Barlow and Forney: Abundance and population density of cetaceans in ttie California Current ecosystem 513 



models were considered for estimating fiOlz^) because 

 hazard-rate models have been shown to give highly 

 variable estimates (Gerrodette and Forcada, 2005) and 

 because hazard-rate models often did not converge on 

 best-fit solutions. In estimating fiO\Zj), data from all 

 years and geographic strata were pooled, and species 

 were pooled into groups with similar sighting char- 

 acteristics (Barlow et al., 2001): delphinids (excluding 

 killer whales); Ball's porpoise; small whales; medium 

 whales; blue, fin, and killer whales; humpback whales; 

 and sperm whales (Table 1). To improve the ability to 

 fit the probability density function, f{Q\z^>, sightings 

 were excluded if they were farther from the trackline 

 than an established truncation distance (Buckland et 

 al., 2001): 2 km for Ball's porpoises and 4 km for all 

 other species. This procedure eliminated approximately 

 15% of sightings. The covariates for the f(0) function 

 were chosen by forward step-wise model building by 

 using the corrected Akaike information criterion (AIC^). 

 Potential covariates included the total group size or its 

 natural logarithm {TotGS or LnTotGS), Beaufort sea 

 state {Beauf), survey year ( Fear: 1991, 1993, 1996, 2001, 

 or 2006), survey vessel (Ship: McArthur or Jordan), 

 geographic region (Region), the presence of rain or 

 fog within 5 km of the ship (RainFog), the presence 

 of glare on the trackline (Glare), the estimated vis- 

 ibility in nautical miles (Vis), the method used to first 

 detect the group (Bino: 25x binoculars or other tool), 

 and the cue that first drew an observer's attention to 

 the presence of a group (Cue: splash, blow, or other). 

 As covariates, TotGS, LnTotGS, Beauf. and Vis were 

 treated as continuous variables and the others as cat- 

 egorical. Categorical covariates were used only if all 

 factor levels had at least ten observations. See Barlow 

 et al. (2001) for a more complete description of these 

 covariates and their influence on the distance at which 

 various species can be seen. When sample size permit- 

 ted, another covariate (SppGroup. a coded value for 

 the most abundant species within a group) was added 

 to sub-stratify a species group, allowing for differences 

 in detection distances between members of the a priori 

 species groupings (Table 1). Because very few cryptic 

 species, such as small whales and Ball's porpoise, are 

 seen in rough conditions and sample sizes were too 

 small to estimate ^(0) for those conditions, the abun- 

 dance of these species was estimated by using search 

 effort conducted only in calm seas (Beaufort sea state 

 to 2); abundance of other species was based on search 

 effort in Beaufort sea states to 5. 



Some animals sighted could not be identified to spe- 

 cies or probable species, and, for completeness, we also 

 estimated the abundance of the cetaceans represented 

 by these sightings. Sample sizes were small; therefore 

 these unidentified categories were pooled with other 

 similar species for estimating /"( 01 z^l. Unidentified del- 

 phinoids were pooled with all delphinids; unidentified 

 small whales were pooled with Ziphius, Mesoplodon 

 and Kogia spp.; unidentified rorquals were pooled with 

 all rorqual species; and unidentified large whales were 

 pooled with rorquals and sperm whales. 



In traditional (noncovariate) line-transect analyses, 

 effective strip width (ESW) gives a measure of the dis- 

 tance from the trackline at which species were seen 

 (with an upper limit defined by a chosen truncation 

 distance). For the covariate line-transect method, ESW 

 varies with the covariates for each sighting. The mean 

 ESW was calculated as the truncation distance mul- 

 tiplied by the mean probability of detecting a group 

 within that distance for all sightings of a species. 



The total abundance, A^ , for a species was estimated 

 as the sum over the four geographic regions of the den- 

 sities, Dj, in each stratum multiplied by the size of the 

 stratum, A, : 



4 



Ar = ^D,.A,. (3) 



1=1 



Abundance and density were not estimated for harbor 

 porpoises (Phocoena phocoena), gray whales (Eschrich- 

 tius robustus), or the coastal stock of bottlenose dolphins 

 (Tiirsiops triincatus) because their inshore habitats were 

 inadequately covered in our study and because good 

 abundance estimates are available for these species from 

 specialized studies (Carretta et al., 1998; Rugh et al., 

 2005; Carretta et al., 2006). 



The areas. A, , within each stratum were limited to 

 waters deeper than 20 m (the safe operating limit of 

 the vessels). The total areas between the coast and the 

 offshore boundaries were estimated with the program 

 GeoArea (available from Gerrodette^). The stratum 

 areas were estimated by subtracting the area between 

 and 20 m depth (and the areas of the Channel Is- 

 lands in the southern California stratum) from these 

 total areas. The area between the 0- and 20-m depth 

 contours in the southern California stratum (including 

 the Channel Islands) was estimated with the ArcGIS 

 9.1 software package. The 20-m contour was derived 

 from a bathymetry data set with grids providing 200 

 m horizontal resolution, 0.1 m vertical resolution) from 

 the California Bepartment of Fish and Game, Marine 

 Region. Coastline data from the NOAA National Ocean 

 Service Medium Resolution Bigital Vector Shoreline 

 (1:70,000 scale) was used for the 0-m contour. 



The coefficients of variation (CV) for abundance were 

 estimated by using mixed parametric and nonparamet- 

 ric bootstrap methods (Efron and Gong, 1983). Vari- 

 ance attributed to sampling and model fitting were 

 estimated with the nonparametric bootstrap method 

 by using 150-km segments of survey effort as the sam- 

 pling unit (roughly the distance surveyed in one day). 

 Adjacent survey segments, sometimes from different 

 days, were appended together to make bootstrap seg- 

 ments. A new bootstrap segment was begun for each 

 survey and whenever a ship crossed into a new region. 

 Within each geographic region, effort segments were 



1 Gerrodette, T. 2007. National Oceanic and Atmospheric 

 Administration, Southwest Fisheries Science Center, 8604 La 

 Jolla Shores Dr., La JoUa CA 92037. Website: http://swfsc. 

 noaa.gov/prd.aspx (accessed 26 June 2007). 



