A Method for Estimating Age-Composition from Length-Frequency by Using Stochastic Growth Equation

Abstract

The present paper proposes a method for estimating the age-composition from the length-frequency by postulating a theoretical length frequency at age under a randomly varying environ-ment, and presents numerical examples. The theoretical frequency is derived from the stochastic growth equation. Goodness of fit is measured by the sum of the log-likelihood of a mixture of normal distributions of length and that of the theoretical growth curve as the penalty. The par-ameters are estimated by maximizing the goodness of fit. The applications to fifteen samples of bastard halibut show that the penalty controls the behavior of the mean of length at age and pro-vides smooth growth patterns. The penalty causes some loss of the goodness of fit, which is paid for by a biologically reasonable age-composition. Advantages and defects of this method and dif-ficulties in its application are discussed.