Perkins and Edwards Capture rate as a function of scfiool size for Stenella attenuata 



545 



Data from individual sets made by non- 

 U.S. vessels were not available; however, 

 count data summarizing obsei-ved num- 

 bers of sets and trips made by all vessels 

 were available. From these data, we used 

 the numbers of sets on the target stock 

 observed each year, by both U.S. and non- 

 U.S. vessels, during the study period and 

 for the entire year (Table 2 ). Additionally, 

 the total annual number of fishing trips 

 that involved sets on dolphins has been 

 estimated each year from tuna vessel log- 

 book data (e.g. lATTCM. Dividing the 

 annual number of observed trips by the 

 annual total number of trips gives the 

 annual trip sampling fraction ("cover- 

 age"), which we took as known exactly. 

 We further assumed that observer cov- 

 erage was constant throughout the year 

 and took the sampling fractions as ap- 

 plicable for the study period as well as 

 the entire year. 



Statistical model 



We modeled the true population of NE 

 offshore spotted dolphin schools within 

 the stock boundaries as an independent 

 identically distributed (i.i.d.) sample of 

 unknown size from a hypothetical infi- 

 nite superpopulation of schools having a 

 smooth probability density for their 

 school sizes. To characterize the true 

 population of school sizes, both the total 

 number of schools, N,, , , and the prob- 



' schools^ ^ 



ability density fi-om which their school sizes 

 were drawn, iris), needed to be estimated. 

 Although school size is really a discrete 

 quantity, we approximated it using a con- 

 tinuous-valued random variate. 



Dolphin school sightings are made 

 from visual clues such as surface distur- 

 bances or associated bird flocks, and 

 larger schools in general provide a more 

 visible target. Thus, the sighting prob- 

 ability for schools at a given range de- 

 pends on school size, leading to a selection bias ( rela- 

 tive to nis)} towards larger schools in the research 

 vessel observations. We modeled these observations 

 as a biased sample of size n,^;,^^,,, from the true popu- 

 lation. Because the ships" tracklines were random 

 with respect to the dolphin population, we assumed 

 that there were no other selection biases. We denoted 

 the probability density of observed school sizes by 

 TT^'is) to distinguish it from ;rts), and note that 



Research vessel observer data 

 n = 483 

 median = 106 



200 



400 



600 



800 



B 



o 

 o 



CM 



O 

 ID 



Tuna vessel observer data 

 n = 3454 

 median 560 



1,000 



2,000 



Estimated school size 



3,000 



4,000 



Figure 2 



Estimated observed school sizes tor northeastern offshore spotted dol- 

 phins. These data include observations from both geographic strata. The 

 fitted Imes are kernel density estimates i see text I for these observations. 

 Note the different x- and y-axis scalings. (A) Research vessel sightings, 

 1986-90 and 1992-93. These data are the mean observer estimates and 

 are not corrected for size selection bias isee te.xtl. They include on-effort 

 sightings with perpendicular distance <5.5 km; 8 observations >800 are not 

 shown. (B) Tuna vessel sets. 1986-90; 19 observations >4000 not shown. 



Tlis) 



W,.f, 



l^\./I^S) 



-n is). 



/her 



e w Js'. 



w 



eff 



- the line transect effective strip half- 

 width for schools of size s ; and 



= the size-averaged effective strip 

 halfwidth (Appendix D in Burnham 

 et al., 1980). 



