Models of Inter-Moult Period for Antarctic Krill - Lack of Progress and Promulgation of Unreliable Models Calibrated Using Indirect Observations

Abstract

Aims: Two methods of calibrating regression models of inter-moult period (IMP) as a function of temperature exposure (T) for crustaceans, in particular, Antarctic krill (Euphausia superba) are reviewed in terms of both theoretical and empirical properties in order to make recommendations on the application of the methods and/or the use of the resultant fitted models. Methodology: The method and fitted model that used a meta-analysis of published results from laboratory-reared krill using means of directly observed IMP for a range of controlled, constant temperature regimes has valid theoretical and empirical support. The alternative used moult frequencies obtained as a “byproduct” of 5-d Instantaneous Growth Rate (IGR) experiments carried out at sea for which individual IMPs were not directly observed. Instead mean IMP given T and animal total length (L) was predicted using the moult frequencies disaggregated to binary data of moulted versus not-moulted as dependent variable in the calibration of a logistic regression on T and L. The shape of the daily development rate, R, the inverse of IMP, versus T response curve fitted using direct observations is a classical monotonically increasing curve whereas for combinations of sex/maturity classes the curves fitted using indirect observations are parabola-like with sexually dimorphic concavities of either up or down. Four sources of bias in predictions of mean IMP using the indirect observations and estimation method are described. One source due to an unrepresentative sampling frame can lead to large positive bias in estimated mean IMP based on theory which has been absent until now and that applies a discrete uniform distribution for next moult date corresponding to ideal asynchrony. This bias and that due to IGR experimental measurement error in T cannot be remedied. Conclusion: The indirect method and the corresponding fitted models are unreliable and should not be used.