Differences in predicted catch composition between two widely used catch equation formulations

Fishing gear selectivity varies among different types of fish (e. g., species, age, sex, or length groups), but their relative catch composition also depends on the fishing process. The continuous (Baranov) formulation assumes that fishing mortality and natural mortality occur together during the fishing season and that there are multiple encounters between fish and fishing gear. For this formulation, predicted catch composition depends on fishing mortality, and at high fishing mortality levels the entire population can be caught provided the selectivity is nonzero for all age groups. In contrast, the discrete formulation assumes that fishing mortality occurs separately from natural mortality and that fish encounter at most only one set of fishing gear. The discrete formulation is easier to compute, but the predicted catch composition is independent of fishing mortality, and some of the population remains unexploitable. The correct choice of equations depends on the particular fishery and fishing mortality levels; at low fishing mortality levels the predictions differ little, but at high fishing mortality levels where multiple gear encounters could occur, the continuous formulation is preferable.