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Fishery Bulletin 1 13(3) 
Table 1 
Independent variables that parameterized the general- 
ized additive models used to predict presence, absence, 
and abundance of Pacific ocean perch ( Sebastes alutus). 
Sponge morphogroups were coded as presence-absence 
factors (1 or 0, respectively), and the units for continu- 
ous variables are temperature (°C), depth (m), local 
slope (°), and for velocity measures (cm/s). Note that Sp 
is a composite term substituted for all sponge morpho- 
groups and U during model formulation. 
Factors 
Continuous variables 
A=arborescent 
T=temperature 
C=clavate 
D=depth 
E=encrusting 
Sl=local slope 
F=flabellate 
Long.=longitude 
Fl=flagelliform 
C x =cross current 
G=globular 
/Vs=trawl velocity 
Gp =globular-papillate 
M=massive 
0=ovate 
P=papillate 
Pe=pedunculate 
R=repent 
S=stipitate 
Tu=tubular 
V=vase 
U=Porifera unidentified 
Sp=all sponges, composite 
Co=all corals, composite 
Br=all bryozoans, composite 
Vr=tide velocity 
tional scale by dividing individual CPUE estimates by 
the sum of the annual CPUE within each cruise year; 
by design, this approach ignored interannual differenc- 
es in Pacific ocean perch abundance in favor of allow- 
ing interannual comparisons during model validation. 
Modeling 
Pacific ocean perch distribution and abundance were 
modeled with the nonparametric regression technique 
of GAMs (Hastie and Tibshirani, 1986) in R statistical 
software, vers. 2.13.1 (R Core Development Team, 2011) 
and the mgcv package (Wood, 2006). This fish species is 
patchily distributed across our survey area and, typi- 
cal of field collected data, presents a greater proportion 
of zero catches than would be expected from a Pois- 
son distribution, resulting in abundance data that are 
overdispersed (McCullagh and Nelder, 1989). To model 
these zero-inflated catch data, we followed the recom- 
mendation of Barry and Welsh (2002) and undertook 
independent GAM selection for the Pacific ocean perch 
presence-absence and conditional abundance data sets. 
The presence-absence GAMs used a binomial distribu- 
tion with a logit link function; the conditional abun- 
dance models employed a Gaussian distribution with 
an identity link function. 
Probability of presence and conditional abundance 
of Pacific ocean perch was predicted from GAMs pa- 
rameterized with a variety of physical, environmental, 
spatial, and biogenic variables (for a list of these vari- 
ables and their abbreviations, see Table 1). To reduce 
the tendency of GAMs to over-fit data, we constrained 
the degrees of freedom (dP for some of the smoothed 
continuous terms in the models (i.e., df=4 for local slope 
[SI], Up C x , and N s \ df=10 for depth and temperature 
combined [D,T]). To identify interdependencies amongst 
continuous predictor variables we examined Pearson’s 
correlation coefficient (r; Krebs, 1989) for all pairwise 
comparisons and determined that only depth and tem- 
perature were moderately correlated ( | ?' | =0.55). Con- 
sequently, we combined depth and temperature into a 
bivariate interaction term in the GAM. To determine 
interdependency of sponge morph, bryozoan, and coral 
presence-absence factors, we computed Pearson’s coef- 
ficient of mean square contingency (O; Zar, 1984), found 
that for all pairwise comparisons |0| was <0.50, and 
consequently included each biogenic presence-absence 
factor as an independent predictor in the GAM. 
Four candidate models for the prediction of presence 
or conditional abundance of juvenile and adult Pacific 
ocean perch underwent backward stepwise term selec- 
tion (Weinberg and Kotwicki, 2008; Zuur et al., 2009). 
The 4 initial model formulations for both of those re- 
sponse variables were 
-A + C + E + F + FI + G + Gp + M + 0 + 
Pe + R + S + Tu+V+U + Co + Br + (1) 
s(Long.) +s(Sl) + s(Nq) + s(C-g) + s(D,T), 
-A + C + E + F + FI + G + Gp+M + 0 + 
P + Pe + R + S + Tu + V + U + Co + Br + (2) 
s(Long.) + s(Sl) + s (Vy) + s(D,T), 
~ Sp + Co + Br + s(Long.) + s(Sl) + s(N$) 
+ s(CJ + s(D,T), 
~ Sp + Co + Br + s(Long.) + s(Sl) + ^ 
s(V^) + s(D,T). 
Formulations 1 and 2 contained the full suite of 18 
presence-absence factors for biogenic structures (15 
sponge morphogroups [for abbreviations of these fac- 
tors, see Table 1] and 1 term each for Porifera uniden- 
tified [U], all corals, composite [Co], and all bryozoans, 
composite [Br]) as well as the smooth terms longitude 
(Long.), SI, and D,T. These model formulations differed 
by using either (1) the 2 smoothed vector components 
of Vt (C x and Wg) or 2) simply smoothed Vt- Formu- 
lations 3 and 4 used a reduced predictor variable set 
by combining all sponges into a single presence-ab- 
sence term (Sp) and then testing both suites of smooth 
terms as applied in formulations 1 and 2. Backward 
stepwise term selection involved fitting each of the 4 
formulations above independently with a GAM and 
then removing the least significant terms iteratively 
until only significant predictor terms remained. Signifi- 
cance for all models and statistical tests was inferred 
