Lytton et al.: Age validation of Polyprion amerlcanus based on bomb radiocarbon ( l4 C) 
79 
To prevent cross-contamination between samples we 
used a new carbide cutting wheel for each otolith and 
removed the core under a ventilation system. We re- 
moved additional surface contaminants by rinsing the 
extracted otolith cores for two 30-s intervals in deion- 
ized water, followed by an acid bath in 10% HNO3 for 
30 s, and a final rinse with deionized water. 
After the otoliths had dried overnight, we measured 
each otolith core to the nearest 0.01 mg to ensure that 
enough material (>8 mg) had been obtained for bomb 
radiocarbon analysis. We did not obtain enough materi- 
al from a single section for several specimens; for such 
specimens, we removed and processed a second section 
from the same otolith using the same technique, add- 
ing the additional material to the original sample. 
We shipped the resultant core samples in plastic 
5-mL vials to the National Ocean Sciences Accelerator 
Mass Spectrometry Facility (NOSAMS) at the Woods 
Hole Oceanographic Institution. Preparation of the 
samples for bomb radiocarbon analysis followed the 
protocol outlined by NOSAMS for inorganic carbonate 
materials. First, samples underwent acid hydrolysis, 
with an H3PO4 solution, to form CO2. The evolving 
CO2 was then removed by using an automated system 
that included acidification and sparging with nitrogen, 
and the CO2 was reduced with a catalyst (Fe or Co) 
in the presence of excess hydrogen to form graphite. 
The graphite was then loaded into the accelerator 
mass spectrometer for reading 14 C levels. Staff of the 
NOSAMS subsequently compared the observed 14 C con- 
centrations for each specimen to 14 C levels found in 
19 th century wood formed before nuclear testing, us- 
ing 13 C concentrations to correct for any natural or 
machine-generated fractionation effects. The resultant 
statistic (A 14 C, in parts per million) provides a measure 
of the increase in 14 C due to uptake of 14 C from nuclear 
bomb testing in the 1950s through early 1970s com- 
pared with 14 C levels found in early 19 th century wood. 
To facilitate comparisons with other studies, we 
transformed the raw A 14 C chronologies to proportion of 
total bomb radiocarbon (%C 44 ), 
/~il4 
%c } 4 - 
+ c‘ 
14 
C u 4-C L 
''■'min 1 max 
>14 
(i) 
where C u = the inverse of the lowest radiocarbon lev- 
nun 
c 
14 
el found; 
'max = the highest radiocarbon value found; 
C ; 14 = the 14 C level of the i th sample; and 
%C ; 14 = the percentage of total bomb radiocarbon 
of the i th sample. 
We then fitted %C 14 values to a logistic curve, 
%C 14 = 
l + e ^- BlrtllY,iar /d ’ 
( 2 ) 
where a (asymptote), (3 (inflection point), and X (scaling 
parameter determining curve shape) are the 3 para- 
meters of the logistic curve to be estimated by non- 
linear regression. 
We analyzed the accuracy of our initial increment 
counts as a proxy for age by comparing the wreckfish 
%C\ 4 chronology to a reference %C\ 4 chronology of val- 
idated ages for haddock ( Melanogrammus aeglefinus) 
collected from Newfoundland (Campana, 1997). We 
used a variance ratio test to determine if there was 
any significant difference between the 2 chronologies. 
We conducted all analyses using R, vers. 3.0.2 (R Core 
Team, 2012). 
Age and growth analysis 
Because of our desire to use more recently caught 
fish, which presumably would better represent recent 
growth patterns in the population, we excluded all 
specimens used in previous bomb radiocarbon analy- 
sis, instead randomly selecting 500 specimens col- 
lected from 2000 through 2011. Almost all randomly 
selected fish measured between 800 and 1000 mm FL 
because of the high availability of these size classes in 
the sample archive — an availability that is likely due 
to commercial fishing practices. To improve growth 
curve fit, we included all available specimens from 
2000 through 2011 that were smaller than 700 mm 
FL (n=44) or larger than 1100 mm FL (n= 24) and that 
were not already randomly selected in the age and 
growth analysis. Our intent with this selection strat- 
egy was to reduce the sensitivity of the growth curve 
to small sample sizes of younger and older age class- 
es. Furthermore, inclusion of the oldest fish, under the 
assumption that larger fish are generally older, im- 
proves our probability of identifying the oldest fish in 
the fishery-dependent sample database. Because many 
mathematical estimators of natural mortality ( M ) 
make use of maximum age, proper identification of the 
oldest fish in the sample is vital. 
For specimens used in the age and growth analysis, 
we processed otoliths to the same approximate thick- 
ness (0.25-0.35 mm) and mounted them as we did for 
the bomb radiocarbon study. We used only the left oto- 
lith for age estimates, and the 2 readers, once again, 
performed the readings blindly and independently. If 
readers disagreed on an age, the otolith was aged con- 
currently to reach a consensus on age. If disagreement 
persisted, the otolith was excluded from this study. 
We fitted the length-at-age data to the VBGM, 
L t = L oo (l-e“ ka “ <0) ), (3) 
where L t (in millimeters) = length at age t (in years); 
L 0 o (in millimeters) = the asymptotic length; 
k (1/year) = the Brody growth coeffi- 
cient; and 
tp = the theoretical age (in 
years) at which length is 
0 (von Bertalanffy, 1938). 
We fitted the VBGM and obtained estimates of growth 
model parameters, using a nonlinear regression in R, 
vers. 3.0.2. 
