Applications in adaptive cluster sampling of Gulf of Alaska rockfish

Fishery Bulletin, July, 2003 by Dana H. Hanselman, Terrance J. Quinn, II, Chris Lunsford, Jonathan Heifetz, David Clausen

Abstract--Adaptive cluster sampling (ACS) has been the subject of many publications about sampling aggregated populations. Choosing the criterion value that invokes ACS remains problematic. We address this problem using data from a June 1999 ACS survey for rockfish, specifically for Pacific ocean perch (Sebastes alutus), and for shortraker (S. borealis) and rougheye (S. aleutianus) rockfish combined. Our hypotheses were that ACS would outperform simple random sampling (SRS) for S. alutus and would be more applicable for S. alutus than for S. borealis and S. aleutianus combined because populations of S. alutus are thought to be more aggregated. Three alternatives 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. Systematic 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 yielded gains in precision (SE) over SRS. Bootstrapping showed that the distribution of an ACS estimator 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 precision. When time-efficiency was examined, 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 previously 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.

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In nature, populations are sometimes distributed in a patchy, rare, or aggregated manner. Conventional sampling designs such as simple random sampling (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; Hanselman et al., 2001).

Recently papers about ACS have included efficiency comparisons (Christman, 1997), restricted ACSs (Lo et al., 1997; Brown and Manly, 1998), bootstrap 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 following 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 different criterion values after the survey. We also compare the efficiency of ACS to SRS.

In the basic adaptive cluster sampling (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, below, 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 j, then unit j is in the neighborhood of i. The "unbiasedness" of the estimators relies on all neighborhood units of y>c being sampled. If logistics cause the sampling to be curtailed before the sampling is complete, then biased estimators can result. For our study, all samples were called "tows" because our study was a trawl survey.

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When little information is available to preset a fixed criterion value, order statistics are often used to choose a criterion value (Thompson and Seber, 1996). The basic idea is that an initial random sample is conducted. Next, the values of the random tows are ordered, and ACS is conducted around the top r stations. The variable r is decided by the experimenter and depends on the amount of resources available and the suspected aggregation of the population. The criterion value is then set at the value of the next highest tow (r 1). This was the design used in the 1998 adaptive cluster sampling survey for rockfish (Quinn et al., 1999, Hanselman et al., 2001). The use of order statistics has several limitations, however. First, initial random samples must be taken before the adaptive phase can begin. This procedure can be inefficient, because the experiment may have to move a large distance back to the previous tows that exceeded the criterion, by which Lime the aggregation may have moved or dispersed. In some cases, this procedure may result in a very small criterion value that leads to an overwhelming amount of adaptive sampling around some tows. Second, the process of achieving simple unbiased estimates of abundance is more complicated with order statistics because the criterion value is dependent on the sampling.