Pennington et a\ Assessing the precision of frequency distributions from trawl survey samples 



79 



s 

 s 



f i 



i 8 

 o - 



24 A 24 6 24 6 25 25 2 25 4 25 [ 



Effective sample size 



Mean length (cm) 



tu. 



Effective sample size 



*= 10 



^ fTl 



100 110 120 



Effective sample size 



24 4 24 6 24 8 25 25 2 25 4 25 6 



Mean length (cm) 



24 4 24 6 24 8 25 25 2 25 4 25 6 



Mean length (cm) 



Figure 2 



Simulated estimates of the distribution of the effective 

 sample size. n\.,^, and of the mean length, R. when the total 

 number of fish measured is reduced for the 1999 winter 

 survey in the Barents Sea. The top panel is when a max- 

 imum of k = 100 fish are selected per subsample for a 

 total of m = 17,615 fish in each run; the middle panel, k = 

 30, m = 7240; and the bottom panel, k = 10, m = 2597. 

 The estimate of the population mean based on the entire 

 sample (m=21,769) is 24.96 and its 95*?^ confidence interval 

 is (22.26, 27.66). 



Ifp = 0,then var{R) = aj/M and the effective sample size is 

 equal toM. However if p> li.e. fish of similar length tend 

 to be caught together), then the terms in the parentheses 

 can greatly increase the variance and thus drastically 

 reduce the effective size. In particular, the term ap M 

 is relatively large for trawl surveys. Finally, if p < 0, which 

 is rarely if ever the case for trawl surveys, then the effec- 

 tive sample size will be larger than M. 



The precision of estimates of other population charac- 

 teristics, such as age distribution, can also be relatively 

 low compared with the number of fish sampled if the par- 

 ticular attribute or measurement is more similar for fish 

 caught together than for those in the general population. 

 For example, the precision of estimates of mean stomach 

 contents (Bogstad et al. , 1995) or diet composition (Tirasin 

 and Jorgensen, 1999) can be relatively low because of in- 

 trahaul correlation. 



An effective sample size of one fish per tow does not 

 mean only one fish should be measured at each station, 

 but it implies that the only way to improve survey pre- 

 cision significantly is to increase the number of stations, 

 i.e. to sample fish from as many locations as possible. The 

 bootstrapped estimates of precision and the sampling sim- 

 ulations showed that reducing or increasing the number of 



Winter 1995 



ll 



Jiilii, 



Winter 1999 



n. 



~^si«....._. 



20 40 60 



100 120 140 



20 40 60 80 100 120 140 



Lengtti (cm) 



Figure 3 



Bootstrapped estimates of the 95'7r confidence intervals 

 for the proportion of cod in the Barents Sea in each 5-cm 

 length bin. for winter 1995 and for winter 1999. The inner 

 brackets denote the confidence intervals if the estimates 

 are based on all the cod measured during the surveys and 

 the outer brackets denote the confidence intervals if 10 fish 

 arc measured for each subsample. 



fish measured (or caught and measured) at a station will 

 not significantly affect the precision of length-distribution 

 estimates. In general, if intracluster correlation is positive 

 for an attribute, then it is usually best to take a small 

 sample from as many locations as possible (e.g. Bogstad et 

 al.. 199.5; McGarvey and Pennington, 2001 ). 



It has been shown that tows of short duration are in 

 general more efficient for estimating stock abundance 

 than long tows (Godo et al., 1990; Pennington and Vols- 

 tad, 1991; Gunderson. 1993; Carlsson et al.. 2000). There- 

 fore one way to collect samples from more locations and 

 improve overall survey efficiency without increasing sur- 

 vey cost is to reduce tow duration and use the time saved 

 to increase the number of survey stations (Pennington 

 and Volstad, 1994). For example, if tow duration were re- 

 duced from 60 minutes to 15 minutes for a trawl survey of 

 shrimp off West Greenland, then 44^^^ more stations could 

 be surveyed (Carlsson et al., 2000). Likewise, a reduction 

 in tow duration from 30 minutes to 10 minutes for a trawl 

 survey on Georges Bank would increase the number of 

 survey stations by about 30*7^ (Pennington and Volstad, 

 1994). 



The total number of fish caught would be fewer, on av- 

 erage, if tow duration was reduced, but estimates of fish 

 density would be more precise and the resulting sample 

 of individuals would be more representative of the entire 

 population (Pennington and Volstad. 1994). 



