FISHERY BULLETIN: VOL. 76, NO. 3 



Table l. — Systematic and stratified random sampling designs used in studies A and B. 



characteristics of the environment (Figure 2), and 

 larger strata were assigned to the layers in which 

 environmental gradients were small and several 

 narrow strata were placed in the region of the 

 chlorophyll maximum. The 35-m boundary 

 marked the average depth of the mixed layer; 95 m 

 was the approximate depth of penetration of 19( of 

 the surface radiation, and 125 m represented the 

 beginning of the nutricline. Design SR-1 consisted 

 of 10 strata, each with one sample; in design SR-2, 

 adjacent strata were lumped giving five strata 

 with two samples in each. Designs SR-3 and SR-4 

 were those used in study B (below) and were thus 

 based on environmental characteristics observed 

 at that time. Each of the nine populations was 

 sampled 20 times with each of the stratified ran- 

 dom designs. To facilitate comparison with the 

 systematic samples, for which there was only one 

 cast of each design per profile, it was desirable to 

 examine a series of unreplicated stratified random 

 samples. For this purpose, 10 subsets were 

 selected at random from the replicate casts, each 

 subset containing nine stratified random casts, 

 one from each population. Total chlorophyll was 

 calculated from the mean (arithmetic) concentra- 

 tion per strata times the width of that strata, 

 summed over all strata. This is the classical proce- 

 dure for summarizing data collected by SR. 



Four RSS designs were employed: RSS-1, one 

 sample at the surface and every 20 m thereafter; 

 RSS-2, the design actually employed in September 

 1968 in which the cast was partially determined 

 by standard hydrographic depths; RSS-3, a design 

 which was based upon complete knowledge of the 

 vertical distributions which were being sampled 

 and which was derived from application of the 

 general rules of sample allocation, i.e., samples 

 were concentrated in the region of maximum var- 

 iability (the chlorophyll maximum layer); RSS-4, 

 a design based on stratified random design 1 (and 

 therefore more strictly comparable to it) with a 

 sample at the top of the upper stratum (0 m) and 



bottom of the lowest stratum (180 m) and at the 

 center of all intermediate strata. 



Two methods of calculating total chlorophyll 

 from systematic samples were investigated. In the 

 first, the layer between adjacent samples was rep- 

 resented by the arithmetic mean of the two sam- 

 ples (equivalent to integration with linear inter- 

 polation). In the second, the layer was represented 

 by the geometric mean of adjacent samples. This 

 latter procedure is sometimes recommended when 

 the population exhibits large, nonlinear changes 

 between adjacent samples. A comparison of the 

 two procedures was made in study A, on the basis 

 of which the method using geometric means was 

 rejected. 



Study B 



Study B, conducted in June 1977, combined two 

 10-sample designs, one restricted systematic 

 (RSS-1) and one stratified random (SR-3 or SR-4) 

 into a single 20-bottle cast. The strata boundaries 

 were primarily determined from two preliminary 

 18-bottle casts which defined the regions of 

 chlorophyll gradients and from a single STD trace 

 which defined hydrographic strata (Figure 3). As 

 in study A, narrower strata were established at 

 the depths of maximum gradients of chlorophyll 

 (the region of the maximum layer). The major 

 differences between designs SR-1 and SR-2 and 

 designs SR-3 and SR-4 were due to a shallower 

 mixed layer and broader, deeper maximum layer 

 observed in June 1977. 



Over a period of 21 days, a total of 18 casts were 

 made, 9 employing RSS-1 and SR-3 and 9 employ- 

 ing RSS-1 and SR-4. All casts were located within 

 a rectangle bounded by lat. 28°21.6'N and 

 28°45.9'N, and by long. 155°14.0'W and 

 155°33.5'W. Fourteen casts were taken in con- 

 junction with another program between the hours 

 of 2200 and 0300 (with one exception, delayed by 

 winch failure until 0550). Twelve casts were 



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