Brown-Peterson et al.: Meta-analysis of reproductive parameters of Lutjanus campechanus in the Gulf of Mexico 
41 
All models were written with Stan software, vers. 
2.17 1 (Carpenter et al., 2017). Pre- and postprocess¬ 
ing data were analyzed in R, vers. 3.4.1 (R Core Team, 
2017). Results were checked for nonconvergence as 
recommended in the Stan user manual (Stan Devel¬ 
opment Team, 2017), and model fit was checked with 
posterior predictive checks. To assess the robustness of 
the models to prior assumptions, we re-ran each model 
multiple times with different hyperparameters. Prior 
sensitivity was assessed by comparing the posterior 
predictive summary statistics. Full details of all analy¬ 
ses and validations are provided in the online Supple¬ 
mentary methods (online only) section. 
Results 
Model performance 
All models converged onto stationary posterior distri¬ 
butions (Suppl. Figs. 1-4) (online only). Posterior predic¬ 
tive checks showed the spawning seasonality model 
(Suppl. Figs. 5 and 6) (online only), the spawning interval 
models for OM (Suppl. Figs. 7-10) (online only) and POF 
(Suppl. Figs. 11-14) (online only) and the batch fecundity 
models (Suppl. Figs. 15 and 16) (online only) performed 
well, with summary statistics matching the real data. 
Although the batch fecundity models had difficulty pre¬ 
dicting individual fecundity values because of the large 
amount of variation among individuals (Suppl. Figs. 17 
and 18) (online only), they predicted group-level fecun¬ 
dity well (Suppl. Figs. 19 and 20) (online only). Forest 
plots showed there was not a consistent temporal trend 
in study-level effects for spawning seasonality (Suppl. 
Fig. 21) (online only), and no temporal or regional trend 
for spawning interval (Suppl. Figs. 22 and 23) (online 
only) or fecundity (Suppl. Fig. 24) (online only). Finally, 
the sensitivity analyses showed qualitative agreement 
and therefore robustness to prior assumptions across 
the different sensitivity trials for all models (Suppl. 
Figs. 25-31) (online only). Details about model validity 
checks are provided in the Validation Results section 
of the Supplementary methods (online only). 
Spawning seasonality 
Spawning seasonality was modeled by using data com¬ 
bined from the northeastern and northwestern GOM. 
Owing to the complexity of the GSI model, we did not 
have enough data to estimate monthly GSI parame¬ 
ters for each region separately. No data were available 
from 2003 through 2008 and therefore models are not 
presented for these years. In general, the estimated 
monthly GSI values were a close match to the observed 
mean monthly GSI values, with the exception of May 
1994 and 1995, April, May, and September 1999 and 
April and June 2001, when some studies had much 
1 Mention of trade names or commercial companies is for iden¬ 
tification purposes only and does not imply endorsement by 
the National Marine Fisheries Service, NOAA. 
higher mean GSI values than the estimates (Fig. 2A). 
Lower mean GSI values than the estimates were seen 
in July 1999, May 2000, June and July 2001, April 
2013, May 2014 and June 2016 (Fig. 2A). 
Our analysis showed that peak spawning occurs dur¬ 
ing June, July and August for the entire 27-year time 
period of analysis (Fig. 2A). A high spawning probabil¬ 
ity is also estimated in May for 1994-2017. During the 
months of high spawning probability, the 95% credible 
intervals rarely extended below the threshold GSI val¬ 
ue of 1.0. Additionally, the reproductive season extend¬ 
ed from April to September for 1995 through 2017, and 
a 25-50% probability of spawning was estimated for 
these months (Fig. 2A). The estimated probability of 
spawning was <10% between November and February 
and the 95% credible intervals were larger, likely be¬ 
cause of limited data during these months. There was a 
low probability of spawning (<25%) during March and 
October in some years, although limited data collection 
lends uncertainty to these estimates, particularly for 
collections in March. 
The estimated spawning season based on GSI val¬ 
ues >1 remained relatively constant from 1994 through 
2017; the average duration was 4.54 months (Fig. 2B). 
The spawning season was shorter from 1991 through 
1993 (average 2.59 months), and longest in 2001 (6.03 
months). However, variability within the data and the 
lack of data during most of the colder months (i.e., No- 
vember-March) could result in less precise estimates of 
spawning season duration. 
Spawning interval 
Mean spawning interval varied among studies and by 
method. No data were available from 2003 through 
2008 and therefore models are not presented for these 
years. In the northeastern GOM, spawning interval 
varied from 1.5 days (August 2011) to 4.5 days (April 
2011) (overall mean (±SE): 3.18 ±0.26 with the OM 
method, whereas spawning interval estimated with 
the POF method varied from 1.0 days (July 2011) 
to 35 days (2009) (overall mean: 6.57 ±2.45). In the 
northwestern GOM, spawning interval varied from 1.7 
days (September 2011) to 16 days (April 2011) (over¬ 
all mean: 5.32 ±1.01) for the OM method, whereas the 
spawning interval estimated with the POF method var¬ 
ied from 1.4 days (July 2011) to 8.1 days (2009) (overall 
mean: 4.66 ±0.81). Data from some studies suggest red 
snapper are capable of spawning daily (i.e., spawning 
interval=l). Histological evidence of actively spawning 
red snapper with POF < 24 h (Fig. 3) confirms that at 
least some individuals are capable of daily spawning, 
although this was not reported for fish collected before 
2000 . 
Minimal increases in spawning interval were esti¬ 
mated between 1991 and 2017 for the northern GOM 
with both methods when data from the eastern and 
western regions were combined (Fig. 4, A and D; 2.4-2.9 
d with the OM method, 1.9-2.3 d with the POF meth¬ 
od), although there was greater uncertainty with the 
