Fishery Bulletin 90(1). 1992 



plausible, even if full allowance is made for the preci- 

 sion of the estimates. An example is the 1983 estimate 

 for the northern offshore stock of spotted dolphins, 

 which is significantly lower than either the 1982 or the 

 1984 estimate. This has been attributed to the strong 

 El Nino event of that year (Buckland and Anganuzzi 

 1988a). The change in environmental conditions ap- 

 peared to cause spotted dolphins to split into smaller 

 schools and to disperse more widely than is normal, so 

 that tuna vessels were unable to locate areas of con- 

 centration. If, in normal years when concentrations 

 occur in known areas, there is positive bias in the abun- 

 dance index, then a relatively low estimate might be 

 expected for 1983. This effect would be enhanced if 

 many animals wandered beyond the normal range of 

 the stock, so that the abundance index for 1983 cor- 

 responded to only that portion of the stock remaining 

 within its normal bounds. Such effects may be regarded 

 either as bias that fluctuates over time or as an addi- 

 tional source of variability that is unaccounted for in 

 the variances of the abundance indices. Provided the 

 effects are essentially random, and do not exhibit a con- 

 sistent linear trend over time, the smoothing algorithm 

 described above smooths out the large fluctuations and, 

 in conjunction with the bootstrap, provides variance 

 and interval estimates for the smoothed abundance 

 indices that take full account of variability not allowed 

 for in the variance estimates of the unsmoothed indices. 

 The validity of estimating trends in dolphin abun- 

 dance from tuna-vessel sightings data has been ques- 

 tioned by Edwards and Kleiber (1989). They used a 

 simple simulation model of non-random search vessel 

 effort coupled with clustered distributions of dolphin 

 schools to investigate bias. By allowing the clustering 

 of schools to be slight in one year and extreme in the 

 next, they showed that bias in the relative abundance 

 estimates can be inconsistent between years. They 

 define a change estimate as the ratio of relative abun- 

 dance estimates for the two years. They state, "This 

 two-sample change estimate is only a rough approx- 

 imation to a trend estimate derived from a series of 

 measurements . . . However, conclusions about the ef- 

 fects of inconsistent biases on this change estimate will 

 be valid for trend estimates also, except for the unlikely 

 case in which effects of various inconsistent biases 

 cancel each other out, so that the trend estimate 

 reflects the actual trend, but only fortuitously." (The 

 emphasis on "change" and "trend" is theirs.) They also 

 note that "It is obvious. . .that even relatively small 

 changes of bias can lead to considerably inaccurate 

 estimates of change and, by implication, estimates of 

 trend." If this is so, there would be little value in 

 estimating trends in abundance from tuna-vessel sight- 

 ings data. We question whether the simulation model 

 of Edwards and Kleiber (1989), which is a considerable 



simplification of reality, allows such strong conclusions. 

 However, we use their results to assess the validity of 

 their argTiments. We take their worst-case scenario of 

 a static environment, using the stratified and smoothed 

 option, and average across their four replicates for the 

 high-density case. The calculations indicate a down- 

 ward bias of about 20% for the "simple, gentle" en- 

 vironmental topography of year 1 and an upward bias 

 of about 100% for the "complex, steep" topography 

 of year 2. Thus, if the population comprised 2500 

 schools (as in their simulations), the expected estimate 

 would be around 2000 schools in the first year and 5000 

 in the second, a 2.5-fold estimated increase for a pop- 

 ulation that has constant size. Is this conclusion "valid 

 for trend estimates also"? Suppose a population com- 

 prised 4 million animals in 1975, and decreased at a 

 rate of 5% per annum until 1989. Suppose we again 

 take an extreme scenario in which the "simple, gentle" 

 environmental topography applied in El Nino years, 

 and the "complex, steep" topography applied in all 

 other years. The expectations of the estimates are 

 shown in Table 1. Also shown are simulated estimates, 

 for which errors were generated from a lognormal 

 distribution which yields a coefficient of variation of 

 15%, close to that observed for estimates based on tuna 

 vessel data. The errors were then added to the ex- 

 pected estimates. The estimated rate of decrease for 

 the expected estimates is 5.0% per annum (SE2.5%), 

 and that for the simulated estimates is 4.7% per annum 

 (SE 2.6%). Thus a scenario of extreme and inconsistent 



