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Fishery Bulletin 101(3) 



Statistical analysis of the results was based on adap- 

 tive cluster sampling (Thompson and Seber, 1996). First, 

 we estimated the abundance (kg/km) for the targeted 

 rockfish species from the n initial random tows using the 

 standard simple random sampling (SRS) estimator Then, 

 two adaptive estimators of abundance, a Hansen-Hurwitz 

 estimator (HH) and a Horvitz-Thompson estimator (HT), 

 were calculated. We computed standard error (SE) as a 

 measure of precision. The unbiased HH estimator for the 

 ACS mean is 



1 " T "_ 



(1) 



where w^ and y* = the mean and total (respectively) of 

 the X, observations in the network that 

 intersects sample unit /. 



The HH estimator essentially replaces tows around which 

 adaptive sampling occurred with the mean of the network 

 of adaptive tows that exceeded the criterion CPUE. 

 The unbiased HT estimator for the ACS mean is 



1 ^ •' 



A'-f-i'or, 



(2) 



where y^ = the sum of the y-values for the kth network; 

 K = the number of distinct networks in a sample; 

 rtf. = the probability that network k is included in 



the sample; and 

 N = the total number of sampling units. 



If there are .r^ units in the kth. network, then 



N-.v, 



(3) 



where N = the total number of sampling units; 

 n = the initial random sample; and 

 X)^ = the number of units in the network. 



The HT estimator is based on the probability of sampling 

 a network given the initial tows sampled and involves the 

 number of distinct networks sampled (in contrast to the 

 HH estimator which is based only on the initial tows). The 

 HT estimator often outperforms other estimators as seen 

 in simulation studies (Su and Quinn, 2003). Both estima- 

 tors use the network samples and initial random samples, 

 but not the edge units. This sample size is referred to as v' 

 (convention established by Thompson (1990) and used in 

 Thompson and Seber (1996)). To include edge units into 

 the estimates Thompson and Seber (1996) and Salehi 

 (1999) used the Kao-Blackwcll theorem, which is a com- 

 plex method that could theoretically result in more precise 

 estimates. However, it had little effect for the 1998 survey 

 data (<1% improvement, Hanselman, 2000); therefore 

 these calculations were not used in our study. 



When a stopping rule is used, the theoretical basis for 

 the adaptive sampling design changes. It may result in 



incomplete networks that overlap and are not fixed in rela- 

 tion to a specified criterion — changing with the pattern of 

 the population. In contrast, the nonstopping-rule scheme 

 has disjoint networks that form a unique partition of the 

 population for a specified criterion. This partitioning is 

 the theoretical basis for the unbiasedness of pi^^ and fifjj. 

 Thus with a stopping rule, some bias may be introduced. 



Recent simulation studies (Su and Quinn, 2003) have 

 estimated the bias induced by using a stopping rule on each 

 estimator with order statistics, but not with a fixed crite- 

 rion. Because the use of a fixed criterion is design unbiased, 

 its estimate should be less biased by the stopping rule than 

 a sample with order statistics. Therefore, we can use the 

 Su-Quinn simulation results to approximate the maximum 

 bias induced by the stopping rule. With a stopping rule of 

 three and the HH estimator, the maximum positive bias is 

 17% for a highly aggregated simulated population. With 

 a stopping rule of three and the HT estimator, the maxi- 

 mum bias is approximately 12%. Considering our design, 

 we accepted the tradeoff of relatively small bias for gains 

 in precision and logistical efficiency. 



Additionally, nonparametric bootstrap methods were 

 adapted from Christman and Pontius (2000) and we used 

 the HH version of the estimates to examine bias from our 

 survey. Five thousand resamples were performed by using 

 n for the SRS bootstrap, and the sample size from the origi- 

 nal criterion value of 220 kg/km ( v) was used for the ACS 

 bootstrap. Bootstrap distributions of the data were exam- 

 ined for SRS and ACS designs to examine the capability of 

 each design to clearly demonstrate a central tendency. 



We evaluated two hypotheses: 1) Adaptive sampling 

 would be more effective in providing precise estimates of 

 POP biomass than would a simple random survey design; 

 and 2) Assessment of POP abundance would benefit more 

 from an adaptive sampling design than would SR-RE be- 

 cause POP are believed to be more clustered in their dis- 

 tribution than SR-RE. SRS estimates were obtained from 

 the initial random tows, and variance estimates were cal- 

 culated for the initial sample size in ) and for the equivalent 

 sample size that included the adaptive tows but not the 

 edge units (\''). This procedure makes the theoretical com- 

 parison fair because each estimate is based on the same 

 number of samples. Total sample size including edge units 

 (v) was not used in the theoretical precision comparison 

 but was considered when efficiency issues were examined 

 later These hypotheses were assessed by comparing the 

 standard errors (SEs) of ACS to those of SRS. Substantial 

 reductions in SE with ACS for POP would support the 

 first hypothesis, whereas no reductions of SE using ACS 

 for SR-RE would support the second hypothesis. This com- 

 parison is qualitative because relevant significance tests 

 are unavailable and the two methods are different in terms 

 of efficiency. 



To evaluate different alternatives and criterion values, 

 each network was reconstructed as if the higher criterion 

 values had been used in the field. We also examined the 

 tradeoff between amounts of additional sampling com- 

 pared with the gains in precision. A comparison was made 

 oftiu' SRS results by using sample sizes constructed with 

 the number of possible samples with the time-per-sample 



