FIEDLER f'KECISION OF SIMl'LATEn TRANSECT Sl'RVFYS 



N 



180 



Figure 2. — A model northem'anchovy population. Densities of 

 school groups in schools per square mile. Simulated survey 

 transects are oriented horizontally. The numbers on the axes are 

 the coordinates of the array and the dimensions, in miles, of the 

 survey area it represents. 



4. 5. 7, 10, 12, 15, 20, 25, 30, and 40 mi were used. A 

 survey with a transect interval of d miles con- 

 sisted of 180 c/ transects. For each transect inter- 

 val, 20 replicate surveys were run by randomly 

 choosing the initial transect from the first d tran- 

 sects in the survey area. The replicate survey esti- 

 mates were used to calculate an unbiased mean 

 population estimate and a coefficient of variation 

 (standard deviation of the replicate estimates di- 

 vided by the mean), which is a measure of the 

 precision of the estimate (Wiebe 1971). This pro- 

 cedure was repeated on the 15 different model 

 populations. 



Random surveys were simluated in an analo- 

 gous manner to allow a direct comparison of sam- 

 pling errors. For each of the transect intervals (c/i 

 of the systematic surveys, 20 replicate surveys 

 were run consisting of 180 (/ transects chosen at 



random without replacement la transect was not 

 repeated within a survey). Coefficients of varia- 

 tion were calculated as a measure of precision. 



Stratified systematic surveys were simulated 

 after dividing each of the model populations into 

 four 45-mi wide strata. The schools along three 

 transects in each of the four strata were counted to 

 obtain a preliminary estimate of relative popula- 

 tion sizes. Then a total of 60, 36, 18, 12, 9, 7, or 6 

 transects were divided among the strata according 

 to the estimated population fractions. For exam- 

 ple, if a stratum contained one-half of the schools 

 counted in the preliminary survey, one-half of the 

 total number of transects was allocated to that 

 stratum for the stratified survey. At least one 

 transect was allocated to each stratum to avoid 

 biasing the final population estimate. For each 

 total number of transects, 20 replicate systematic 

 surveys were run by randomly choosing the initial 

 transect and simulating a systematic survey 

 within each stratum with the allocated number of 

 transects. Once again, coefficients of variation of 

 the replicate population estimates were calculated 

 for each of the 15 model populations. 



RESULTS 



The results of the systematic survey simula- 

 tions indicate that the sampling error represented 



e 5 F, 



IT o q: 



09 

 000 



O ^ CO 

 CO o 



o o 



S 9 i" 

 o f^ — 

 iC o 



o o 



O O o 



8° 



c\j o 



1 I 11 — 1 1 — I i I I 1^ 



2 34 5 7 10 12 15 20 25 30 



TRANSECT INTERVAL-MILES 



40 



Figure 3. — Results of the simulations of systematic surveys of 

 the 15 models for northern anchovy populations. Relative ef- 

 ficiency is proportional to precision (the reciprocal of the 

 coefficient of variation) divided by relative cost (see text). Aver- 

 ages and 95% confidence limits are given for coefficients of varia- 

 tion. 



681 



