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Fishery Bulletin 101(3) 



(0.95 h/sample) for POP. Sampling time efficiency for SR- 

 RE was approximately the same for adaptive sampling (1.5 

 h/sample) and simple random sampling (1.49 h/sample) for 

 SR-RE. These results are confounded by the fact that the 

 random tows are spread apart because of the lesser effort 

 applied to them. The average distance between random 

 tows (20.2 km) was adjusted to a distance of 4.73 km as 

 if there were 106 random tows distributed throughout the 

 area. This distance is still larger than the average distance 

 between tows in adaptive sampling (3.22 km). 



From these time and distance data, we re-estimated the 

 precision of SRS under three new sample sizes in order to 

 further compare the relative efficiency of ACS. We denoted 

 the sample size that could have been taken under SRS, using 

 the same amount of time as was used during the adaptive 

 sampling including edge units, as v.. An alternative sample 

 size V, was the equivalent SRS sample size if the amount of 

 time to sample edge units in ACS was negligible. This sta- 

 tistic would be useful if edge units could be determined (i.e. 

 hydroacoustically or visually [presence or absence] ) without 

 actually trawling them. A third alternative was to find the 

 equivalent SRS sample size v^^ that would result from apply- 

 ing the total distance traveled in the ACS design on random 

 stations instead. For \'^., more random POP samples would 

 have been taken than were included in the adaptive estima- 

 tors (Table 4). The SEs of ACS were still much lower across 

 all criterion values (Table 2). When we used v, (Table 4), SRS 

 was much less precise than ACS (Table 2). Finally, when we 

 used distance instead of time (\'^), the results were almost 

 exactly the same as those for \\, (Table 4). 



Discussion 



Our two hypotheses were that ACS would be more precise 

 than SRS for POP and no more precise for SR-RE com- 

 bined. The results from the 1999 field study showed that 

 the SEs for the adaptive POP estimates were smaller than 

 both SRS estimates, with n and \'', and thus support the 

 first hjrpothesis. One curious result is that in both 1998 

 and 1999, the SRS estimate of density was substantially 

 larger than the ACS estimate, even though, on average, 

 they were both essentially unbiased. We attributed this 

 curiosity to the more variable and skewed SRS distribution 

 in which large sampling error on the high side is possible 

 more often than in the ACS estimation. Of course we fully 

 expected that both estimates would average to be the same 

 value if the experiment could be repeated many times. ACS 

 reduced the influence of one large CPUE in the relatively 

 small initial sample, as illustrated by the symmetric and 

 near-normal shape of the ACS bootstrap distribution. Con- 

 sequently, we concluded that ACS is a more robust estima- 

 tor of density than SRS for aggregated populations. One 

 caveat is that the precision of the estimates, if measured 

 in terms of coefficient of variation, is similar between the 

 two methods because of the nuich larger moan estimate for 

 the SRS estimate. Monte Carlo simulations would be useful 

 to examine the properties of the estimators under different 

 criterion values and population densities along the lines of 

 Su and Quinn (2003). 



The SR-RE adaptive estimates all have higher SEs than 

 the SRS estimates, and this finding supports the second hy- 

 pothesis. More than twice as many samples were directed 

 toward POP than SR-RE, yet the POP density estimates 

 are much more variable than those for SR-RE. This much 

 larger variability for POP was indicative of the clustering 

 that we expected. 



This experiment showed that for POP, ACS with a fixed 

 criterion has some distinct advantages over simple random 

 sampling and over adaptive cluster sampling with order 

 statistics, which was used in the previous 1998 survey. 

 Lower SEs were obtained, at one third less effort than if 

 we just added an equivalent number of random samples. 

 Sampling over a broader area yielded better results than 

 the tightly stratified 1998 design. Our study also assumed 

 stationary aggregations of fish. This assumption may 

 have been better satisfied with a fixed criterion because 

 the adaptive sampling was conducted immediately after a 

 sample exceeded the criterion value. 



Although the fixed criterion eliminates bias induced by 

 a variable criterion value, we still used stopping rules. If 

 bootstrapping is a good indicator of bias, then the bias in- 

 duced by stopping rules is negligible. Additionally, we have 

 shown that a relatively high criterion value could be used 

 to help minimize the use of these stopping rules. 



Our study showed that ACS is a fast and efficient way 

 to gain a large number of samples. However, if edge units 

 do not contribute to a better estimate and they have a sim- 

 ilar cost or time expense as included samples, then little 

 is gained. This deficiency shows the need for some method 

 of determining edge units without actually sampling them. 

 In fisheries surveys, this use might be a double sampling 

 design with hydroacoustics as an auxiliary variable 



