Fishery Bulletin 93| 



1995 



42" 



39° - 



-a 



B 36° 



35° 

 34° 

 33° 

 32° 

 31°- 



30° 



Pacific 

 Ocean 



127° 126° 125° 124° 123° 122° 121° 120° 119° 118° 117° 127° 126° 125° 124° 123° 122° 121° 120° 119° 118° 117° 



Longitude Longitude 



Figure 2 



Completed transects (solid lines) for 1991 and 1992, and a posteriori geographic strata (separated by broken lines) used in the 

 analysis. Area numbers are shown in circles. 



Abundance estimation 



Line transect methods (Burnham et al., 1980; Buck- 

 land et al., 1993a) were applied to estimate abun- 

 dances separately for each species in each stratum: 



N h 



yy A n ij,k 



\j,k 



/}<0) 



2L, gj (0) 



(1) 



where 



Ni = 



l u,k 



'ij.k 



estimated total number of animals of species 

 k in the study area; 



number of sightings of species k in area i and 

 species/group-size category,/'; 

 average group size of species k in area i and 

 species/group-size category J, calculated as 

 the total number of animals in all groups di- 

 vided by the number of groups sighted; 



/"■(0) - the probability density function evaluated at 

 zero perpendicular distance for species/group- 

 size category j; 



giO) = the probability of detecting a group of ani- 

 mals on the transect line for species/group- 

 size category j ; 



L = the length of transect surveyed in area i (in 



km); and 

 A- = the size of area i (in km 2 ). 



Values for/(0) were obtained for each species/group- 

 size category by fitting the distribution of all per- 

 pendicular sighting distances (primary and second- 

 ary; measured in km) to the Hazard rate model with 

 the statistical software program HAZARD 

 (Buckland, 1985). A value for ^(0) was estimated fol- 

 lowing the methods described in Forney and Barlow 

 ( 1993 ), but because of small sample sizes, it was not 

 possible to estimate the variance ing(0). This should 

 result in a downward bias in the variance of the abun- 

 dance estimates, but bias in the abundance estimates 

 themselves will be reduced. The lengths of transect 

 lines flown, L- (and total sizes, A-), for the four areas 

 are 3,715 km (46,300 km 2 ) for area 1; 2,831 km 

 (63,772 km 2 ) for area 2; 4,461 km (120,108 km 2 ) for 

 area 3; and 2,035 km (34,090 km 2 ) for area 4. 



Variance estimation 



Variance in estimated abundance was calculated with 

 bootstrap techniques applied to the complete data 



