118 



Fishery Bulletin 105(1) 



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1,0 - 



0,8 - 



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6 - 



0.4 - 



0.2 



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/WlVCl/=0,98{n/c)-°59 

 r2 = 0,98 



10 



20 



30 



40 



F 



Sample size per length class (n/c) 



Figure 1 



The mean weighted coefficient of variation (MWCV) 

 for 596 subsamples was closely related to the sample 

 size (n ) divided by the number of per length classes in 

 the sample (c). A good fit was obtained for the power 

 function indicated by the solid line; its parameters 

 are given at the top of the plot. The dashed line 

 indicates the theoretical maximum MWCV (Eq. 4.). 

 The histograms show the distribution of the samples 

 on both axes. 



excessively large sample sizes. The range of sample 

 sizes was between 2.2 and 24.7 times the number of 

 length classes (2.5% and 97.5% quantiles), resulting 

 in a range of MWCVs between 0.14 and 0.61. With 

 a minor increase in effort, the sample size might be 

 increased to 10 per length class for each subsample, 

 resulting in an MWCV of around 0.25 for all samples. 

 Considering that the precision deteriorates very rap- 

 idly for sample sizes of less than 10 per length class, a 

 minimum sample size of 10 times the number length 

 classes in the sample is suggested as a rule-of-thumb 

 in the present case. 



The previous analysis shows that, in order to ob- 

 tain the same level of precision for all subsamples, 

 the sample size should be directly proportional to the 

 number of size classes. In absence of specific guid- 

 ance on the sample size during the 2005 survey, the 

 chosen sample size was only weakly correlated to the 

 number of length classes in the sample of poor cod 

 and haddock, whereas no significant correlation was 

 found for blue whiting and Norway pout (Fig. 2). The 

 same figure also shows that the MWCV in subsamples 

 tended to increase with the mean length of the fish in 

 the sample. This increase indicates that samples with 

 a large mean size tended to be sampled with lower 

 precision than samples of smaller fish of the same 

 species. 



Discussion 



Length distributions that result from combining a 

 number of different samples exhibit greater variation 

 than predicted under the multinomial model given in 

 Equation 1 (Smith and Maguire, 1983). Fish populations 

 are usually not uniformly mixed; therefore individual 

 samples are not random samples from the population 

 (Pennington et al., 2002). The simple multinomial model 

 does not take account of the between-sample variability 

 and will therefore underestimate the total variance. 

 However, Equation 1 does provide an unbiased estimate 

 of the variability within each sample, which is the vari- 

 ability that would occur if one could repeatedly take 

 a random sample at the same location and time and 

 measure these without error. This is the variability that 

 is of interest when deciding whether the sample size is 

 large enough to estimate the length distribution from a 

 particular haul with a certain precision. Therefore, the 

 MWCV is a suitable measure for this exercise. 



In order to obtain a precise population estimate, it 

 is important to maximize the number of sampling lo- 

 cations because of the considerable between-sample 

 variability that is usually present (Pennington et al., 

 2002). Pennington et al. (2002) suggested maximiz- 

 ing the number of sampling locations at the expense 

 of the number of fish measured. However, the number 

 of hauls is often limited by practical considerations, 

 and length measurements can be obtained quickly and 

 cheaply. Therefore, it seems prudent to sample enough 

 fish from each haul to obtain a length distribution that 

 is representative of that catch at that particular loca- 

 tion. Detailed information on the length distribution 

 at each station can be valuable for exploratory data 

 analysis, such as investigating the spatial structure in 

 the data. Nevertheless, this level of sampling may not 

 be strictly necessary for a precise population estimate of 

 the length-frequency distribution for an age- or length- 

 based assessment. 



The samples in Figure 1 included a large range of 

 species and size categories offish, but the variability in 

 the MWCV was small after taking account the sample 

 sizes. This small amount of variability indicates that 

 the MWCV is not very sensitive to the exact shape of 

 the distribution and can be predicted with high preci- 

 sion, at least within the range of distributions encoun- 

 tered on the survey. A minimum sample size of 10 times 

 the number of length classes in the sample appears to 

 be a reasonable compromise between effort and preci- 

 sion in the present case. 



The current analysis has focused on subsampling 

 during surveys; however the same principles can be 

 applied to any process of collecting data for which the 

 shape of the distribution is of interest. The desired pre- 

 cision level for these cases will depend on a number of 

 factors. For certain species that are of little commercial 

 or scientific interest, but which may span across a large 

 number of length classes, the suggested sample size of 

 10 per length class may be excessive. Likewise, as the 

 MWCV is directly proportional to the number of length 



