FIEDLER: F^RECISION OF SIMll.ATED TKANSECT SIRVEYS 



systematic surveys were significantly more pre- 

 cise than stratified systematic surveys iP<0.025). 

 although there is still a significant interaction 

 between survey design and model population 

 (P<0.001). For smaller sample sizes, there was no 

 significant difference between the precision of the 

 two designs. 



In the model populations, school groups were 

 located randomly within the survey area. How- 

 ever, the distribution of schools between strata 

 was never random because of the wide range of 

 school group sizes and the small number of school 

 groups in a population. The 15 model populations 

 were divided into three groups (low, intermediate, 

 and high nonrandomness) based on the index of 

 dispersion of the number of schools per stratum. 

 Analysis of variance revealed that for highly non- 

 random populations, stratified systematic surveys 

 were significantly more precise than unstratified 

 surveys (P<0.025). On the other hand, there was 

 no significant difference between the survey de- 

 signs for populations of intermediate or low non- 

 randomness. The effect of the nonrandomness of 

 the populations, in the limited sense used here, is 

 illustrated more dramatically below. 



In summary, these results indicate that both the 

 number of transects and the spatial distribution of 

 the population can affect the precision of a survey 

 estimate. The effect of survey design involves 

 complex interactions with the other two factors. 

 These factors should be considered, if possible, 

 when choosing the optimum design for a survey. 



DISCUSSION 



In general, systematic sampling may result in 

 considerable gains or losses in precision compared 

 with simple random sampling. The greatest in- 

 crease in precision occurs when there is a high 

 degree of correlation between adjacent sampling 

 units and the correlation decreases as the interval 

 between units increases. In this situation, sys- 

 tematic sampling resembles stratified sampling. 

 On the other hand, precision may be greatly re- 

 duced when there is a periodic variation in the 

 population and the sampling interval is equal to 

 this period or a multiple of it (Hansen et al. 1953). 



Correlograms between sampling units (tran- 

 sects) in five of the model anchovy populations indi- 

 cated that transects <10 mi apart had a high posi- 

 tive correlation, while the correlation tended to be 

 slightly negative at distances >20 mi (Figure 5). 

 This autocorrelation structure was due to the fre- 



FlGURE 5. — Autocorrelation of transect counts in five mode! 

 northern anchovy populations. 



quency distribution of school group sizes. The 

 mean distance at which the autocorrelation func- 

 tion passed through zero was 15.0 mi, while the 

 mean diameter of the individual school groups in 

 the five model populations was 11.8 mi. Distribu- 

 tion of school groups within the model populations 

 was random. However, real populations are likely 

 to be nonrandom in this respect and additional 

 correlations would be expected from this factor. 

 The strong positive correlation between transects 

 separated by short distances explains why sys- 

 tematic surveys with small transect intervals 

 were more precise than random surveys with an 

 equivalent number of transects. As the transect 

 interval increased, the correlation between tran- 

 sects decreased to near zero and the imprecision of 

 systematic sampling approached that of random 

 sampling (Figure 4). 



In order to reduce total sampling error, a com- 

 mon strategy is to allocate effort proportional to 

 the sampling error within parts of a sampling 

 program. The variation observed in the population 

 estimates of the simulated surveys was caused by 

 the large variance in the number of schools per 

 transect. It can be shown in the model populations, 

 as in many biological populations, that the stan- 

 dard deviation was positively correlated with the 

 mean number of schools per transect in a stratum. 

 Therefore, it was thought that the stratified sys- 

 tematic surveys would reduce the total sampling 

 error by allocating more transects where the var- 

 iance was large. The simulations failed to show 

 any gains in precision from this strategy. This 

 result was not expected, but is possibly due to the 

 random distribution of school groups. The model 

 populations may have been ideal in this sense, but 

 we had relatively little information on the dis- 

 tribution of school groups within the range of the 



683 



