Perkins and Edwards: Capture rate as a function of schiool size for Stenella attenuate 



549 



mates are an integration of the information pre- 

 sented in Figure 2 and Figure 3, i.e. 



scaled by a suitable estimate of the overall av- 

 erage capture frequency. The magnitude and 

 direction of the trend in N.^ f,,,.^. was almost en- 

 tirely due to the estimates of pis) and n'-'(s). 

 Estimates of the factor u\,Js) varied only by 

 about 509( over the range of sizes considered, 

 whereas the estimated ratio of p(s ) to n^'Hs ) var- 

 ied by two orders of magnitude. 



The precisions of our estimates of capture fre- 

 quency depended on the precisions of the indi- 

 vidual estimated factors involved in N^.„.j,„,.Jf<)- 

 We were able to estimate those different preci- 

 sions using the output of the bootstrap proce- 

 dure and found that they varied widely. Much 

 of the variability was in our estimates of ;r''(s), 

 with bootstrap estimates of CV ranging from 9% 

 at a school size of 100 up to 24^^ at 1000. Boot- 

 strap CVs for u\,,As} were low, ranging from IS"^.^ 

 down to 1%, but, as mentioned above, wJs) was 

 the factor most constrained by the model. Boot- 

 strap CVs for pis) were lower than those for 

 Tc *{s ), ranging from M'^f at a school size 100 down 

 to 6'''^ at 1000. Set counts and sighting counts both 

 had bootstrap CVs of approximately 6.59^ . 



Figure 5 shows the estimated annual capture 

 frequencies due to the U.S. fleet and due to the 

 combined U.S. and international fleet. The es- 

 timate of the combined capture frequency for 

 schools of size 1000 is 36.1 sets per year, or one 

 set every 10 days, compared with well under 

 once a year for schools of 100 animals. The esti- 

 mate for the median school size set on (560 ani- 

 mals) was 10.1 sets per year, or just under once per 

 month. The U.S. fleet accounted for an estimated 31*^ 

 of sets during the years 1986-90. Although we were 

 not able to estimate standard errors in these annual 

 estimates, the error bars in Figure 4 should give at 

 least a rough idea of the potential precision. 



Because of the extrapolation of school-size distri- 

 butions necessary to make annual and combined fleet 

 estimates, the two curves in Figure 5 are identical 

 in shape to that in Figure 4, but have different scale 

 factors. The scale factor for the lower curve was an 

 estimate of the overall (size-averaged) annual capture 

 frequency, N.^, /N , , , due to the U.S. fleet, whereas 

 the scale factor for the upper curve was the correspond- 

 ing estimate for the combined fleets. These two overall 

 capture frequency estimates were not extrapolated from 

 data collected during the study period, but were based 

 on annual set counts for the two fleets. 



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



School size 



Figure 4 



E.stimatcd capture frequency as a function of dolphin school size, 

 for schools of northeastern offshore spotted dolphins. The esti- 

 mates are of the average number of times a school was set on 

 each year by U.S. tuna purse-seiners, between 28 July and 10 

 December (19.4 weeks i. for the years 1986-90. Error bars indi- 

 cate plus or minus one standard error and should not be inter- 

 preted as confidence intervals. 



Using the estimated school sizes from the sight- 

 ing data, and weighting by the estimated effective 

 strip width, w^,Js}, we estimated the cumulative per- 

 centage of individual dolphins in schools gi'eater than 

 or equal to a given size, i.e. 



His) = Prja dolphin is in a school of size > s] 

 = [t7iit)dt [tK(t)dt 



//(s) = 



(s, 



where I\s, > s]  



[1, if.s, >s 



[0, otherwise 

 and the sums are over research vessel sightings. 



