Estimating growth parameters and growth variability from length frequency data using hierarchical mixture models

Analysis of length frequency distributions from surveys is one well-known method for obtaining growth parameter estimates where direct age estimates are not available. We present a likelihood-based procedure that uses mixture models and the expectation-maximization algorithm to estimate growth parameters from length frequency data (LFEM). A basic LFEM model estimates a single set of growth parameters that produce one set of component means and standard deviations that best fits length frequency distributions over all years and surveys. The hierarchical extension incorporates bivariate random effects into the model. A hierarchical framework enables inter-annual or inter-cohort variation in some of the growth parameters to be modelled, thereby accommodating some of the natural variation that occurs in fish growth. Testing on two fish species, haddock (Melanogrammus aeglefinus) and white-bellied anglerfish (Lophius piscatorius), we were able to obtain reasonable estimates of growth parameters, as well as successfully model growth variability. Estimated growth parameters showed some sensitivity to the starting values and occasionally failed to converge on biologically realistic values. This was dealt with through model selection and was partly addressed by the addition of the hierarchical extension.