Hurst et al.: Growth rates of Gadus macrocephalus 
385 
of the experiment. Wet mass (M w ) of individual fish 
at earlier sampling points was estimated from regres- 
sions based on measurements of fish collected but not 
used in this experiment and the final experimental 
measurements. 
Growth rates (g L and g M ) of juvenile cod were deter- 
mined by regression of the measurements of fish length 
and ln-transformed mass against sampling date. In lieu 
of marking the 7-10 individual fish in each tank, we 
assumed that size rank was maintained within each 
replicate tank during the experiment. Fish that died 
during the experiment were not included in statistical 
analyses. 
Growth models 
For each of the life stages examined (egg-embryos, 
preflexion larvae, postflexion larvae, juveniles), tem- 
perature-dependent growth functions were estimated 
for growth in length and mass. For consistency with 
the most commonly applied field measures of body size, 
growth rates of embryos and larvae were expressed in 
terms of L s and M D , and juvenile growth rates as L T 
and M w . Growth of postflexion larvae were expressed 
in both sets of measures. 
For each life stage, a second-order polynomial func- 
tion was fitted to describe the relationship between 
temperature and growth rate. For consistency in best- 
fit models, the second-order term was maintained, al- 
though it was not statistically significant in some cases. 
For these models, mean temperatures measured during 
the growth interval were applied, rather than experi- 
mental target temperatures. The mean growth rate 
measured in each replicate tank (n - 3 per temperature) 
was used as the level of observation. 
In addition to stage-specific models, an integrated 
model of size- and temperature-dependent growth 
(STDG) was developed (Folkvord, 2005). Data for the 
model were derived from the above experiments on 
larvae and juveniles and from previously published 
data on the hatching times and sizes as a function of 
temperature (Laurel et ah, 2008). Despite represent- 
ing easily identified discrete life stages with differing 
habitats, data on growth of embryos before hatching 
were included with posthatch data to clarify intrinsic 
patterns in potential growth rates through the early 
life stages. Growth rates of prehatch embryos were es- 
timated from the size and age (days after fertilization) 
at hatching, assuming M D= 0.01 pg and L s= 0.0 mm at 
fertilization. In order to standardize measures across 
life stages, measured M w for juveniles was converted 
to M d and measured L r was converted to L s on the 
basis of measurements of similarly size fish (Hurst, 
unpubl. data). 
The integrated STDG model was initially fitted with 
generalized additive models (GAM) to examine the po- 
tential effects of nonlinear interactions between mass 
and temperature on growth. These nonlinear, nonpara- 
metric regression techniques do not require a priori 
assumptions on the shape of the relationship between 
the dependent and independent variables. After evalu- 
ation of potential interactions based on evaluation of 
the generalized cross validation (GCV), a parametric 
model formulation was selected that best represented 
patterns in the growth data. Final models were fitted 
with parametric nonlinear regression in Statistica (vers. 
6.0, StatSoft, Tulsa, OK). This approach was under- 
taken separately to provide STDG models for growth 
expressed in mass (M D ) and length (L s ). 
Results 
Preflexion larvae 
Mean size of larvae at hatch was slightly larger in the 
2007 experiment than in the 2008 experiment (L s 5.16 
vs. 4.90 mm; F (1 60] = 45.4, PcO.001). However, there was 
no significant difference among years in growth rates of 
preflexion larvae reared at 8°C (g L F ^ 4) = 1.52, P- 0.237; 
g M F [14 j = 3.90, P=0.119), therefore data from the two 
experiments were combined to describe the effect of 
temperature on growth rate. In addition, there were no 
differences in growth rates among replicate tanks at a 
given temperature (tested as the interaction between 
day and tank on mean size, all P>0.05). 
Growth in length and mass of Pacific cod larvae was 
significantly affected by rearing temperatures across 
the range examined (Fig. 1; g M F (311 | = 30.0, P<0.001; 
g L (F |3 h]= 59.4, PcO.001). After 35 days, fish reared at 
8°C were 2.6 times larger than fish reared at 2°C (M D 
0.271 vs. 0.104 mg). Growth rates were fitted as a sec- 
ond-order function of temperature (Table 2). 
Postflexion larvae 
The sorting of fish by size before the establishment of 
experimental groups produced significant differences 
in initial sizes of experimental fish (group mean L s 
14.02 to 16.10 mm; P- 0.004). Differences among size 
groups within temperature treatment were generally 
maintained throughout the experiment but growth rates 
were slightly higher in the small-size groups than the in 
large-size groups. The effect of size group was significant 
for growth expressed as g M (P| 26 j= 15.7, P=0.004) but not 
for g L (F [2 6] = 1.78, P=0.248). 
Growth in length and mass of postflexion Pacific cod 
larvae was significantly affected by rearing tempera- 
tures across the range examined (Fig. 2; g M F j3 g] =34.3, 
P<0.001; g L (P [36 j = 63.0, P<0.001). Growth rates (for 
g M and g L ) at 11°C averaged 2.2 and 3.0 times, respec- 
tively those observed at 3°C in similar size treatments. 
Growth rates were described as a second-order function 
of temperature (Table 2). 
Juveniles 
Sorting of fish by size before the experiment resulted 
in significant differences in initial size among repli- 
cates within temperature treatments (L T P[ 8 83) = 9.46, 
