at age are also 

 used to estimate numbers of recruits for the 

 1965-78 year classes and the numbers of spawn- 

 ers that were ultimately derived from these year 

 classes. 



The third series was conducted to estimate 

 numbers of recruits and their parental spawning 

 stock for the 1955-64 fishing seasons. This series 

 included the 1947-64 year classes and used mixed 

 length time intervals. A V2-yr interval, which in- 

 cluded ages 0.50 and 0.75 (quarters 3 and 4), was 

 used to provide estimates of numbers of age-0.5 

 individuals present in the population. The time 

 interval for age-1 fish was annual. Intervals for 

 age-2 and older individuals were alternately 

 three quarters of a year (quarters 1-3), corre- 

 sponding to ages X.0-X.50, and one quarter of a 

 year (quarter 4), corresponding to age X.75. This 

 temporal construction of the numbers at age data 

 required several adjustments which are dis- 

 cussed. 



Additional VPA's were conducted to examine 

 the sensitivity of results to the value of natural 

 mortality used (0.45) and to the initial estimates 

 of fishing mortality rates. A series of annual 



VPA's were conducted for the 1955-78 year 

 classes with M = 0.35 and M = 0.55, which en- 

 compass the range of available estimates dis- 

 cussed earlier. Additional annual runs were con- 

 ducted with varied starting F's for the 1955 year 

 class, which for reasons discussed later, poten- 

 tially represents a worst case situation relative to 

 rates of convergence of estimates. 



VPA Numbers at Age Landed 

 Data Sets 



The annual estimates of numbers at age caught 

 were rearranged from a seasonal format to a year- 

 class format. For the quarterly runs, the weekly 

 catch at age estimates were summed to quarters 

 and rearranged by year class. The mixed time 

 interval VPA data sets were derived from the an- 

 nual set, and thus required some approximations 

 and adjustments to obtain a subyear format. An- 

 nual catches of age (1955-64 seasons) were as- 

 sumed to be in quarters 3 and 4 since the bulk of 

 the age-0 catches occurred after 30 August (be- 

 ginning of the third quarter). The major portion, 

 if not all, of the catches of age-2 + fish (spawning 

 ages) that were made during the fourth quarter 

 time interval, was in the North Carolina fall fish- 

 ery. During the 1965-69 fishing seasons, an aver- 

 age of 58% of the age-2 + fish that were landed in 

 the fall fishery were landed during the fourth 

 quarter. Hence, 58% of the fall fishery landings of 

 age-2 + fish of the 1947-64 year classes were as- 

 sumed to have been taken during the fourth quar- 

 ter. The remainder of the total annual catch was 

 assigned to the single three-quarter time interval 

 (quarters 1-3). The time period used for the age-1 

 fish remained annual, so no adjustments were 

 required. 



579 



