A New Approach to Length–Frequency Analysis: Growth Structure

Abstract

This paper presents a new approach to length–frequency analysis which takes account of biological structure in the mean lengths and standard deviations in length for various age-classes of fish. The new methods help determine biologically meaningful solutions, even when earlier methods lead to an ambiguous set of competing solutions. The structure of the standard deviations turns out to be especially important. For describing the means, new parameters are defined for von Bertalanffy growth which prove to have greater biological meaning and numerical stability than L_∞, K, and t₀. These new parameters can often be estimated easily from the raw data in cases where the species experiences a slowing of growth with age. This paper also presents χ² methods which can be used to rank competing solutions, although the results are not definitive. All methods are illustrated using data previously published for pike and abalone. An appendix describes in detail the computer programs required for the analysis.Key words: length–frequency analysis, aging of samples, von Bertalanffy growth, growth, maximum likelihood estimation, nonlinear estimation