Time for Fishery Biomass Recovery from Overfishing by Mathematical Solution of the Logistic Equation

The aim of this paper is to develop a methodology to estimate recovery times using a wide range of published Ecopath modeled overfished data-rich fisheries that had not recovered in the North Sea, Mediterranean, and South America shelves. Recovery times were estimated by biomass increase according to the Verhulst logistic equation mathematical solution, requiring the intrinsic rate of natural increase, r, and the carrying capacity for a fishery, KE, both derived from documented fishery biological process principles. The mathematical solution indicated recovery from <0.2KE may be possible, initially to the minimum overfished level, BOF, of 0.25, then recovered, BREC, 0.4 of the fishery carrying capacity. It was estimated recovery in about 5 to ≤10 years could be obtained with fishing mortalities at half the intrinsic rate of natural increase. Recovery may require fishery stakeholders to select various strategies for recovery, including potential limitations by phytoplankton production in the fishery area. The documented recoveries for fishery areas of the sardine Namibian shelf fishery and climate-related temperature changes and upwelling effects on biomass of the hake fishery in the northern North Sea and West of Scotland shelves are used as examples. The potential recovery of a data-limited fishery is also shown using the relationships derived from the biological processes of data-rich fisheries. Further research is suggested on how to estimate the biomass of data-limited fisheries for recovery from overfishing.