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Fishery Bulletin 93(3). 1995 



less they are in port for repairs. Any time period that 

 assumes continuous fishing and accounts for unpro- 

 ductive fishing days should be a satisfactory unit of 

 fishing effort (Nicholson, 1971a). Number of land- 

 ings as a unit of effort assumes continuous fishing. 

 Although the number of days that a given vessel was 

 fishing in a week was unknown it was assumed that 

 variations were randomly and normally distributed. 



Calculation of weekly catchability 

 coefficients 



The catchability coefficient is defined as the fraction 

 of a fish stock that is caught by a defined unit of 

 fishing effort (Ricker, 1975). The relation between 

 catch, effort, abundance, and catchability is 



(Sokal and Rohlf, 1981) was used to test for signifi- 

 cant differences in annual patterns of weekly 

 catchability coefficients for each age group between 

 years. This is the nonparametric analog to the para- 

 metric analysis of variance (ANOVA) randomized 

 complete block design, but the rankings of the vari- 

 ates within each block are used rather than the ac- 

 tual measurements. A nonparametric test was used 

 because the relative degree of weekly fluctuations 

 from year to year may vary owing to biotic or abiotic 

 factors. Thus, heterogeneity of variance between 

 years may be expected, making a parametric model 

 inappropriate. 



Results 



[fit 



= g,N t , 



(8) 



where ( Clf) t = average catch per unit of effort over 

 period t; N t = average abundance during period t; 

 and q t = catchability during period t. 



The VPA estimates of abundance are for the be- 

 ginning of a time period. For the short, one-week time 

 periods used in this study, average abundance in a 

 period is assumed to approximate (N f + N f+1 )/2. Av- 

 erage catch per unit of effort in a time period can be 

 calculated as total catch divided by total effort for 

 that period. The above equation can thus be rear- 

 ranged to define the catchability coefficient as 



<lt = 



m 



(M-) 



(9) 



This equation was used to calculate initial weekly 

 catchability coefficients for each age group. No 

 catchability estimate was made for weeks in which 

 there was no catch landed for the age group consid- 

 ered. Also, no catchability estimate was made if abun- 

 dance estimates were not made for both the week 

 being considered and the following week, because the 

 average abundance during the week {N t +N t+l /2) was 

 used to estimate catchability. 



Statistical analysis 



Weekly abundance estimates at age were made in 

 each year from the first week in which a catch was 

 landed until the last. Catchability coefficients by age 

 were estimated for each week for which there were 

 abundance estimates for the current and subsequent 

 weeks. Friedman's method for randomized blocks 



The Friedman's test indicated that at least one year 

 was significantly different from the others at the 0.05 

 alpha level for age groups 1, 2, 3, and 4 but not sig- 

 nificant for the remaining age groups. Subsequent 

 multiple comparisons for these age groups with 

 Friedman's rank sums (Hollander and Wolfe, 1973) 

 failed to show temporal differences. These differences 

 were therefore considered to be random variations 

 about a mean, allowing the annual variations for each 

 week to be averaged to determine the underlying 

 pattern. 



Plots of high, low, and mean weekly catchability 

 were created for each age group (Fig. 1). For most 

 age groups the range of catchability coefficients was 

 greater at the beginning and end of the season than 

 in the middle. The plots were examined visually for 

 signs of fluctuation within a season. The graphs of 

 weekly catchability showed the following pattern: the 

 first part of the catchability curve features an initial 

 peak followed by a rapid decline. This decline is fol- 

 lowed by a gradual increase in catchability as the 

 season progresses, then by a second sharp peak near 

 the end of the season. The height of the initial peak 

 relative to the rest of the plot is most pronounced in 

 age-1 and age-2 fish. It becomes less pronounced and 

 disappears altogether as the fish become older. This 

 first peak does not occur for age-0 menhaden, which 

 are subject to a fishery that is largely directed against 

 catching them in the fall. 



The catchability graph of age-0 menhaden differs 

 from the other age groups. This age group is not tar- 

 geted during most of the year but becomes subjected 

 to a directed fishery off North Carolina in the fall. 

 Catchability for this age group remains at or near 

 zero for most of the season because no age-0 fish are 

 being caught. Near the end of the season, it rapidly 

 rises from zero to a peak and then quickly drops back 

 to zero as the fishery ends. 



