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Fishery Bulletin 91 12), 1993 



where z is a random variable distributed as N (0, a 2 ), 

 and (2) precision of the estimate, represented in 

 the distribution of the simulated bootstrap replicas for 

 year t, I bt , as 



I bt = I t e v ,forb=l, . ..,79, 



where v is a random variable distributed as N (0, e 2 ). 



The rationale for a setup with independent control 

 of two sources of variation and a lognormal error struc- 

 ture lies in the properties of the estimates and in the 

 fact that the linear and smoothed tests deal differ- 

 ently with both components of variation. The choice of 

 a lognormal error structure can be justified by consid- 

 ering that the abundance estimates are naturally con- 

 strained to be positive. The choice of error structure 

 for the simulation can be further justified by an analy- 

 sis of the available TVOD estimates (Fig. 2), which 

 shows that the main target stocks tend to have con- 

 stant CVs, particularly in recent years when observer 

 coverage of the tuna fleet increased and more in- 

 formation was available for abundance estimation. 

 There is considerable variability in some stocks, due 

 to changing levels of targeting from the purse-seine 

 fleet that result in unequal sample sizes from year 

 to year. 



The argument for including two sources of variation 

 in the estimates is based on the possibility that actual 

 relative abundance indices are affected by random bi- 

 ases from year to year. Under standard assumptions, 

 o 2 and e 2 should be equal. However, estimates of dol- 

 phin abundance may exhibit an additional variability, 

 represented in this setup as o 2 >e 2 . This can be attrib- 

 uted to randomly-fluctuating biases, such as those in- 

 troduced by changing environmental conditions or 

 differences in the way the purse-seine fishery oper- 

 ates. It is important to separate these two components 

 since, for example, in the case of the linear test, the 

 results are affected only by the variability represented 

 byo 2 . 



Therefore, it was assumed in the simulation that 

 estimates are lognormally distributed around the un- 

 derlying trend with a constant coefficient of variation. 

 Figure 3 illustrates one simulated series for each of 

 the different scenarios. The simulations were repeated 

 for different combinations of CV a and CV f , the coeffi- 

 cients of variation for both sources of variation. 



To compare the test for trends, two diagnostics were 

 used. 



Figure 2 



Coefficients of variation in relative abundance estimates of 

 dolphin stocks in the eastern Pacific Ocean as a function of 

 time. NOFF=northern stock of the offshore spotted dolphin 

 Stenella attenuata; SOFF=southern stock of the offshore spot- 

 ted dolphin; EAST=eastern stock of the spinner dolphin 

 Stenella hngirostns; WHBL=whitebelly stock of the spinner 

 dolphin; NCOM=northern stock of the common dolphin Del- 

 phinus delphis; CCOM=central stock of the common dolphin; 

 SCOM=southern stock of the common dolphin. 



Number of detected trends For the linear trends, 

 this is the number of 10 yr periods with slopes signifi- 

 cantly different from zero at the 5% significance level. 

 For the smoothed test, it is the number of significant 

 differences between the next-to-last estimate and the 



estimate 10 yr earlier. In this way, the comparison is 

 based on the same number of tests for each method. 

 Since there are 25 yr simulated in each replica, a total 

 of 1500 tests were carried out in the simulation of 

 each scenario. 



