AHRENHOLZ ET AL.: ATLANTIC MENHADEN POPULATION AND FISHERY 



recruit analyses. On the other hand, parameters 

 generated in each area are inappropriate (biased) 

 for describing the entire population (or fishery). 

 For example, growth rates and average size at 

 age values for the north Atlantic area will be 

 greater than those for the population, and simi- 

 larly values estimated for the south Atlantic will 

 be less than true population values. (The only 

 exception is the North Carolina fall fishery, 

 which apparently harvests a reasonably well- 

 mixed migratory population.) 



Size at age and growth estimates for the entire 

 stock are needed for yield-per-recruit analysis for 

 the entire fishery and to ascribe an average size 

 at age for the spawning stock for each year. These 

 estimates are obtained by appropriately weight- 

 ing the sampling results from each fishing area, 

 as will be shown. 



Additionally, since growth of Atlantic men- 

 haden has been shown to be inversely related to 

 year class size (density-dependent) (ASMFC 

 fn. 4), a condition predicated during the estuarine 

 portion of the life cycle (Reish et al. 1985), growth 

 equations must be computed for each year class. 

 The fishing season is divided into quarterly incre- 

 ments for these analyses (Table 2). The analytical 

 steps taken to obtain these size estimates and 

 how they are used follows. 



Table 2. — Quarterly time increments used in 

 stock assessment analysis of Atlantic men- 

 haden. 



Beginning week Ending week 

 Quarter ending date ending date 



1 



2 

 3 

 4 



s 3/01 



> 5/31 



> 8/30 

 >11/29 



= 5/30 

 i 8/29 

 s 11/28 

 = 114/29 



'February of next calendar year, but same season. 



Area-Specific Mean Size at Age 

 and Growth Rates 



Mean lengths at age by area by quarter for each 

 of the 1965-81 seasons were estimated directly 

 from the port sampling data as unweighted arith- 

 metic means. These results were in turn arranged 

 by specific year class and fitted to the von Berta- 

 lanffy growth equation using the computer pack- 

 age BGC3 (Abramson 1971). It was assumed that 

 each mean length estimate was representative of 

 the middle of the quarterly interval, i.e., for the 

 first quarter (age X.0-X.25) the mean value is 

 assigned to age X.125, etc. These fitted area- 



specific von Bertalanffy parameters were used to 

 derive estimates of length at age for the begin- 

 ning of each time interval. These estimates were 

 in turn converted to estimates of weight at age for 

 the area-specific yield-per-recruit analysis. 



Mean Size at Age and Growth 

 for the Entire Fishery 



Predictive equations for growth which are rep- 

 resentative of the population as a whole (entire 

 fishery) are needed to estimate size at age for the 

 spawning stock and for yield-per-recruit analysis 

 of the entire fishery. For years 1965 to 1981, 

 mean lengths at age by quarter for the entire 

 fishery were obtained by weighting each area's 

 estimate of mean length by its corresponding 

 catch in numbers at age by quarter. Age 0.875 

 (fourth quarter age 0) was the youngest age for 

 which mean length was calculated. These values 

 were arranged by year class and were fitted to the 

 von Bertalanffy growth equation. 



Estimates of weighted mean length by quarter 

 could not be calculated for the fish caught before 

 1965 because estimates of numbers at age landed 

 by quarter by area were not available even 

 though size at age is available weekly. Since 

 much of the fourth quarter catch of the North 

 Carolina fall fishery is composed of migratory 

 stocks, it was presumed that a representative es- 

 timate of length at age for the entire population 

 might be obtained from the fourth quarter values 

 from this area alone. To test this hypothesis, 

 mean lengths for the 1965 to 1978 year classes 

 from the fourth quarter in the North Carolina fall 

 fishery were fitted to the von Bertalanffy growth 

 equation. The resultant curves were compared vi- 

 sually with results when all weighted mean 

 length values were used. The results were quite 

 similar when five or more data points were avail- 

 able and dissimilar to relative degrees when <5 

 data points were available. Because all year 

 classes from 1955 to 1964 had at least 5 data 

 points which met the above criteria, von 

 Bertalanffy curves were fitted to these values 

 (Table 3). 



Weight-Length Relationship 



The predictive growth equation used in this re- 

 port uses length at age. Weight-length relation- 

 ships were derived to estimate weight at age val- 

 ues. The greatest potential within year variation 

 in weight-length parameters is expected among 



577 



