Scrabbling around for understanding of Natural Mortality

The authors have collaborated for the past 40 years on a sequence of initiatives for a range of fisheries and marine ecosystems projects. These had natural mortality (M) as a common thread and have helped increase understanding of this elusive parameter. Here, we provide a reprise as well as an extension of our earlier results. Taken together, these help to develop an understanding of M of exploited fish stocks, particularly those of the North Sea. Firstly, a reprisal is given of the key findings about M due to predation by important fish stocks of the North Sea. Estimates were first produced by the ICES Multispecies Working Group using multispecies virtual population analysis (MSVPA) in combination with extensive stomach content data - collected for all four quarters and around the whole North Sea during 1981. Results from this initiative demonstrate that predation mortality (M2) represents a large portion of M for many North Sea fish species, but varies markedly both by age and by year, thus refuting the then widely adopted hypothesis that M was constant. Moreover, these variations were sufficiently large to overturn single species predictions of sustainable yield. M2 results from the 1980’s also indicated that mortality levels were related to prey size and species. The paper then reprises results from studies made by the private working group (PWG) that the authors formed to continue their collaboration. These focused first on size spectra of fish communities both by data analysis and by developing a simple trait-based model (cartoon) of the North Sea - the charmingly simple model (CSM). This modelling led to further questions about the basis of the coexistence of fish species in an ecosystem given that egg production scales approximately with asymptotic weight. This led to a plausible hypothesis that differential natural mortality rates are required that increase with the von Bertalanffy parameters of curvature K and asymptotic length L∞, but decrease with fish length. Data from the literature supported this hypothesis, which was further refined into canonical form: M-K(L_∞/L)^1.5. However, this hypothesis is also questioned because this form might not be compatible with the predicted and observable fact that size-spectra slopes become more negative with increased general levels of fishing. Clearly, changes in size spectra should cause changes in M2. Results of new modelling work are presented where the CSM is modified to include differential natural mortality rates by K and L_∞. The results suggest that M responds both to general levels of fishing and the slope of the ensuing size spectrum. This suggests that a more general expression for predation mortality would be M2=α(F)K(L_∞^χ)(L^β(F)), where χ is likely to be close to the 1.5 value used in the canonical form. The work thus provides a likely form for M2 but by no means a universally applicable formula yet. It remains a hypothesis needing to be tested and perhaps calibrated against data from the sea. Such calibrations might indeed point toward a universal formula for M2.