Barlow. Abundance of cetaceans in California waters: ship surveys 



l j,k 



J j-k 



= number of sightings of species k in 



group size stratum,/'; 

 = mean group size of species k in group 

 size stratum j; 

 f k (0) - sighting probability density at zero per- 

 pendicular distance for group size stra- 

 tum./ of the species group to which spe- 

 cies k belongs; 

 L = length of transect line completed; and 



g k (0) = probability of detecting a group directly 

 on the trackline for group size stratum 

 j of the species group to which species 

 k belongs. 



Perpendicular distance truncation 



Sightings of distant groups add little to the estima- 

 tion of trackline density and can introduce bias. 

 Buckland et al. (1993b) recommend truncating to 

 eliminate at least the most distant 5% of all sightings. 

 In the current study, groups of cetaceans were typi- 

 cally not pursued for species identification and group 

 size estimation if they were farther than 5.5 km (3 

 nmi) from the trackline. Therefore, by survey design, 

 perpendicular distances must be truncated at no 

 more than 5.5 km. I used a truncation distance of 

 3.7 km (2 nmi) for "small delphinids," "cryptic spe- 

 cies," "large delphinids," and "small whales," which 

 eliminated 8.8%, 2.4%, 4.6%, and 12.8% of all groups 

 (respectively). A truncation distance of 5.5 km was 

 used for "large whales," which eliminated 10.9% of 

 groups. 



Group-size estimation 



The estimation of group size for cetaceans is diffi- 

 cult and can lead to bias in the estimation of abun- 

 dance. To avoid bias, correction factors were devel- 

 oped for individual observers. The estimates of four 

 of the six primary observers on the present survey 

 had been previously calibrated by means of aerial 

 photographic estimates to represent "true" group 

 size. 4 The "best" estimates of two of these four were 

 found to indicate group size with accuracy and did 

 not require any correction factors. The other two re- 

 quired correction factors, and, for one, correction fac- 

 tors varied significantly from one year to the next. A 

 helicopter was not available to make aerial photo- 

 graphic estimates of group size on the present sur- 

 vey, so correction factors for individual observers 

 were estimated indirectly by comparison with the two 



4 Gerrodette, T. D., and C. Perrin. 1991. Calibration of shipboard 

 estimates of dolphin school size from aerial photographs. Admin. 

 Rep. LJ-91-36, available from Southwest Fish. Sci. Cent., P.O. 

 271, La Jolla, CA 92038. 73 p. 



observers who, in the previous study, did not require 

 correction. 



Linear regression was used to compare one obser- 

 ver's estimates of group size to another's for the sub- 

 set of groups that were estimated by both. Group sizes 

 were log 10 -transformed to normalize variances. For 

 the two observers who did not require a correction 

 factor in the previous study, 4 the slope of the regres- 

 sion was 1.009 (SE=0.017), indicating that, relative 

 to each other, the observers were still estimating 

 group size consistently. Correction factors for the 

 other four observers were based on the slope and in- 

 tercept of the regression of their "best" estimates 

 against the mean of "best" estimates of the two who 

 did not need calibration. 



The group size for each species in a group was es- 

 timated as the average of all observers' corrected 

 estimates of the size of the group multiplied by the 

 average of all observers' estimates of the percentage 

 of that species present (if in a mixed-species group). 



Probability of detecting trackline groups 



Estimating the probability that a group on the 

 transect line will be seen, g(0), is fraught with diffi- 

 culties (see Buckland et al. [1993b] for a review of 

 previous attempts). In the context of bias from missed 

 groups of marine mammals, it is useful to think in 

 terms of the dichotomy proposed by Marsh and 

 Sinclair ( 1989): bias can result from groups that were 

 available to be seen but were not (perception bias) 

 and from groups that were not available to be seen 

 either because they did not surface or because they 

 surfaced behind a swell (availability bias). I will make 

 a minimum estimate of perception bias based on data 

 collected by the conditionally independent observer 

 and on the approach given in the Appendix. Because 

 the sample of sightings made by independent observ- 

 ers is small (only 37 cetacean groups), f 2 (0) in Equa- 

 tion 7 was estimated for all cetaceans pooled with- 

 out stratification by group size or sea state. Perpen- 

 dicular distance data were fitted with the Hazard 

 rate model to estimate f 2 (0). (Groups are only avail- 

 able to the independent observer if they were missed 

 by the other observers; therefore the distribution of 

 perpendicular distances need not be monotonically 

 decreasing. In this case, however, it was, and a more 

 general model is not likely to have performed better 

 than the Hazard rate model.) The analytical vari- 

 ances of /"j(O) and f 2 (0) (from the information matrix 

 method) were used in estimating the coefficient of 

 variation ofg^O) from Equation 8, and the variances 

 of n 1 and n 2 were estimated by assuming a Poisson 

 distribution. Consideration of availability bias is 

 deferred to the Discussion section. 



