Inherent bias in using aggregate CPUE to characterize abundance of fish species assemblages

We have analyzed the practice of assessing an assemblage of fish species in a multispecies fishery on the basis of aggregate catch per unit effort (CPUE), which is the summed catch of all species per unit of effort. We show that at the onset of fishing or of a large positive or negative change in fishing effort, aggregate CPUE will be hyper-responsive, that is, relative change of aggregate CPUE will be greater than that of aggregate abundance. We also show that as the fishery reaches equilibrium, the aggregate CPUE in most circumstances will continue to be hyper-responsive, with a greater relative change from its value at the start than the aggregate abundance. However, there are less likely circumstances in which the aggregate CPUE will be hyper-stable compared to aggregate abundance. The circumstances leading to hyper-responsiveness or hyper-stability depend on the distribution of productivity and fishery vulnerability parameters among the species in the aggregation.