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Fishery Bulletin 117(3) 
identification to estimate the accuracy of survey personnel 
in field conditions. Specimens that could not be conclusively 
genetically identified were removed from further analysis. 
Measurements and statistical analysis 
Otoliths were prepared for measurements by blotting them 
dry and placing them under a dissecting microscope. The 
otoliths were viewed distal side facing up on a black back¬ 
ground at a magnification of 6.3x. Image-Pro Plus 1 software 
(vers. 7; Media Cybernetics, Inc., Rockville, MD) was used to 
capture otolith images, calculate each otolith’s area, perime¬ 
ter, Feret length, and Feret width, and determine the length 
and width of each otolith from lines intersecting at the cen¬ 
ter of the otolith core (major and minor axes) (Tuset et al., 
2003). Otolith weight was taken to the nearest thousandth 
of a gram by using a Sartorius milligram balance (Sartorius 
AG, Gottingen, Germany). Measurements were imported 
to Microsoft Excel 2010 (Microsoft Corp., Redmond, WA). 
The first 72 blackspotted rockfish and 90 rougheye rockfish 
were tested for asymmetry between their left and right oto¬ 
liths. This test found no significant differences (multivariate 
analysis of variance: P=0.122), and during the remainder 
of the study no distinction was made between left or right 
otoliths. Otolith age was read by scientists from the AFSC 
Age and Growth Program in accordance with established 
protocols (Matta and Kimura, 2012). 
Initial analysis of the data indicated potential differ¬ 
ences between the species in terms of otolith size versus 
age. The significance of these trends in otolith shape or 
otolith weight were compared in each species through 
regression analysis of the form shown in this equation: 
Variable = Intercept + f3j Species + (3 2 log 10 Age 
+ P 3 Species x log 10 Ag-e + e, 1 
where (3 = the estimated coefficient for each model term; 
Species = the genetic identification for each specimen as 
a categorical variable; 
\og 10 Age = the log-transformed age of the specimen; and 
e = an error term with a normal distribution. 
Seven variables were modeled: area, perimeter, otolith 
length, otolith width, major axis length, minor axis length, 
and otolith weight. A log transformation was applied to 
otolith ages to render these comparisons as a linear rela¬ 
tionship. A £-test with a Bonferroni correction was applied 
to judge the significance of all regression parameters. 
Additionally, the von Bertalanffy growth function (von 
Bertalanffy, 1938) was used to model the relationship of 
age to fork length: 
Fork length = L„ (l - e“ K(Age_to) ), (2) 
where = mean asymptotic length; 
K = the growth coefficient; and 
t 0 - the time or age when mean length was zero. 
1 Mention of trade names or commercial companies is for identi¬ 
fication purposes only and does not imply endorsement by the 
National Marine Fisheries Service, NOAA. 
Linear models were fit by using the lm function in sta¬ 
tistical software R (vers. 3.3.3; R Core Team, 2017), and 
parameters of the the von Bertalanffy growth function 
were estimated by using the nls function in R. 
Logistic regression is a standard statistical tool that can 
be used to assign classification probabilities on the basis 
of a variety of parameters (McCullagh and Nelder, 1989). 
For otolith morphometries, the function calculates a prob¬ 
ability (P) between 0 and 1 that corresponds to the likeli¬ 
hood that a given otolith is from a rougheye rockfish and 
probability (1-P) that the otolith is from a blackspotted 
rockfish. The advantage of this method over other classifi¬ 
cation procedures (e.g., discriminant analysis) is that it is 
robust to deviations from normality and heteroscedastic- 
ity that are assumed for most other statistical models and 
is equally effective given a large sample size (McCullagh 
and Nelder, 1989). Growth-related differences in otolith 
measurements were accounted for by including age as an 
interaction for each variable in the model. The model con¬ 
tains 9 predictor variables: otolith area, otolith perimeter, 
otolith major axis length, otolith minor axis length, oto¬ 
lith length, otolith width, otolith weight, fish fork length, 
and fish log 10 -transformed age. The model also contains 8 
interactions with log 10 -transformed age. Here is its abbre¬ 
viated form: 
logit(T’) = In 
1-P 
= Intercept + (3j [-Xj,] + £, 
(3) 
i 7 
where P, = probability for specimen i\ 
X i} = the matrix of j predictor variables, including 
interactions, for specimen i\ 
Pj = the regression coefficient for each j predictor 
variable; and 
Ej = an error term with a binomial distribution for 
specimen i. 
Nonsignificant parameters were removed by using a 
stepwise backward elimination algorithm with Aikake 
information criterion (AIC). In addition to probabilities, 
the standard error of a prediction can be calculated on 
the basis of the linear combination of the standard errors 
in the parameter estimates. In this study, this standard 
error was used to calculate the 95% prediction interval 
around each specimen, and only specimens whose predic¬ 
tion interval did not cross the 0.5 threshold were classi¬ 
fied as rougheye or blackspotted. Other specimens were 
assigned to an uncertain category, reflecting the fact 
that their prediction interval was not confined to a sin¬ 
gle species. This step removed specimens that may have 
been too close to call and improved the specificity of the 
model’s predictions. This model was fit by using the glm 
function in R. 
The practical validity of a classification model is best 
determined by examining its accuracy when given new 
data. With this in mind, we divided the data collected 
during surveys in the 2 years into a training data set and 
a second validation or testing data set (Table 1). Of the 945 
specimens in the sample from 2009, 738 fish were included 
in the actual study. Specimens were excluded because they 
