Description of growth by simple versus complex models for Baltic Sea spring spawning herring

Abstract

The objective was to find a length–growth model to help differentiate between herring stocks (Clupea harengus l.) when their length–growth shows systematically different patterns. The most essential model restriction was that it should react robustly against variations in the underlying age range which varies not only over time but also between the different herring stocks. Because of the limited age range, significance tests as well as confidence intervals of the model parameters should allow a small sample restriction. Thus, parameter estimation should be of an analytical rather than asymptotic nature and the model should contain a minimum set of parameters. The article studies the comparative characteristics of a simple non-asymptotic two-parameter growth model (allometric length–growth function, abbreviated as ALG model) in contrast to higher parametric and more complex growth models (logistic and von-Bertalanffy growth functions, abbreviated as LGF and VBG models). An advantage of the ALG model is that it can be easily linearized and the growth coefficients can be directly derived as regression parameters. The intrinsic ALG model linearity makes it easy to test restrictions (normality, homoscedasticity and serial uncorrelation of the error term) and to formulate analytic confidence intervals. The ALG model features were exemplified and validated by a 1995 Baltic spring spawning herring (BSSH) data set that included a 12-year age range. The model performance was compared with that of the logistic and the von-Bertalanffy length–growth curves for different age ranges and by means of various parameter estimation techniques. In all cases the ALG model performed better and all ALG model restrictions (no autocorrelation, homoscedasticity, and normality of the error term) were fulfilled. Furthermore, all findings seemed to indicate a pseudo-asymptotic growth for BSSH. The proposed model was explicitly derived for of herring length-growth; the results thus should not be generalized interspecifically without additional proof.