Estimating and testing non-additivity in fishing mortality: implications for detecting a fisheries collapse

Common in many fisheries collapses is a disproportionate increase in fishing mortality at younger ages. One mechanism by which this increase could occur is sufficient depletion of the population at older ages due to strong overfishing, which leads to targeting of younger fish. Thus, it is essential for assessments to estimate and test for a change in selectivity in the fishery. We introduce a simple and powerful approach based upon Tukey's one degree of freedom test for non-additivity. This approach can be applied within any statistical age-structured population model that estimates selectivity. We illustrate the approach with data from Atlantic cod (Gadus morhua) from St. Pierre Bank, Canada. The results show significant non-additivity in fishing mortality that translates into an increase in selectivity on younger ages when fishing mortality is high. This approach also can be applied to the output of an age-structured model that assumes catch-at-age is known without error or to any survey or catch-per-unit-effort data for which estimates of abundance are made by year and age. We believe that this approach should be routinely applied in assessments, particularly when overfishing has led to depletion of the overall population or to truncation of the age structure.