FISHKRY Hl'ia.KTIN: Vol, 7(S, NO. 3 



northern anchovy. As slated above, stratified sys- 

 tematic sui'veys were significantly more precise 

 than unstratified surveys for the five model popu- 

 lations with the most nonrandom distribution of 

 schools between strata. If the school groups them- 

 selves are aggregated, it is reasonable to expect an 

 increase in precision by stratifying the survey. 



To test this possibility, the simulations were 

 repeated on model populations in which the school 

 groups were limited to only one-half of the survey 

 area. An analysis of variance (Table 2) indicated 

 in this case that the stratified systematic surveys 

 were more precise than the unstratified systema- 

 tic surveys (P<0.005 that there was no added var- 

 iance due to survey design). The overall mean 

 coefficients of variation were 0.095 and 0.133, re- 

 spectively. However, there were significant in- 

 teraction effects involving survey design, indicat- 

 ing that the advantage of stratifying the survey 

 will depend on the number of transects and the 

 spatial distribution of the population. The addi- 

 tional cost of the preliminary survey in the strat- 

 ified design must also be considered when compar- 

 ing it with the unstratified design. 



The results of the simulated systematic surveys 

 showed that the patchy distribution of schools was 

 an important source of error in estimates of the 

 anchovy population size. Acoustic surveys run by 

 the Southwest Fisheries Center have used tran- 

 sect intervals of 6.6 and 40 mi. The simulations 

 gave evidence that the population estimates from 

 these surveys could be expected to range at least 8 

 and 90''^ (2 x C.V.), respectively, from the true 

 population size. The most efficient simulated sam- 

 pling, in terms of precision per unit cost, occurred 

 at a transect interval of 3 mi. This would require a 

 cruise grid of 4,860 mi, equivalent to a 34-day 

 acoustic survey at 12 kn and 12 h per day, to 

 reduce the coefficient of variation (due to the 

 patchy distribution of schools) to 1.4^7^ . Maximiz- 



ing efficiency is not a valid goal, however, when 

 the precision gained is greater than that required 

 for the problem of managing the fishery, when 

 other sources of error become more important, and 

 when there are absolute limits on cost. Anchovy 

 population estimates within 1W( of the true value 

 might be considered sufficient for management, at 

 least to allow confidence that a consistent change 

 observed over several years is real (pers. commun., 

 P. E. Smith, Southwest Fisheries Center, National 

 Marine Fisheries Service, NOAA, La Jolla, Calif., 

 Oct. 1977). 



As stated before, the anchovy population is 

 patchy on two levels: individuals are aggregated 

 into schools and schools are aggregated into school 

 groups. The simulations have quantified the sam- 

 pling error due to the second level of patchiness 

 only. Although little is known about the distribu- 

 tion of anchovy school groups, it was also de- 

 monstrated that their aggregation is potentially 

 an important consideration in designing a survey. 

 The acoustic survey methods currently used by the 

 National Marine Fisheries Service and the 

 California Department of Fish and Game do little 

 more than count the number of anchovy schools 

 (Hewitt et al. 1976; Mais 1974). The Department 

 of Fish and Game calculates a biomass estimate by 

 multiplying the observed school area by a constant 

 factor thought to represent an average biomass 

 per unit area. More sophisticated methods of es- 

 timating biomass from the acoustic signal re- 

 ceived from a school are now being explored at the 

 Southwest Fisheries Center. For these reasons, 

 the problem of sampling error due to a varying 

 number offish per school (the first level of patchi- 

 ness) was not addressed here. 



Many sources of error may be involved in an 

 anchovy biomass estimate. Patchiness is impor- 

 tant in any type of sampling program. Other 

 sources of error that may be important in an 



Table 2. — Analysis of variance of the coefficients of variation from simulated systematic and 

 stratified systematic surveys of model northern anchovy populations when the model popula- 

 tion school groups are clumped in one-half of the survey area. 



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