FISHERY BULLETIN: VOL. 85, NO. 3 



Table 3. — Estimated von Bertalanffy growth parameters for 

 Atlantic menhaden, year classes 1955-78. 



'Year classes 1955-64 represented by fitted values for 4th quarter, 

 area 5 (see text). 



2Year classes 1965-78 represented by fitted values for weighted quar- 

 terly mean lengths 



VIRTUAL POPULATION ANALYSIS 



Virtual population analyses (VPA's) were con- 

 ducted to reconstruct population sizes and esti- 

 mate rates of fishing mortality. Analyses were 

 conducted on all age groups of the 1947-78 year 

 classes which were represented in the 1955-81 

 landings. The backward sequential computations 

 were performed using the computer program 

 MURPHY written by Tomlinson (1970). 



Instantaneous Rate of Natural 

 Mortality 



The estimate of the annual instantaneous rate 

 of natural mortality (M) used in this report was 

 0.45. Early estimates were from catch statistics, 

 0.37 (Schaaf and Huntsman 1972); from prelimi- 

 nary tag-recovery analysis, 0.52 (Dryfoos et al. 

 1973); and from a more extensive tag-recovery 

 analysis, 0.50 (mean of age-specific rates for 

 ages 2 and 3) (Reish et al. 1985). The 0.45 value 

 represents a mean of the range of available esti- 

 mates. The implications of the selection of 0.45 for 

 M are addressed. 



quarters. Because each area (except perhaps 

 area 5) contains a limited portion of the range of 

 sizes extant in the menhaden population, the 

 weight-length relationship is estimated across 

 areas, but within quarters. Annual variation was 

 also assumed to exist, thus parameter estimates 

 were calculated for each fishing season where 

 subsequent yield-per-recruit analysis was in- 

 tended (1970-78) using logg transformed data and 

 least squares regression (Table 4). 



Annual Mean Weights Weighted 

 by Catch 



Estimates of annual weighted mean weight by 

 age of Atlantic menhaden in purse seine catches 

 were calculated to permit computations of age- 

 specific and year class-specific biomass contribu- 

 tions to landings. Weighted mean weight for the 

 entire fishery was calculated from the average 

 weight by age by season for each of the five recog- 

 nized areas of the fishery and then weighted by 

 the estimated numbers caught by age in each re- 

 spective area. These data were derived directly 

 from the port sampling data and are not from 

 von Bertalanffy derived lengths converted to 

 weights. 



Temporal Organization of Analyses 



The time periods used in these analyses 

 (Table 2) closely correspond to critical life history 

 and fishery events. The birth date for a year 

 class, and the beginning of a new fishing season 

 for Atlantic menhaden, is 1 March. Because of the 

 protracted spawning season of menhaden, young 

 of the year may have been spawned as early as 

 the previous August and as late as the following 

 May or June, but most of the spawning takes 

 place in the fall and winter (Nelson et al. 1977). 

 The beginning of the fourth quarter (week begin- 

 ning > Nov. 29) is used as a finite date to estimate 

 spawning stock size. Thus, the spawning stock in 

 the fall (beginning of the fourth quarter) of the 

 previous calendar year (age X.75) is defined to be 

 the parental stock for a subsequent (1 March) 

 year class. Recruitment is examined at age 0.5 

 (beginning of third quarter, age 0) and at age 1.0 

 (beginning of first quarter, age 1). 



Three sets of VPA's were conducted with the 

 length of the time intervals varied between sets. 

 The first set provided the basic estimates for re- 

 construction of the historical population and the 

 estimates of rates of fishing mortality. This series 

 was done on an annual basis and involved all 

 subject year classes. These estimates are used pri- 



578 



