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

We chose the SR-RE criterion to be the mean CPUE of initial tows. We assumed this was a reasonable criterion value because if the population of SR-RE were somewhat uniform, a lower value would result in too much ACS, but mean CPUE would still be low enough to allow higher criterion values to be examined. Although we concentrated on evaluating criterion alternatives for POP, we present the SR-RE data to illustrate that different levels of aggregation could affect how much can be gained with ACS in terms of precision and efficiency.

A major problem in applying adaptive sampling is that sampling may continue indefinitely because of a low criterion value. To limit the amount of adaptive sampling, an arbitrary stopping rule of S levels was imposed. For those strata where the cross pattern of adaptive sampling was used (POP), the stopping rule was S = 3 levels, allowing for a maximum of 24 adaptive tows around each high-CPUE random tow (Fig. 1). For the strata with the linear pattern of adaptive sampling (SR-RE), the stopping rule was S = 4 levels, for a maximum of eight adaptive tows around each high-CPUE random tow. This stopping rule differs from that of the previous year in which we used a stopping rule of six because we believed that the possible 30-kin difference between the ends of the networks was too large for efficient sampling (Clausen (2)). In addition, no adaptive sampling extended beyond a stratum boundary. The result of adaptive sampling around each high-CPUE tow was a network of tows that extended over and, in some cases, delineated the geographic boundaries of a rockfish aggregation.

Statistical analysis of the results was based on adaptive 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) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [w.sub.i] and [y.sup.*.sub.i] = the mean and total (respectively) of the [x.sub.i] observations in the network that intersects sample unit i.

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

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [y.sup.*.sub.k] = the sum of the y-values for the kth network;

[kappa] = the number of distinct networks in a sample;

[[alpha].sub.k] = the probability that network k is included in the sample; and

N = the total number of sampling units.

If there are [x.sub.k] units in the kth network, then

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where N = the total number of sampling units;

n = the initial random sample; and