Analysis and Comparison of Fish Growth from Small Samples of Length-at-Age Data: Detection of Sexual Dimorphism in Eurasian Perch as an Example

Abstract

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.