Fishery Bulletin 119(1) 
was fixed to a flat piece of wood with synthetic resin. 
Each vertebral centrum was sectioned in a sagittal 
plane through the focus with an IsoMet Low Speed Saw’ 
(Buehler Ltd., Lake Bluff, IL) that had double blades 
separated by 0.24 mm. Each section was mounted on 
a slide and photographed with transmitted light on an 
Olympus SZ61 stereomicroscope (Olympus Corp., Tokyo, 
Japan) equipped with an OptixCam S7N digital camera 
(Microscope LLC, Roanoke, VA). We created a database 
of section images for the interpretation and counting of 
growth bands. 
Age estimation 
Opaque and translucent bands form annually, and under 
transmitted light, these bands appear dark and light, 
respectively (Beamish, 1979). Age estimates were made by 
counting these band pairs (one dark and one light band) 
along the corpus calcareum after identifying the birthmark, 
the first distinct band after the focus (Cailliet et al., 2006). 
The distance from the focus to the edge of a vertebra and the 
thickness of each band were recorded by using Image-Pro 
Plus image analysis software (vers. 6.0, Media Cybernetics 
Inc., Rockville, MD). Images were projected onto a screen for 
the identification of growth bands. We used several verte- 
brae for defining reading criteria, and 3 independent read- 
ers counted the growth bands along the corpus calcareum 
on each vertebral section. We considered only age estimates 
with which at least 2 readers coincided. Otherwise, readings 
were discarded. We used a Bayesian t-test by using refer- 
ence (uninformative) priors for the mean (y) and standard 
deviation (o) of DW (Suppl. Table 1) (online only) to determine 
the support for the difference in mean DW between sexes, as 
previously described by Doll and Jacquemin (2018). We fit 
a Bayesian linear regression with reference priors (Suppl. 
Table 1) (online only) to assess the proportionality of growth 
between vertebral diameter (VD) and DW. 
The agreement of growth band counts was evaluated 
by using a bias plot (Campana et al., 1995). Reproducibil- 
ity and precision of growth band counts were assessed 
by using the index of average percent error (IAPE), the 
coefficient of variation (CV), and the precision index (D) 
for readings of all 3 readers together and between read- 
ers (Beamish and Fournier, 1981; Chang, 1982; Goldman 
and Musick, 2006): 
1 UN 
IAPE = 100 oom 
ans | -@ 
R x 
; and (2) 
' 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. 
otf) : 
where N = the number of vertebrae; 
R = the number of readers; 
x;,; = the age i determined for individual j; 
x, = the mean age calculated for individual j; 
A = the numbers of agreements; and 
B = the number of readings done. 
Periodicity of band formation 
We performed and compared 2 methods to infer the period 
of band formation: edge percentage analysis and relative 
marginal increment (MI) analysis following Cailliet (2015). 
We categorized the edge type of each section of a vertebra 
as opaque or translucent, and the relative frequency of each 
edge type was tabulated in bimesters (2-month intervals). 
The MI analysis was conducted over bimesters by using 
vertebrae from rays at the ages of 1-3 years (number of 
rays=94) to reduce bias that can be caused by the inclu- 
sion of older individuals with many bands (Lessa et all., 
2006). Bimesters with mean MI values close to 1 were 
interpreted to be the time of year when the growth cycle is 
about to be completed (Cailliet et al., 2006): 
MI = [| 
Mh ~"-1 
(4) 
where MI = the marginal increment; 
VR = the vertebral radius; 
r, = the distance from the focus to the last band 
pair; and 
r,-1 = the distance from the focus to the penultimate 
band pair. 
To evaluate differences in the MI values among bimesters, 
we used a Bayesian one-way analysis of variance (Gerro- 
dette, 2011). First, we estimated the posteriors of the mean 
MI for each bimester (7), using reference priors to nullify 
their influence on posterior distribution of mean MI. Then, 
we estimated the difference between bimesters (d) by sub- 
tracting the entire posterior mean MI of one bimester from 
another (i.e., 14—Ws, Hyg - - - » H5—Hg). We used the odds 
of difference, P(d<0)/P(d>0), as an informative statistic of 
the effect of mean MI (Suppl. Table 1) (online only). 
Growth models 
Two models were fit to the observed age—length data. The 
first was the VBGF (von Bertalanffy, 1938), described as 
follows: 
DW, = DW., - (DW. - DW, )e™, (5) 
where DW, = the estimated disc width (in centimeters) at 
a given age ¢ (in years); 
DW., =the theoretical maximum disc width (in 
centimeters); 
DW, = disc width at birth (in centimeters); and 
k = the growth coefficient (year *). 
