Lytton et al.: Age validation of Polyprion americanus based on bomb radiocarbon 0 4 C) 
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Figure 3 
(A) Mean proportion of total bomb radiocarbon (% 14 C) of total A 14 C 
by birth year for otolith cores from wreckfish ( Polyprion america- 
nus) collected in the North Atlantic in 1991. We fitted a logistical 
regression model (solid line) to the data. (B) Mean % 14 C values for 
wreckfish from this study and for haddock ( Melanogrammus aeglefi- 
nus) from Campana (1997). Symbols represent observed values, and 
lines represent fits of the logistic model for wreckfish (dotted) and 
haddock (solid), respectively. In both panels, error bars represent 
the standard errors around the means. 
of a strict aging protocol for these readings, a protocol 
that had not been put in place before the bomb radio- 
carbon readings. 
After completion of the consensus readings, age es- 
timates ranged from 1 to 80 years. There was no clear 
pattern of bias between readers in age estimates (Fig. 
2C). The CV decreased with increasing age, and the 
average CV for age estimates was 17.4% (PcO.OOl; 
Fig. 2D). The highest CV value of 75.4% occurred for 
fish aged as 1 year old by reader 1. When we exclude 
the CV for age-1 fish, because the CV is susceptible 
to inflation as the mean approaches 0 and only reader 
1 estimated specimens to be 1 year old, the CV esti- 
mate dropped to 12.2%. The reduced CV 
estimates, after development of aging pro- 
tocols, are in the range of CV reported by 
other researchers for long-lived, deepwater, 
difficult-to-age species (Friess and Sedberry, 
2011; Harris et al., 2004). 
The VBGM fit to the remaining sample 
of 554 wreckfish used for age and growth 
analysis resulted in 
L t = 1026(1 - r 0 - 1211 - 4 ' 961 ). 
This result indicates that wreckfish experi- 
ence rapid growth during the early years of 
life, attaining approximately 95% of asymp- 
totic length, on average, by 20 years of age. 
After age 20, growth in length slows dra- 
matically, and fish older than approximately 
20 years in the population exhibit similar 
size distributions (Fig. 5). 
To allow for comparison of VBGM param- 
eters from previous age and growth stud- 
ies on wreckfish, all FL measurements were 
converted to TL measurements and the 
VBGM was rerun, resulting in 
L t = 1071(1 - e-° 12(t - 4 - 96 )). (8) 
In comparison with the 2 previous studies 
of wreckfish (Fig. 6, Table 2), our data in- 
dicate a more rapid growth rate at younger 
ages and a smaller asymptotic length. 
Natural mortality 
For calculation of our M estimates, we used 
the maximum age (t ma =80 years) observed 
in the fish aged for growth curve analy- 
sis and the estimates of von Bertalanffy 
growth curve parameters k (0.124) and 
(1026 mm FL). Age-constant estimates of M 
based on the methods reported in Then et 
al. (2015) yielded M=0.088 with equation 4 
and M=0.091 with equation 5. These 2 es- 
timates are remarkably similar given that 
they are based on 2 fundamentally different 
estimators. The M estimates from both age- 
varying estimators indicate a type-3 sur- 
vival curve, which is common among finfish 
species, for North Atlantic wreckfish (Fig. 7). The Char- 
nov et al. (2013) method yielded M at age 0=0.398, and 
with an expected rapid decrease in M values to age 15 
years and a leveling off at around M=0.120. The Gisla- 
son et al. (2010) method (eq. 6) yielded a lower value 
of M at age 0 (M=0.231), than that with the Charnov 
et al. (2013) method (eq. 7), but with a similar rapid 
decline up to age 15 years and reaching an asymptotic 
M value of around 0.060. 
For evaluation of age-varying estimators against the 
age-constant M estimators, we compared the propor- 
tion of recruits surviving from age at full recruitment 
to the fishery to maximum age as estimated from each 
