501 



Abstract — Adaptive cluster sampling 

 (ACS) has been the subject of many 

 publications about sampling aggregated 

 populations. Choosing the criterion 

 value that invokes ACS remains prob- 

 lematic. We address this problem using 

 data from a June 1999 ACS survey 

 for rockfish, specifically for Pacific 

 ocean perch {Sebastes aliitus). and for 

 shortraker (S. borealis) and rougheye 

 (S. aleutianus) rockfish combined. Our 

 hypotheses were that ACS would out- 

 perform simple random sampling ( SRS ) 

 for S. aliitiis and would be more appli- 

 cable for S. alutiis than for S. borealis 

 and S. aleutianus combined because 

 populations of S. alutus are thought 

 to be more aggregated. Three alterna- 

 tives for choosing a criterion value were 

 investigated. We chose the strategy that 

 yielded the lowest criterion value and 

 simulated the higher criterion values 

 with the data after the survey. System- 

 atic random sampling was conducted 

 across the whole area to determine the 

 lowest criterion value, and then a new 

 systematic random sample was taken 

 with adaptive sampling around each 

 tow that exceeded the fixed criterion 

 value. ACS jaelded gains in precision 

 (SE) over SRS. Bootstrapping showed 

 that the distribution of an ACS estima- 

 tor is approximately normal, whereas 

 the SRS sampling distribution is 

 skewed and bimodal. Simulation 

 showed that a higher criterion value 

 results in substantially less adaptive 

 sampling with little tradeoff in preci- 

 sion. When time-efficiency was exam- 

 ined, ACS quickly added more samples, 

 but sampling edge units caused this 

 efficiency to be lessened, and the gain in 

 efficiency did not measurably affect our 

 conclusions. ACS for S. alutus should 

 be incorporated with a fixed criterion 

 value equal to the top quartile of previ- 

 ously collected survey data. The second 

 hypothesis was confirmed because ACS 

 did not prove to be more effective for S. 

 borealis-S. aleutianus. Overall, our ACS 

 results were not as optimistic as those 

 previously published in the literature, 

 and indicate the need for further study 

 of this sampling method. 



Applications in adaptive cluster sampling 

 of Gulf of Alaska rockfish 



Dana H. Hanselman 



Terrance J. Quinn II 



School of Fisheries and Ocean Sciences 



University of Alaska Fairbanks 



11275 Glacier Hwy. 



Juneau, Alaska 99801 



E-mail address (for D. H. Hanselman); ftdhh@uaf.edu 



Chris Lunsford 

 Jonathan Helfetz 

 David Clausen 



Auke Bay Laboratory 



Alaska Fisheries Science Center 



National Manne Fishenes Service 



11305 Glacier Hwy. 



Juneau, Alaska 99801 



Manuscript approved for publication 

 •30 January 2003 by Scientific Editor. 

 Manuscript received 4 April 2003 at 

 NMFS Scientific Publications Office. 

 Fish. Bull. 101:501-.513 (20031. 



In nature, populations are sometimes 

 distributed in a patchy, rare, or aggre- 

 gated manner. Conventional sampling 

 designs such as simple random sam- 

 pling (SRS) do not take advantage of 

 this spatial differentiation. Thompson 

 (1990) introduced a sampling design 

 called adaptive cluster sampling (ACS) 

 to survey these types of distributions. 



Adaptive cluster sampling, in theory, 

 can be much more precise for a given 

 amount of effort than conventional 

 sampling designs (Thompson, 1990). 

 In practice, however, this is not always 

 the case. In some cases, the variance 

 is greatly reduced, but bias is induced 

 from stopping rules and criterion values 

 that are sometimes changed mid-survey 

 (Lo et al., 1997). In 1998, we conducted 

 a survey on Gulf of Alaska rockfish in 

 which ACS was efficient and successful, 

 but the gains in precision, if any, were 

 small compared to those of a SRS of the 

 same size (Quinn et al., 1999; Hansel- 

 man et al., 2001). 



Recently papers about ACS have in- 

 cluded efficiency comparisons (Christ- 

 man, 1997), restricted ACSs (Lo et al., 

 1997; Brown and Manly, 1998), boot- 

 strap confidence intervals (Christman 

 and Pontius, 2000), and bias estimates 

 (Su and Quinn, 2003). However, little 

 work has been done on determining 

 the criterion value that, when exceeded, 



invokes additional sampling. In the fol- 

 lowing study, we examine the details for 

 choosing this criterion value by using 

 data from a 1999 field survey for Gulf 

 of Alaska rockfish. We then simulate 

 the outcome of the experiment with dif- 

 ferent criterion values after the survey. 

 We also compare the efficiency of ACS 

 to SRS. 



In the basic adaptive cluster sam- 

 pling (ACS) design, a simple random 

 sample (SRS) of size n is taken; if _y 

 (the variable of interest) exceeds c (a 

 criterion value), then neighborhood 

 units are added (e.g. units above, be- 

 low, left, and right in a cross pattern. 

 Fig. 1) to the sample. These are called 

 network units. If any network unit has 

 y>c, then its neighborhood is added. 

 Units that do not exceed the criterion 

 are called edge units, and sampling 

 does not continue around them. This 

 process continues until no units are 

 added or until the boundary of the area 

 is reached (Thompson and Seber, 1996). 

 Neighborhoods can be defined in any 

 general way. The only condition is that 

 if unit i is in the neighborhood of^, then 

 unit j is in the neighborhood of i. The 

 "unbiasedness" of the estimators relies 

 on all neighborhood units of >'>c being 

 sampled. If logistics cause the sampling 

 to be curtailed before the sampling is 

 complete, then biased estimators can 



