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Fishery Bulletin 115(3) 
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Figure 2 
Scatter plots of pseudo-observations, or approximations of distribution functions (F and G ), 
from simulations (A) where Markov chains of estimated von Bertalanffy growth function 
(VBGF) parameters were used directly and (B) where copulas were applied to the posterior 
distribution of VBGF parameters. 
In Figure 2B, the relationship between both parame- 
ters was recovered by using a Gaussian copula drawing 
from the empirical posterior distribution. Both plots 
corresponded with a graphical representation of the 
intrinsic dependence of the pseudosamples. 
Figures 3A and 3B show the estimated parameters 
from chains and their marginal histograms are dis- 
played in Figures 4A and 4B. The histograms in Fig- 
ure 4C and 4B were built by assigning a roughly heu- 
ristic normal distribution to each marginal, but other 
alternatives are still possible. These plots ensure the 
dependence and shape between K and L„ parameters. 
We can also include the related quantile functions in 
the sample generation if the exact distributions for K 
and are known. In our study, we particularly consid- 
ered the Gaussian copula in Figure 3B because of the 
dependence between pseudosamples generated for both 
marginal posterior distributions of K and which 
looked linear and strongly negative (Fig. 3A; coeffi- 
cient of correlation [r]= -0.912 (standard error 0.006; 
£-value= -157.14; P-value <0.001). 
Additionally, both methods showed a strong correla- 
Figure 3 
Scatter plots of asymptotic length (L x ) and growth rate coefficient ( K) of the von Bertalanffy growth 
function showing results (A) from simulations based on posterior distribution and (B) from the copula 
approach. 
