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Sexually dimorphic growth models are typically estimated by fitting growth curves to individuals of known sex. Yet, macroscopically ascribing sex can be difficult, particularly for immature animals. As a result, sex-specific growth curves are often fit to known-sex individuals only, omitting unclassified immature individuals occupying an important region of the age–length space. We propose an alternative whereby the sex of the unclassified individuals is treated as a missing data problem to be estimated simultaneously with the sex-specific growth models. The mixture model that we develop includes the biological processes of growth and sexual dimorphism. Simulations show that where the assumed growth model holds, the method improves precision and bias of all parameters relative to the data omission case. Ability to chose the correct combination of sex-specific and sex-generic parameters is also improved. Application of the method to two shark species, where sex can be ascribed from birth, indicates improvements in the fit but also highlights the importance of the assumed model forms. The proposed method avoids discarding unclassified observations, thus improving our understanding of dimorphic growth.

A relatively simple approach is presented for statistical analysis and comparison of fish growth patterns inferred from size-at-age data. It can be used for any growth model and small sample sizes. Bootstrapping is used to generate confidence regions for the model parameters and for size and growth rate at age. Significance of differences between growth patterns is tested with a likelihood ratio test, the validity of which was confirmed by Monte Carlo simulations. As an illustration of the applicability of this approach, we analyzed a set of length-at-age data on female (N = 57) and male (N = 27) Eurasian perch Perca fluviatilis from a shallow, eutrophic Dutch lake, Tjeukemeer. We used the von Bertalanffy growth curve to model length at age for both sexes separately. This analysis showed a significant difference in length between males and females between age 2 and age 6, with females being larger. At older ages the confidence regions became too wide to detect sexual dimorphism. The applicability of our approach was furthermore shown by comparing the results for Tjeukemeer with existing data for two other lakes. Eurasian perch in IJsselmeer (The Netherlands) showed comparable maximum lengths and dimorphism among sexes, but significant lower initial growth rates. Eurasian perch in Lake Windermere (UK) showed significantly lower maximum lengths; initial growth rates showed a wide range, with maximum values equal to those of Tjeukemeer. Because we used nonparametric tests (randomization techniques), which only assume independence of the model deviations, our conclusions are statistically well founded, despite the small size of the samples on which they are based.

A relatively simple approach is presented for statistical analysis and comparison of fish growth patterns inferred from size-at-age data. It can be used for any growth model and small sample sizes. Bootstrapping is used to generate confidence regions for the model parameters and for size and growth rate at age. Significance of differences between growth patterns is tested with a likelihood ratio test, the validity of which was confirmed by Monte Carlo simulations. As an illustration of the applicability of this approach, we analyzed a set of length-at- age data on female (N = 57) and male (N = 27) Eurasian perch Perca fluviatilis from a shallow, eutrophic Dutch lake, Tjeukemeer. We used the von Bertalanffy growth curve to model length at age for both sexes separately. This analysis showed a significant difference in length between males and females between age 2 and age 6, with females being larger. At older ages the confidence regions became too wide to detect sexual dimorphism. The applicability of our approach was furthermore shown by comparing the results for Tjeukemeer with existing data for two other lakes. Eurasian perch in IJsselmeer (The Netherlands) showed comparable maximum lengths and dimorphism among sexes, but significant lower initial growth rates. Eurasian perch in Lake Windermere (UK) showed significantly lower maximum lengths; initial growth rates showed a wide range, with maximum values equal to those of Tjeukemeer. Because we used nonparametric tests (randomization techniques), which only assume independence of the model deviations, our conclusions are statistically well founded, despite the small size of the samples on which they are based. [KEYWORDS: Eutrophic lake-tjeukemeer; individual variability; vonbertalanffy; parameters; model; size; equation; fluviatilis; temperature; food]