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ICES Journal of Marine Science: Journal du Conseil 2004 61(2):218-230; doi:10.1016/j.icesjms.2003.12.006
© 2004 by ICES/CIEM International Council for the Exploration of the Sea/Conseil International pour l'Exploration de la Mer
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Fitting growth models to length frequency data

Geoff M. Lasletta,*, J. Paige Evesonb and Tom Polacheckb

a CSIRO Mathematical and Information Sciences Private Bag 10, Clayton South MDC, Clayton, Victoria 3169, Australia
b CSIRO Marine Research GPO Box 1538, Hobart, Tasmania 7001, Australia

*Correspondence to G. M. Laslett: tel: +61 3 9545 8018; fax: +61 3 9545 8080. e-mail: geoff.laslett{at}csiro.au; paige.eveson{at}csiro.au; tom.polacheck{at}csiro.au.

A novel two-stage procedure for fitting growth curves to length frequency data collected from commercial fisheries is described. The method is suitable for species in which cohorts are spawned over a limited time period, and samples of length frequency data are collected regularly (e.g. in weekly, fortnightly, or monthly time intervals) over an extended time period. In the first stage of analysis, Gaussian mixtures are fitted separately to the data for each time interval, and summary statistics (component means and standard errors) are extracted. In the second stage, parametric growth models, such as the von Bertalanffy seasonal growth curve, are fitted to the summary data. The error structure in this second stage of analysis incorporates random between-year effects, random within-year age-group effects, random within-year time-interval effects, random within-year age-group and time-interval interactions, and sampling errors. This complex error structure incorporating unbalanced crossed and nested random effects acknowledges that commercial fishing is not an exercise in random sampling, and allows for the inevitable additional sources of random variation in such an enterprise. The method is applied to South Australian southern bluefin tuna length frequency data collected from 1964 to 1989, and leads to the conclusion that juvenile tuna grew faster in the 1980s than in the 1960s, with the 1970s being a decade of highly variable growth.

Keywords: maximum likelihood, mixture decompositions, variance components

Received 10 May 2003; accepted 17 December 2003.


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