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Fishery Bulletin 112(2-3) 
Table 2 
Covariates and summary statistics for the best-fit detection function models by species group from analyses of data from 
line-transect surveys conducted off Southern California from 2004 to 2008. The distribution of perpendicular sighting dis- 
tances for pooled species was used to parameterize the detection function models summarized here, where f( 0) is the prob- 
ability density function evaluated at a perpendicular distance of zero, bin width (m) is the interval chosen to show the 
fraction of probability distribution, truncation value excludes the 5% of sightings by species group that were farthest from 
the transect line and therefore considered outliers, ESW is the effective strip (halDwidth for which the number of groups 
outside the ESW is equal to the number missed inside the ESW, and CV is the coefficient of variation. The hazard-rate 
key function was used in the best-fit model for all species groups. Species groups were selected on the basis of factors that 
influence sightability, such as common school sizes, body shape, and behavior. The species group of large whales consisted of 
the blue, fin, humpback, sperm, and killer whales. Delphinids included the short- and long-beaked common, northern right 
whale, Pacific white-sided, Risso’s, and bottlenose dolphins and the Dali’s porpoise. For detection function plots, see Figure 2. 
Species groups 
for estimating 
fl 0) 
Number of 
observations 
Covariates 
Bin width 
(m) 
Truncation 
(m) 
Average ESW 
(m) 
CV 
Large whales 
127 
Perpendicular distance 
500 
2348 
1294 
0.11 
Delphinids 
211 
Perpendicular distance, sea state, 
species, log( group size) 
100 
1098 
298 
0.10 
Dali’s porpoise 
48 
Perpendicular distance, sea state 
100 
1098 
305 
0.22 
seasonal period (winter-spring and summer-fall) and 
between the distance from shore and depth by the 
season, with Systat (vers. 13; Systat Software, Chica- 
go, IL). Because our data had a bimodal distribution, 
Kruskal-Wallis one-way ANOVAs and Mann-Whitney 
[/-tests were run to examine variation in encounters by 
habitat, year, and season with Minitab software (vers. 
15.1.30; Minitab, State College, PA). 
We used line-transect methods (Buckland et al., 
2001) with multiple covariates (Marques and Buck- 
land, 2003) to estimate cetacean abundance for 2 sea- 
sonal periods and 2 depth categories (defined below) in 
Distance software (vers. 6.0; Research Unit for Wild- 
life Population Assessment, University of St. Andrews, 
UK; Thomas et al., 2010). Distance software uses the 
perpendicular distance of the encounter to the transect 
line rather than the straight line distance (observer 
to animal) made at the time of the sighting; therefore, 
we calculated perpendicular distance as r sin 0 before 
uploading these data into Distance. Small sample size 
by season precluded our ability to estimate abundance 
quarterly; therefore, we estimated abundance within 4 
strata in the study area. The strata were defined by 
2 seasonal periods, winter-spring (cold water) or sum- 
mer-fall (warm water), and 2 depth categories, shal- 
low (<2000.5 m and deep (>2000.5 m). On the basis 
of known ecological differences between shelf or slope 
and basin, with greater density of cetaceans near the 
coast, we chose to look at these data in 2 depth cat- 
egories. Additionally, a histogram of effort as a func- 
tion of depth showed that depth in our study area was 
strongly bimodal and that the depth of 2000.5 m was 
an appropriate cutoff point. Sample units were speci- 
fied by survey number, line number, season, and depth 
to ensure that each of the 6 transect lines from each 
survey would be divided into a shallow and a deep 
sample unit. 
To estimate density and abundance for a species, 
it is necessary to reliably estimate the detection func- 
tion (the probability of seeing an animal at x distance 
from the transect line), and that requires a relatively 
large sample size (Buckland et al., 2001). The neces- 
sary sample sizes were not available for all species in 
this study; therefore, we pooled multiple species with 
similar surfacing characteristics (Barlow et al., 2001) 
and pooled (binned) sightings across season-and-depth 
strata to estimate the detection function (Table 2, 
Fig. 2). Pooled species groups were defined as 1) large 
whales, which included blue (Balaenoptera musculus), 
fin ( Balaenoptera physalus ), humpback (Megaptera no- 
vaeangliae), sperm (Physeter macrocephalus), and killer 
whales ( Orcinus orca)\ 2) delphinids, which included 
short- and long-beaked common, northern right whale 
(Lissodelphis borealis ), Pacific white-sided, Risso’s 
( Grampus griseus ), and common bottlenose ( Tursiops 
truncatus) dolphins; and 3) Dali’s porpoises ( Phocoe - 
noides dalli). Beaked whales and several other species 
of delphinids were encountered too infrequently to esti- 
mate abundance. Cetaceans that could not be identified 
to genus and species levels were not included in the 
pooled species groups for estimation of the detection 
function, and density and abundance levels were not 
estimated for them. 
Potential covariates for building the detection func- 
tion models included group size (a categorical variable 
that denotes whether sightings were greater or less than 
20 individuals), cluster size (best estimate of group size), 
sea state (a numerical variable of 0-5), vessel, and spe- 
cies. Cut off points for group size were based on obvious 
breaks in histograms of group size for each species cat- 
