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Fishery Bulletin 97(3), 1999 



"Discussion" section). Although dependence 

 does not add a bias to our estimates, it does de- 

 crease the effective sample size, which affects our 

 estimates of precision. We accounted for this prob- 

 lem by using bootstrap standard error estimates, 

 and by defining our bootstrap resampling units 

 so as to make them as independent as possible 

 while keeping a reasonably large sample size. For 

 research vessel data, we took days as the 

 resampling unit; for tuna vessels, we resampled 

 by trips. For each bootstrap iteration, we 

 resampled from the research vessel data to 

 achieve approximately the same amount of search 

 effort in each stratum as was actually achieved. 

 We resampled fi-om the tuna vessel data to achieve 

 exactly the actual observed number of trips. 



Results 



Estimated distribution of school sizes 



Figure 2 shows the kernel estimates of the den- 

 sities ;r*(s) andp(s). Both estimated densities 

 were much smoother at large school sizes than 

 at small school sizes. This is partially due to 

 the variable bandwidth in the kernel estima- 

 tor, but primarily due to the data themselves. 



Estimated effective strip halfwidth 



Figure 3 shows the estimated values for the ef- 

 fective strip halfwidth as a function of school 

 size. Because ;r*(s)o^ii'p/^s);r(s).uv/f's) represents 

 the relative amount of "thinning" for schools of 

 different sizes, i.e. Weff(s)lw is the probability 

 of a school of size s being detected from the re- 

 search vessel, given that it is within the trun- 

 cation distance w. The estimated values indi- 

 cate that approximately one third of schools of 

 size 100 within the truncation distance (5.5 km) were 

 missed by the research vessel observers, and essen- 

 tially all schools of size 1000 were detected. The re- 

 sult shown in Figure 3 is, qualitatively at least, par- 

 tially constrained by the bivariate line transect 

 model, i.e. if the data indicate dependence of detect- 

 ability upon school size, then the parametric form 

 for tiV/f<s' dictates that the estimated curve must vary 

 smoothly and monotonically with size and must ap- 

 proach w asymptotically. However, the model fit need 

 not have any dependence on school size, and the spe- 

 cific direction and rate of increase shown in Figure 3 

 are due to the data, and agree with observer experi- 

 ence in terms of reaching the limiting value within 

 the range of sizes shown. 



in 

 in 



}=I-I-i-J 



100 200 300 400 500 600 700 800 900 1,000 

 School size 



Figure 3 



Estimated effective strip halfwidth as a function of dolphin school 

 size. These maximum likelihood estimates are from the bivari- 

 ate hazard rate Hne transect model as discussed in the text, and 

 are based on northeastern offshore spotted dolphin school 

 sightings from observers aboard NMFS research vessels during 

 the months July to December, 1986-90 and 1992-92. Error bars 

 indicate plus or minus one standard error and should not be in- 

 terpreted as confidence intervals. The horizontal line at 5.5 km 

 indicates the perpendicular truncation distance in the line 

 transect model. 



The standard error bars in Figure 3 exceed w in 

 some cases, although it is not possible for «',.,»(«• to 

 exceed the truncation distance w. These error bars 

 are presented simply to represent the estimated pre- 

 cision for each estimate, and should not be inter- 

 preted as confidence intervals. Confidence intervals 

 for the estimated halfwidths would tend to be asym- 

 metric and would not exceed the truncation distance. 



Estimated capture frequency 



Figure 4 shows the estimated capture frequency due 

 to U.S. tuna vessels. These estimates represent the 

 average number of times a school of a given size was 

 set on each year during the study period. The esti- 



