Comparing the steady state results of a range of multispecies models between and across geographical areas by the use of the jacobian matrix of yield on fishing mortality rate

Like other fisheries models, multispecies models are subject to various sources of error. However, with regard to their use for ecosystem-based fisheries management (EBFM) between model errors are likely to be most important. As multispecies models are by definition many-dimensional, comparing them is potentially a complex task. The paper uses a simple approach. This is to calculate the Jacobian matrix of long term steady state catch by species with respect to the fishing mortality relative to status quo levels on all species. This enables the comparison of the relative strength of species interactions among models both within and between regions. This Jacobian matrix approach to comparing multispecies models is applied to available models for the North Sea, the Baltic Sea and from Icelandic waters. Moreover, this information is used to provide the basis for estimating a multidimensional quadratic yield surface for each model in the near field. Used this way it is possible to compare different model estimations of fishing mortality rate changes needed to approach yield-related management goals. The results suggest considerable variation between models in their detailed results but more coherence in suggesting directions for changing fishing mortality rate. Thus the approach is of considerable importance in specifying the confidence with which it is possible to make multispecies predictions for EBFM.