Henderson et al . : Effects of sea-surface temperature on the occurrence of small cetaceans off Southern California 
163 
Environmental data 
Three variables were used to represent variations in 
SST on different temporal scales: quarterly SST aver- 
ages, ENSO indices, and PDO indices. Monthly aver- 
aged SST data from 1985 to 2009 were from NOAA 
Advanced Very High Resolution Radiometer (AVHRR) 
Pathfinder satellite data, which have a spatial resolu- 
tion of ~4.1-km (http://www.nodc.noaa.gov/Satellite- 
Data/pathfinder4km). For 1981-84, NOAA AVHRR 
data (multichannel averaged SST with a 5.7-km reso- 
lution) were also used. No satellite data were avail- 
able before 1981; therefore, a missing data filter and 
a single imputation method were used to create val- 
ues for 1979 and 1980 with the mean of the SSTs 
for the other years (Hastie, 1991; Nakagawa et al., 
2001 ). 
With Windows Image Manager, vers. 6 (WimSoft, 
San Diego, CA), seasonal SST averages were calculated 
from the monthly SST data. These SST averages were 
estimated for each quarter and each grid cell (see the 
following paragraph) for the period 1979-2009 (spring: 
February-April; summer: May-July; fall: August- 
October; winter: November-January ). NOAA ENSO 
anomaly data, derived from the Oceanic Nino Index as 
a 3-month running mean of SST anomalies from 1971 
to 2009 in the Nino 3.4 region (http://www.cpc.ncep. 
noaa.gov/products/analysis_monitoring/ensostuff/ 
ensoyears.shtml), were used as a proxy for ENSO 
for 1979-2009. The Nino 3.4 region is centered on the 
equator; therefore, the index indicates the relative 
strength of the ENSO event rather than SST anomaly 
values for Southern California waters. PDO anomaly 
data, averaged for the period from 1900 to 2009, from 
the University of Washington (http://jisao. Washing- 
ton. edu/pdo) were used as a proxy for the PDO regime 
from 1979 to 2009. The PDO index is derived from a 
monthly averaged SST for North Pacific waters pole- 
ward of 20°N. 
Depth data were taken from the NOAA Nation- 
al Geophysical Data Center’s ET0P02 2-min global 
relief database (http://www.ngdc.noaa.gov/mgg/ 
fliers/06mgg01.html). The study area was divided 
into 52 grid cells of 1° (111 km or 60 nmi) latitude 
by 1° longitude, leading to grid cell areas that ranged 
from 2940 to 3120 km 2 . The gridded depth data were 
then assigned to each of the grid cells, and minimum, 
maximum, and mean depth values were calculated for 
each grid cell, along with the maximum seafloor slope 
per cell. These large grid cells correspond to approxi- 
mately one day of effort for each of the surveys and 
were designed to be large enough to smooth out the 
mesoscale features that occur on shorter temporal and 
spatial scales than were of interest here. Although 
mesoscale features, such as fronts or eddies, are of- 
ten observed to be hotspots for marine mammals, the 
multidecadal data set used in our study allowed for a 
synoptic examination of changing distribution patterns 
throughout the study area. 
Modeling cetacean sighting rates 
Generalized additive models (GAMs) of species sight- 
ing rates as a function of the temperature data and 
depth values were created with the mixed GAM com- 
putational vehicle (mgcv) package in R software, vers. 
2.14.2 (R Core Team, 2012) (Hastie and Tibshirani, 
1990; Wood, 2006). GAMs use a link function to relate 
the predictor variables to the mean of the response 
variable. GAMs also allow nonparametric functions to 
be fitted to the predictor variables through the use of 
a smoothing function to describe the relationship be- 
tween the predictor and the response variables (Has- 
tie and Tibshirani, 1990). 
For model development, the grid cells described 
previously were used as data units, and all effort, 
sighting, and seasonal SST data were calculated for 
each cell. This approach allowed for the normalization 
of spatial and temporal differences in survey data. 
The type of survey was included as a categorical vari- 
able to account for differences in sighting rates due 
to survey method and platform. For example, because 
many vessels of different heights were used and 
heights for some vessels were not reported, standard- 
ization of observations for platform heights was not 
possible. Survey types included SWFSC (1979-2005), 
CalCOFIa (1987-2004), and CalCOFIb (2004-09). For 
each survey type, the number of group sightings of 
each species within each 1° cell, standardized by the 
log of the amount of effort per cruise (in kilometers), 
was modeled by assuming a Poisson distribution with 
a log link function. 
Potential predictor variables in the model were the 
following: seasonal SST averages of each grid section 
(SeasAv); ENSO index (ENSO); PDO index (PDO); the 
mean (DepthMean), minimum (DepthMin), and maxi- 
mum (DepthMax) depth (in meters) for each grid sec- 
tion; the maximum slope for each grid section (Slope); 
and the quarter (Quarter) as a categorical variable 
for identification of interannual patterns. Although 
sea state has been shown to be an important predic- 
tor of sighting rates in other cetacean habitat and 
trend models (Becker, 2007), the condition of the sea 
surface was not recorded in early CalCOFI observa- 
tions and, therefore, sea state was not included in 
this analysis. Instead, only data recorded when the 
sea state was rated 0-3 on the Beaufort scale during 
SWFSC cruises and later CalCOFI cruises were used 
to standardize for differences in survey effort and, 
thus, make the different platforms as comparable as 
possible. 
We used the number of group sightings, rather 
than the number of individuals, as our measure of 
relative encounter rate, essentially creating encounter 
rate models of group sightings per unit (kilometer) of 
survey effort (SPUE) (Bordino et al., 1999; Stockin, 
2008). A correlation analysis of annual rates of group 
sightings in relation to mean group size per year 
