Age-Groups from Size-Frequency Data: A Versatile and Efficient Method of Analyzing Distribution Mixtures

Abstract

For estimating age-group parameters from size-frequency data, conventional efficient statistical methods, such as maximum likelihood, can be more effective than the commonly used graphical methods of dissecting a mixed distribution. Fisheries size-frequency data are usually grouped over size intervals and the efficient methods are easily programmed on a computer for this case. We show that several published alternatives offer no computational advantages over our method. We describe an interactive computer program that assists the user in determining which parameters may be estimated from a set of data. The program alternates between constrained direct-search optimization and fast iterative calculations. Two examples of fisheries length-frequency data show that fitting is made easier by employing a subsample aged by biological methods for the preliminary starting values of parameters, and that the best fit may involve a trade-off between statistical precision and biological plausibility. The value of mixture analysis to the fishery worker is to reduce field and laboratory time in the aging of large samples. Key words: length-frequency data, size-frequency data, aging of samples, polymodal distributions, distribution mixtures, maximum likelihood estimation, nonlinear optimization, Phoxinus phoxinus, Esox lucius