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



551 



mean annual number of sets on NE offshore 

 spotted dolphins during the period of this study. 

 From tuna vessel observer data, an estimate 

 for the mean school size for those sets is 773 

 animals. When combined with an estimate for 

 the total number of NE offshore spotted dol- 

 phins (Wade and Gerrodette, 1993), this gives 

 (7610 X 773 dolphins set on) ^ (731,000 dolphins) 

 = 8.04 sets per dolphin per year. 



The true picture certainly lies between these 

 two extremes. On the other hand, if the compo- 

 sition and spatial location of some large schools 

 are static over periods of weeks or longer, then 

 animals in those schools could be subject to 

 short-term capture rates even higher than those 

 of our estimates because of the clustered distri- 

 bution of fishing effort. 



Geographic stratification 



Holt et al. ( 1987) partitioned the ETP into sev- 

 eral geographic strata primarily on the basis of 

 spotted dolphin density as observed from tuna 

 vessels during years prior to the study period. 

 In an alternate analysis for capture frequency, 

 we used Holt et al.'s partition to fit separate 

 densities for p(s) in each of two strata (Fig. 1), 

 and used separate counts n , and n , , . The 



^ ^'t=^s schools 



estimates of p(s) from the two strata were sig- 

 nificantly different (Kolmogorov-Smirnov good- 

 ness-of-fit test, P=0.002), but primarily at 

 smaller school sizes, less than 200 animals, and 

 this stratification made little difference in ab- 

 solute terms from the unstratified estimates of 

 capture frequency. The similarity in capture 

 frequency estimates between strata indicates 

 that fishing pressure was approximately pro- 

 portional to dolphin school density. 



We did not stratify geographically to estimate ;r*(s ) 

 or u\,y{s) because we found that the number of ob- 

 servations in the middle stratum (n , ,=81) was too 

 small to allow stratification and still have reason- 

 able precision. A Kolmogorov-Smirnov test and Q-Q 

 plots indicated that there was no substantial differ- 

 ence (P=0.62) in ;r*(s) between strata for the research 

 vessel observers. On the other hand, we fitted the 

 bivariate line transect model to data from the two 

 strata separately and found that the estimate of 

 i<-\,fyis) for the middle stratum was 10-20^^^ smaller 

 than that for the inshore stratum, depending on 

 school size. However, there were few data on which 

 to base either result. One reason why u\,f-As) might 

 actually have differed between the two strata was a 

 difference in observed sea state conditions; a higher 

 average Beaufort sea state was reported in the 



CO 



d 



d 



d 



CM 



d 



o 



d 



100 



= 300 



.J = 500 



i =800 



i = 1 ,000 



10 20 30 



Minimum number of times set on per year 



40 



Figure 6 



Estimated percentage of northeastern offshore spotted dolphins 

 subject to different levels of capture frequency. The horizontal 

 axis represents the minimum number of times a dolphin school 

 is set upon per year by U.S. and non-U. S. tuna vessels in the 

 ETP purse-seine fleet, for the years 1986-90. The vertical axis 

 represents the estimated fraction of the stock (not the fraction of 

 schools I subject to at least that rate of being set upon, s is the 

 minimum school size accounting for that percentage. 



middle stratum. The practical impact is that our es- 

 timates of capture frequency may have been overin- 

 fiuenced by data from the inshore stratum. 



Observer size-estimation errors 



Our statistical model for the school size data included 

 terms for selection biases, that is, which schools were 

 included in the sighting or set data. However, there 

 was also a potential for observer size-estimation bi- 

 ases. That is, given a sighting of, or a set on, a spe- 

 cific school, an observer had to estimate size of the 

 school. The results presented here treated the ob- 

 server estimates as exact counts. We did not include 

 an error term for size estimates in either the kernel 

 density estimates of ;r*(s) and p(s) or the bivariate 

 line transect estimates of u' ,,(s). 



