Where Yij is the otolith size observation of individual i at Time j and T is time of the observation (fish age in years). L∞ is the maximum length (in the current analysis of otolith increment), K is the relative growth rate, t0 is the theoretical age for time at which length is zero. The vBGF is widely used in fisheries biology [49, 50] and our aim was to facilitate comparison of historical Atlantic cod growth rate to previous studies as well as to test for parameter differences between periods. Two models were fitted, 1) a model assuming the same parameters values for all 220 otoliths and 2) a model allowing all parameters to differ between the three periods. vBGF models 1 and 2 were then compared using a likelihood ratio test. Models were implemented in R version 3.0.2  using the package FSA . The current growth data is based on otolith increments and within individual measures are expected to be non-independent. Therefore, we attempted to fit a non-linear mixed model with a user defined vBGF using nlme in the lme4 package v. 1.1–12 . However, vBGF models including random effects did not converge (data not shown). Code for statistical analysis can be found in S2 File.