Assessing MWET effects on the Atlantic Croaker population off the U.S.
Second, variability of productivity for the Atlantic Croaker stock in response to climate anomaly was examined by regressing the credible medians of surplus production, [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII], and instantaneous surplus production, [[rho].sub.t] ([[rho].sub.t] = log[([G.sub.t] + [B.sub.t])/[B.sub.t]]), against MWET, because [G.sub.t] and, especially, [[rho].sub.t] are sensitive to environmental change (Jacobson et al., 2001; Mueter and Megrey, 2006).
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 variables, and the linear effect of MWET were determined by the techniques outlined above (see also Grosbois et al., 2008; Wilson et al., 2011).
For competing models with or without MWET, the posterior means and percentiles of the parameters were of the same magnitude.
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 [alpha] varied less than those time series estimated with the prior [alpha]~N(0,0.02) (Fig.
The components of the DIC statistics (Table 2) for models without MWET were the NEFSC index, SEAMAP index, depletion time series, and process error variance.
The former result for competing models, with or without MWET, was mainly due to the extra parameter [alpha] that clearly had no explanatory power.
On the basis of [DELTA]DIC, they were comparable with those DIC statistics for their counterparts without MWET and, therefore, should be considered for making inferences (Table 2).
Therefore, comparisons of models indicated that the complexity of (base and sensitivity) M2 brought about by the introduction of MWET was not warranted by the data.
The plots of discrepancy checks (not shown) and the Bayesian P-values (0.53-0.55) indicated that the fitted linear models were adequate for the relationships between 1) the process errors and MWET, 2) surplus production and MWET, and 3) instantaneous surplus production and MWET (Fig.
The process errors from M1 and MIB increased with MWET at a 0.95 probability given that zero was outside the 95% BCIs of the mean slopes (0.133 and 0.124) of the corresponding relationships: those 95% BCIs were (0.017, 0.247) and (0.035, 0.212), respectively.
Estimates from M2N, M2rUN, and M2BN of the posterior credible medians of the coefficient for MWET ([alpha]) were 0.42, 0.29, and 0.50, respectively, suggesting positive effects of MWET on the Atlantic Croaker production dynamics.