Munyandorero: Climate effects on Micropogomas undulatus 
57 
against MWET recorded from December of year t to 
March of year f+1, given that 1) juvenile, first-overwin- 
tering Atlantic Croaker born in year t recruit during 
the spring-summer months of year t + 1 (ASMFC 1 ) and 
2 ) the winter water temperatures prevailing during 
late year f-early year f +1 determine the t year-class 
strength and influence recruitment and average bio- 
mass in year t+1 (Hare and Able, 2007; Hare et al., 
2010 ). 
Second, variability of productivity for the Atlantic 
Croaker stock in response to climate anomaly was 
examined by regressing the credible medians of sur- 
plus production, G t (G t = B t+ i - B t + ?Rft), and instan- 
taneous surplus production, p t (p t = log[(Gt + B t )/B t ]), 
against MWET, because G t and, especially, p t are sen- 
sitive to environmental change (Jacobson et al., 2001; 
Mueter and Megrey, 2006). Finally, a linear effect of 
MWET was considered statistically supported if zero 
was outside the 95% BCI of the coefficient controlling 
MWET impacts, consistent with runs of models M2N, 
M2rUN, and M2BN. 
Visual inspections of the scatter points indicated 
that simple linear regressions were appropriate to fit 
the relationships between the process error, surplus 
production, or instantaneous surplus production and 
MWET. The fitting and adequacy of these regressions, 
the types of association between the regressed vari- 
ables, and the linear effect of MWET were determined 
by the techniques outlined above (see also Grosbois et 
al., 2008; Wilson et al., 2011). 
Stock status 
The ratios H t /H ^ isy (#t - 5-Hft) and Bt/BMSY were com- 
pared with the 1:1 ratio — herein considered a criterion 
of status determination — to judge whether overfishing 
was occurring (H t /H ] qgY >D or whether the stock was 
overfished (B t /By [ gY <D- The probability that H t /Hy[ sy 
>1, P(H t /H msy >D, and the probability that B t /B msy 
< 1 , P(B t /By[QY < 1 ), were used to estimate the risks of 
overfishing and of overfished status, respectively (Jiao 
et al., 2009). POi^/Hyi gy >1) and P(B^/Byisy <1) cor- 
responded with the proportions of iterations where the 
most credible means of H t /HyiQY >1 and the most cred- 
ible means of Bt/^MSY <1- The previous risk of over- 
fishing relate to Ml, MlrU, and M1B. The risk of over- 
fishing for M2 and its variants was P(H t /HYlSY, >D- 
These control rules do not conform to the legal sense 
used by the NMFS, but they are consistent with the 
rules considered in the ASMFC 1 BDMs. 
Results 
Goodness of fit and comparisons of models 
The standardized median residuals for stock biomass 
and biomass indices were comparable and trended sim- 
ilarly across models (Fig. 2). Their credible estimates 
ranged from - 1.8 to 1 . 2 , except for the disproportion- 
ate (-5.2 to -4.2) 1972 residuals for the NEFSC index, 
which indicated excessive overestimation of the corre- 
sponding observed values (Fig. 2, C and D). The latter 
residuals were clearly outliers and were omitted in the 
residual diagnostics. 
The plots of discrepancy checks (not shown) and the 
Bayesian P-values (0.52-0.55) indicated that the fit- 
ted linear regressions were adequate for the trends in 
various standardized residuals. The negative posterior 
means and medians of all trend slopes evidenced con- 
sistent, negative trends in the residuals. Regardless, at 
a 0.95 probability, those trends stabilized at zero (i.e., 
the 95% BCIs of their slopes included zero). Moreover, 
the probabilities of decline were closer to 0.5 than to 
one (P*=0.58-0.74 for biomass, P*=0.52-0.68 for NEF- 
SC index, and P*= 0.62-0.64 for SEAMAP index; the 
largest Revalues were associated with residuals from 
MlrU and M2rU), and, indeed, the posterior distribu- 
tions of those slopes were bell-shaped and centered 
near zero. This result agreed with fair fits of biomass 
indices that were nearly identical across models (Fig. 
3) and indicated that the lognormal distribution was a 
reasonable assumption for the latent biomass and ob- 
served indices. 
The means of most parameters were slightly differ- 
ent from the medians owing to right-(or left-) skewed 
posterior marginal distributions (to conserve space, 
the related details were not provided but are avail- 
able upon request). Such distributions were therefore 
slightly better summarized by the percentiles. For 
competing models with or without MWET, the poste- 
rior means and percentiles of the parameters were of 
the same magnitude. In comparison with base Ml and 
M2, Ml and M2 sensitivity runs showed the follow- 
ing aspects about the stock productivity, management 
benchmarks, and initial depletion. Use of the prior r 
or ro~U(0.01,1.5) led to 1) nearly doubling the rate of 
population increase (note: median r=median ^q~ 0.47 
for base Ml and M2, respectively), H^i sy> and MSY; 2) 
predicting similar posterior medians for (= 220,000 
t) and BmsY’ and 3) estimating lower (75-78%) poste- 
rior medians of the 1972 depletion, 61972 (note: 61972 = 
0.07 for base Ml and M2). 
Inclusion of the SESTF bycatch yielded comparable 
posterior medians for r, 7 - 9 , or^Hyfgy but increased the 
credible estimates of B M and MSY by about 1.27 times 
and doubled the 1972 depletion (61972). As a result, for 
M2 variants in particular, year-specific posterior medi- 
ans of the parameters r and Hmsy estimated by using 
M2rU were nearly twice the medians produced by M2 
and M2B (Fig. 4); year-specific MSY from M2B were 
on average 1.3 times higher than those estimates from 
M 2 but averaged 81% of those estimates from M2rU. 
It was also observed that, in all models with MWET, 
the r (and related metric) time series mimicked the 
MWET trend well, but those time series where the 
prior G(0. 01, 0.001) was used for the MWET coefficient 
a varied less than those time series estimated with the 
