Where Yij is the otolith size observation of individual i at Time j, β0i is the intercept, β1i is the linear slope and β2i the quadratic curvature, εij is the residual error and T is time of the observation (fish age in years). The mean estimated date (AD) for each archaeological deposit (Table 1) formed a fixed effect on both the linear and quadric term and fish ID and fish age at mortality were set as random effects. We used the deposit closest to modern times as the reference point (AD 1910). Statistical significance (p-values) for parameter estimates was assessed using the normal approximation (i.e., treating the t-value as a z-value). Models were fitted using the lme4 package v. 1.1–12  in R version 3.0.2 .