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How reliable are the Powell–Wetherall plot method and the maximum-length approach? Implications for length-based studies of growth and mortality

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Abstract

Length-based methods are the cornerstone of many population studies and stock assessments. This study tested two widely used methods: the Powell–Wetherall (P–W) plot and the Lmax approach (i.e., estimating L∞ directly from Lmax). In most simulations, P–W estimates of the ratio total mortality/growth (Z/K ratio) were biased beyond acceptable limits (bias > 30%). Bias in Z/K showed a complex behavior, without possible corrections. Estimates of asymptotic length (L∞) were less biased than Z/K, but were very sensitive to intra-cohort variability in growth and to changes in the occurrence of large individuals in the sample. Exclusion of the largest size classes during the regression procedure or weighing by abundance does not solve these issues. Perfect linearization of the data and extremely narrow confidence intervals for Z/K will lead users to erroneous overconfidence in outputs. Clearly, the P–W method is not suitable for the assessment of Z/K ratios of natural populations. Estimation of L∞ may be tentatively possible under very specific conditions, with necessary external verifications. Also, this study demonstrates that there is no way to estimate L∞ directly from Lmax, since there is no particular relationship to expect a priori between L∞ and Lmax. Errors in estimating L∞ directly affect the estimate of the growth constant K and all other subsequent calculations in population studies, stock assessments and ecosystem models. New approaches are urgently needed for length-based studies of body growth (e.g., unconstrained curve fit with subsequent bootstrapping), that consider the inherent uncertainty regarding the underlying data and processes.

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Acknowledgements

Many thanks to Daniel Pauly for initiating this work many years ago and for numerous inspiring comments. Thanks to M. L. ‘Deng’ Palomares for encouraging the formation of a new working group on this subject and for her enthusiasm regarding this new project. Many thanks to Marc Taylor and Tobias Mildenberger for their enthusiasm and competence in forming a working group to develop new bootstrap-based methods. Many thanks to the reviewers for their valuable suggestions, which helped to improve the earlier versions of this article. Many thanks to Eduardo T. Paes, Matthias Wolff, Tommaso Giarrizzo, Marc Taylor and Tobias Mildenberger for helpful comments regarding this controversial subject.

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    Ralf Schwamborn

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Schwamborn, R. How reliable are the Powell–Wetherall plot method and the maximum-length approach? Implications for length-based studies of growth and mortality. Rev Fish Biol Fisheries 28, 587–605 (2018). https://doi.org/10.1007/s11160-018-9519-0

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