where the first component of variance is due to individualvariability in L∞and the second component is additional mea-surement/process error in the otolith data. The likelihood for theotolith data is just the product of Gaussian densities over all fish.Unlike with the tag-recapture likelihood, the parameters that canbe estimated from optimizing the otolith likelihood include a0.While overly simplistic, we input the age estimates to themodel as if they were known accurately. Statistically rigorousapproaches for dealing with uncertainty in explanatory variables(often referred to as errors-in-variables models) exist, but giventhe limited amount of otolith data available, the extra complexityand computational time required to implement these approachesdid not seem worthwhile.As for the tag-recapture data, we calculated standardized resid-uals for the otolith data as observed minus fitted length divided bythe standard deviation in length at age.