Age composition and growth without age data: a likelihood-based model

We proposed models capable of jointly estimating age composition and somatic growth parameters (L∞ and K) from length-frequency data without the need to obtain age data. The proposed approach consists of a linear regression in which both the regression coefficients (age composition) and the predictor variables (size distribution at each age) are unknown. The predictor variables correspond to theoretical simulated values ​​from a growth curve, whose parameters are jointly estimated with the regression coefficients using a robust global optimization algorithm, differential evolution, which uses stochastic procedures with parallel methods of direct search. The proposed models were assessed using a simulation study with two sets of virtual fish populations, representing two different growth curves. The parameter estimates of the age composition were equally precise and accurate among models in which the growth parameters were estimated or known a priori. Furthermore, the estimates obtained by the models that also estimated the growth parameters were unbiased and accurate. The estimates of growth parameters are an alternative for cases in which the relationship between length and age is unknown, outdated or limited. The models presented in this study can be applied to various groups of organisms other than fish.