18 
Fishery Bulletin 1 11 (1) 
byproducts from the derivatization process. Finally, the 
laboratory performs periodic standard calibrations of 
the spectrometer at varying levels of concentration to 
determine the limit-of-detection for each compound. 
Several criteria were used to evaluate the suitability 
of each fatty acid compound for inclusion in mixture 
modeling. At a minimum, each compound had to pass 
GC-MS verification, have a minimal variance for the 
majority of samples collected (<20% relative standard 
deviation), and average at least 1% of the total fatty 
acid contained in each sample. The compounds needed 
to be predominately from a dietary source, as delin- 
eated in Iverson et al. (2004). Compounds 18:2n-6 and 
18:3n-3 were automatically included as neither com- 
pound is biosynthesized by seals. These selection crite- 
ria led to a suite of 22 fatty acid compounds to be used 
in mixture modeling: C16:2n-6, Cl6:2n-4, C16:4n-1, 
C18:ln-9, C18:ln-7, C18:2n-6, C18:3n-6, C18:3n-4, 
Cl8:3n-3, C18:4n-3, C20:ln-ll, C20:ln-9, C2Q:ln-7, 
C20:2n-6, C20:3n-6, C2Q:4n-6, C20:3n-3, C20:4n-3, 
C20:5n-3, C22:6n-3, C21:5n-3, and C22:5n-6. Data are 
available at the Biological and Chemical Oceanography 
Data Management Office of the National Science Foun- 
dation (http://osprey.bcodmo.org/project.cfm?flag=viewr 
&id=224&sortby=project). 
Estimating diet composition 
Obtaining unique estimates of diet composition with 
mixture models requires the number of prey classes 
to be no greater than the number of fatty acids (e.g., 
Phillips, 2001). Furthermore, combining prey classes 
reduces the dimensionality of the parameter space and 
can increase estimation precision. Linear discriminant 
functions were used to identify prey classes with po- 
tential to be merged, with R software, vers. 2.10.1 (R 
Development Core Team, 2009) and function Ida of 
package MASS (Venables and Ripley, 2002). The ac- 
curacy of classifying individual prey into correct prey 
classes was estimated with discriminant functions and 
cross validation. Data from each prey specimen were 
removed temporarily, discriminant functions were es- 
timated from the remaining data, and the estimated 
functions were used to classify the excluded specimen 
to a prey class. Prey classes with the largest misclas- 
sification rates were candidates to be merged, provided 
that the mean adipose masses of the 2 classes were 
similar. 
Methods of QFASA mixture modeling closely fol- 
lowed those of Iverson et al. (2004) and Beck et al. 
(2007), methods that have been applied to the re- 
search of numerous marine species, including harbor 
seals (Nordstrom et al., 2008), gray seals ( Halichoerus 
grypus ; Iverson et al., 2004; Beck et ah, 2007; Tucker 
et ah, 2008; Lundstrom et ah, 2010), harp seals (Pag- 
ophilus groenlandicus; Iverson et ah, 2004), northern 
fur seals (Callorhinus ursinus; Hofmeyr et ah, 2010), 
Steller sea lions ( Eumetopias jubatus; Hoberecht, 
2006), polar bears ( Ursus maritimus; Thiemann et ah, 
2008) , and various species of seabirds (Williams et al., 
2009) . A mixture model based on the Kulibaek-Liebler 
(KL) distance measure (Iverson et ah, 2004) was used 
to estimate the diet composition of each seal. The cali- 
bration coefficients for harbor seals reported by Nord- 
strom et al. (2008) were used to convert prey fatty acid 
signatures (FAS) to the scale of predator FAS, and the 
distance measure was evaluated on the predator scale; 
note that Iverson et al. (2004) converted predator FAS 
to the prey scale. Estimation variance for each seal was 
estimated with 1000 bootstrap replications of the prey 
FAS data. The resulting estimates of diet composition 
(fat unadjusted, the p k of Iverson et ah, 2004), also 
were transformed to account for adipose mass per prey, 
expressing diet composition in terms of the number of 
animals consumed (fat adjusted, the a b of Iverson et 
ah, 2004). 
Multivariate analysis of variance (function manova 
in R; R Development Core Team, 2009) was used to 
explore diet composition estimates for structure as- 
sociated with the following covariates: sampling loca- 
tion, season (spring, fall, winter), and sex. The initial 
model contained these 3 main effects and all 2-way in- 
teractions, and nonsignificant terms were sequentially 
eliminated from the model. A significance level (a) of 
0.01 was used for all tests. The mean diet composition 
for a class of predators (e.g., males or females) was 
computed as the sample average of their individual 
diet composition estimates. The variance of mean diet 
composition was assessed with the estimator of Beck 
et ah (2007). Mixture proportions and variances were 
estimated with a custom computer program written in 
Fortran (Metcalf et ah, 2004) and compiled with the In- 
tel Visual Fortran Compiler Professional Edition, vers. 
11.1 (Intel Corp., Santa Clara, CA). 
Results 
Estimating diet composition 
Given the suite of 22 fatty acid compounds used to 
form FAS, the 27 original prey classes needed to be 
reduced to no more than 22 prey classes for mixture 
model estimates to be unique (Phillips, 2001). Among 
the 27 original prey types, Black and Yellowtail Rock- 
fish; medium-size Chinook and Coho Salmon; small 
Chinook, Chum, Sockeye, and Pink Salmon; young Pa- 
cific Herring aged 0 to 1 and Pacific Sand Lance; and 
Kelp Greenling, Pacific Staghorn Sculpin, and Starry 
Flounder were combined to reduce discriminant analy- 
sis misclassification among prey classes (Table 2). The 
resulting prey data set contained 19 prey classes, for 
which 251 of 269 prey animals (93.3%) were assigned 
to the correct prey class. 
The mean diet composition of all 49 seals, both ad- 
justed and unadjusted for differential fat mass among 
prey, was estimated with FAS for 22 fatty acid com- 
pounds and data for 19 prey classes. The species esti- 
