Buckland et al : Estimating abundance of tuna-associated dolphin stocks in the eastern tropical Pacific 



bias does not invalidate the procedures when applied 

 to a long sequence of estimates. In practice, a rate of 

 change in abundance is unlikely to be roughly constant 

 over such a long time-period, yet tests for trend over 

 a short time-period have low power. Figures 1-10 pro- 

 vide a simple method to test for change over longer 

 time-periods without the necessity of assuming the rate 

 of change is constant. 



The smoothing procedure used for generating trend 

 estimates can perform poorly at the start (e.g.. Fig. 7) 

 or at the end of a sequence of estimates, so that sharp 

 increases or declines during the first or last year or two 

 should be treated with suspicion. The first and last 

 smoothed estimate in a sequence are especially un- 

 reliable, and are omitted from Figures 1-10. Thus, 

 changes in abundance are assessed relative to 1988 

 rather than 1989. 



To assess the current status of dolphin stocks, and 

 the effects of recent levels of mortality, it is necessary 

 to determine whether trends in dolphin abundance are 

 best estimated from tuna vessel data or research vessel 

 data, or whether some combination of estimates from 

 both sources is preferable. Given sufficient data and 

 adequate coverage of the entire range of each stock, 

 research-vessel estimates of trend would be preferred, 

 since they are likely to be less biased. However, Holt 

 and Sexton (1989, 1990ab), to exploit fully the small 

 number of research vessel sightings, made assumptions 

 that might be seriously violated. Firstly, data are pool- 

 ed across all sightings of dolphin schools of at least 15 

 animals, irrespective of species, to improve precision 

 of effective search-width estimates. This may introduce 

 bias which is not consistent over time, especially if non- 

 target species (those which are seldom associated with 

 tuna, and are therefore seldom encircled by purse 

 seines) have a different effective search width and a 

 different rate of change in abundance than target 

 species. Secondly, although abundance estimates are 

 given by stock, encounter-rate estimates by stock area 

 are ignored for stocks that are not separated in the 

 field. Thus for offshore spotted dolphins, a single abun- 

 dance estimate per year is generated and then prorated 

 by stock area, to yield separate estimates for the north- 

 ern and southern offshore stocks. If the southern off- 

 shore stock became extinct, and the northern offshore 

 stock increased at a rate that ensured overall abun- 

 dance remained constant, the expected trend in re- 

 search vessel estimates would be zero for both stocks. 

 The same applies to common dolphin stocks. The esti- 

 mates of Holt and Sexton indicate that there are large 

 numbers of common dolphins in the western sector of 

 the eastern tropical Pacific, yet the species is seldom 

 recorded there. Using the estimation methods of Holt 

 and Sexton, valid trend estimates from research vessel 

 data are not available separately for northern and 



southern offshore stocks of spotted dolphin or for the 

 main stocks of common dolphin. 



In Figures 12-15 we show the valid estimates of 

 trend (i.e., those obtained after pooling data from 

 stocks that are not differentiable in the field) from the 

 research-vessel relative abundance estimates for 

 1986-89, taken from Sexton et al. (1991) and Gerro- 

 dette and Wade (1991). Also shown are the corre- 

 sponding unsmoothed trend estimates from tuna vessel 

 data. Vertical bars show ± 2 standard errors. Plots are 

 based on the relative abundance estimates and stan- 

 dard errors of Tables 2 and 3. The research vessel 

 estimates indicate changes in abundance that are 

 biologically implausible, even with full allowance for the 

 estimated precision of the estimates. Thus either the 

 precision of the surveys is appreciably worse than 

 estimated or there is strong and inconsistent bias in 

 the estimates from one year to the next. By contrast, 

 despite the concerns over the validity of tuna vessel 

 estimates, they yield biologically plausible rates of 

 change during 1986-89 when the precision of the 

 estimates is accounted for. 



