Munyandorero: Climate effects on Micropogonias undulatus 
55 
Table 1 
Specifications of the probability density functions (PDFs) of priors for parameters implemented in Bayesian state-space bio- 
mass dynamic models: without minimum winter estuarine temperature, MWETtmodel 1, Ml), and with MWET (model 2, M2) 
for Atlantic Croaker off the U.S. Atlantic coast, 1972-2008. The lognormal, gamma, and uniform prior PDFs are symbolized 
by LN, G, and U, respectively. Priors are vague except for the parameter r (Ml) or the parameter /-q (M2). Tuning indices 
were the National Marine Fisheries Service-Northeast Fisheries Science Center (NEFSC) fall index and the Southeast Area 
Monitoring and Assessment Program (SEAMAP) fall index. 
Parameter 
Definition 
PDFs of priors for Ml or M2 
r 
Intrinsic growth rate 
LM -0.756,0. 0086P 
ro 
Scale factor of the intrinsic growth rate 
LM -0.756,0. 0086F 2 
a 
Coefficient of the linear effect of MWET 
G(0. 01,0.001) 2 
6oo 
Inverse of carrying capacity (B„) 
1/(0.0000005,0.000005) 
1/(0.0000004, 0.000004) 3 
°r 
Process error variance 
G(0.01, 0.001) 
°NEFSC72-93 
Observation error variance for NEFSC index, 1972-1993 
G(0.01,l) 
°NEFSC94-08 
Observation error variance for NEFSC index, 1994-2008 
G(0.01,l) 
°SEAMAP 
Observation error variance for SEAMAP index, 1990-2008 
G(0.01,l) 
a NEFSC72-93 
Inverse of the stock availability coefficient inferred 
from NEFSC index CAnefsc 72 - 93 )> 1972—93 
G(0.01,10) 
a NEFSC94-08 
Inverse of the stock availability coefficient inferred 
from NEFSC index (Anefsc 94 -os). 1994-2008 
1/(0.01,10) 
a SEAMAP 
Inverse of the stock availability coefficient inferred 
from SEAMAP index (Aseamap). 1990-2008 
G(0.01,10) 
<f>NEFSC 
Inverse of the NEFSC survey’s global efficiency W j nefsc), 1972-2008 
G(0.01,1000) 
<f>SEAMAP 
Inverse of the SEAMAP survey’s global efficiency (<Aseamap), 1990-2008 
G(0.01,1000) 
&1972 
The 1972 expected depletion 
G(0.1,10) 
1 The 25 th and 75 th percentiles of this prior in arithmetic scale were 0.413 and 0.512, respectively. 
2 Prior for a parameter specific to M2. 
3 When the southeastern (North Carolina-east Florida) shrimp trawl fishery bycatch were included. 
Model configurations 
Models Ml and M2 consisted of the base-case scenarios 
when using the prior PDF developed for the parame- 
ters r or ro and excluding the SESTF bycatch. Sensitiv- 
ity to Ml and M2 outcomes was performed by using an 
alternative prior for r or ;-q, 17(0.01,1.5), and including 
the SESTF bycatch (also treated as “known”) among 
fishery removals. The prior r or 7 - o~t/(0.01,1.5) has 
been tested on Whitemouth Croaker ( Micropogonias 
furnieri) exploited in southern Brazil (Vasconcellos and 
Haimovici, 2006) and spans the range of possible r val- 
ues for marine fish populations (Jensen et ah, 2012). 
Models Ml and M2 configured with r or ro~t/(0.01,1.5) 
were denoted as MlrU and M2rU, respectively; those 
models involving the SESTF bycatch were termed M1B 
and M2B. 
A reviewer recommended that a diffuse normal pri- 
or centered on 0 for the MWET coefficient (a) would 
be appropriate. Consequently, an alternative prior 
a~N(0,0.02) was used to examine its effects on infer- 
ences and especially on the statistics of model com- 
parison. These models were denoted M2N, M2rUN, 
and M2BN. For these models, estimates of a were con- 
strained to be greater than -5 and the precision of 0.02 
was so chosen to reflect moderate ignorance as advised 
by Kery (2010) and Kery and Schaub (2012). 
Model goodness of fit and comparisons of models 
The standardized median residuals by year for biomass 
or depletion ( std?\ ) and for biomass indices (stdo \ Jt ) 
were calculated as 
stdr t = [log(B t ) - log(fi t )] / sd <=> 
stdr t = [log(fc» t ) -log (& t )] /sd » 
where sd - the standard deviation of residuals in log- 
space for biomass or depletion; and 
stdo\ tj = m-.tjT-jj with = log(j tj ) - log(z' tj ). 
Their time trajectories were monitored to check wheth- 
er the stock biomass or depletion and the biomass indi- 
ces conformed to the assumed lognormal distributions. 
Upon visual inspections of their scatter points, normal 
linear regressions were used to fit their trends. 
