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Fishery Bulletin 101(3) 



suggested that the basic ratio methods (mean of the ratios) 

 might actually be less biased for lognormally distributed 

 data than for normally distributed data. Both the CPE 

 and F:S basic ratio estimators showed only about 10% of 

 the bias with the delta lognormal data that they had with 

 normally distributed data. The change in underlying dis- 

 tribution made very little difference to the bias shown by 

 the grand CPE ratio method and increased the bias in the 

 grand F:S method. For the CPUE-mean-per-unit method, 

 the normally distributed data had less bias by an order of 

 magnitude than the delta lognormal data, but neither of 

 the biases was statistically significant, and both were much 

 less than a 1% overestimate. 



Cochran (1977) stated that the ratio estimator is the 

 best linear unbiased estimate if the relationship between 

 >',, which is the catch of the bycatch species, and.*,, which is 

 the auxiliary variable, is a straight line through the origin 

 (indicating that the ratio of bycatch to shrimp or the catch 

 of bycatch per hour fished is constant over all observations) 

 and if the variance ofy, about this line is proportional to 

 X,. In practice, these conditions rarely hold true. The ratio 

 of fish to shrimp catches and the bycatch per hour fished 

 from field data often vary considerably among observa- 

 tions because of the patchy spatial distributions offish and 

 shrimp, seasonal differences in the relative abundances of 

 fish and shrimp, movements associated with development 

 through different life stages, and environmental factors. In 

 addition, the bias of a ratio estimator is on the order of 1/n, 

 indicating that the bias will be small if « is large (Cochran, 

 1977). In practice, n, or the number of onboard bycatch 

 observations, is often very small, particularly if the data 

 are stratified by season or area, leading to large biases in 

 ratio estimators. 



The Hartley-Ross ratio estimator, which is a form of the 

 basic ratio estimator method, may in some cases be an 

 unbiased or less biased ratio estimator for small samples 

 (Cochran, 1977). However, the Hartley-Ross method was 

 not effective for the field data in the present study, giving 

 nonsensical negative estimates of bycatch for all species 

 in the southern region, although the estimates in the 

 northern region were generally (but not always) some- 

 where between the basic and grand F;S ratio methods. 

 The problems with the Hartley-Ross ratio estimator in the 

 southern region may have been due to two factors: 1) the 

 very low value for total shrimp landings from trip tickets 

 in the southern region, and 2) discrepancies between the 

 observed average catch of shrimp per day and the fleet 

 shrimp catch per day from the trip ticket database. The 

 Hartley-Ross equation starts with the mean of the indi- 

 vidual fish to shrimp ratios expanded by the total shrimp 

 landings (the basic F:S ratio estimator) and corrects the 

 estimate based on the sampling fraction multiplied by 

 a quantity that includes the average observed catch of 

 shrimp per day (Eq. 8). The total shrimp landings recorded 

 on trip tickets for the southern region were extremely low, 

 about 16 times lower than the total shrimp landings in the 

 northern region, although the number of days fished was 

 about half as many in the southern region. In addition, the 

 average shrimp catch per day on vessels that I observed in 

 the southern region was much greater than the average 



reported on trip tickets (173.4 kg per day observed vs. 20.6 

 kg per day from trip tickets), whereas the average shrimp 

 catch per day of shrimp that I observed in the northern 

 region was much lower than the catch per day shown on 

 trip tickets (55.6 kg per day observed vs. 173.5 kg per day 

 from trip tickets). The result of this combination of factors 

 was that the estimated total bycatch before correction in 

 the southern region was very small due to the low amount 

 of total shrimp landings, whereas the correction factor was 

 very large because of the high observed average catch of 

 shrimp, leading to negative estimates of total bycatch. 

 These problems did not occur in the northern region. Low 

 shrimp landings in the southern region compared to the 

 northern region may have been due to an actual difference 

 in the abundance of shrimp or differences in fishing habits 

 such as a smaller number of nets per boat, tows per day, 

 or tow times per tow in the southern region. However, it is 

 also possible that more fishermen in the southern region 

 than the northern region keep their catch or sell part 

 of their catch independently without generating a trip 

 ticket, which would reduce the total landings of shrimp 

 in the trip ticket database. The differences in the average 

 observed catch of shrimp per day were probably due to a 

 combination of factors, most of them based on the prob- 

 lem of nonrandom or nonrepresentative sampling of boats. 

 Because I depended on volunteer fishermen, the observed 

 shrimp boats and captains were not randomly selected. In 

 addition, because no records are kept of the boat size, gear 

 used, fishing habits, or effort history of fishermen in the 

 fleet, sampled boats could not be compared to unsampled 

 boats for these factors. However, most of the fishermen 

 whose boats I observed in the Cape Fear River (the south- 

 ern region) owned large boats and made an average of 5 

 tows per day, whereas the fishermen I observed in Pamlico 

 Sound (the northern region) generally had smaller boats 

 and made an average of 3.2 tows per day. If the fishermen 

 whose boats I observed in the Cape Fear River fished more 

 than the average number of tows per day and the observed 

 fishermen in Pamlico Sound fished fewer than the aver- 

 age number of tows per day, then the catch per day values 

 would show these discrepancies. Other factors could have 

 been differences between observed boats and average 

 boats in the number of nets per boat, or tow times. 



All of the methods that I used for bycatch estimation for 

 the field data were based on the summed catches over all 

 tows on a single day, because in this study the variance of 

 catches among tows within days was much less than the 

 variance among days. The use of tows as the basic unit of 

 effort would therefore have underestimated the total vari- 

 ance. Sampling only day-trips probably contributed to the 

 covariance among tows because tows spread over several 

 days (and probably several locations) in a multiday trip 

 would probably vary more among tows within a trip than 

 tows in a single day. For randomly sampled multiday trips, 

 estimation methods based on tows rather than days or trips 

 may be preferred to those based on a trip as the unit of ef- 

 fort because the sample size of tows increases faster than 

 the sample size of days or trips, which would tighten the 

 confidence intervals around the estimates. However, the 

 use of tows as the unit of effort could be considered pseu- 



