The Interaction Between Stock Dynamics, Fishing and Climate Caused the Collapse of the Jack Mackerel Stock at Humboldt Current Ecosystem - Lima, Mauricio; Canales, T. Mariella; Wiff, Rodrigo; Montero, José (Frontiers in Marine Science, 2020)
The collapse of marine fisheries had caused a cascade of dramatic ecological, social and economic consequences. Recognizing the complex nature of the fisheries collapses, two basic minimum elements should be included in fishery models. First, the dynamics of the fish population and second the changes in the fishing effort that are co-determined by the harvest and economic forces. The rapid and abrupt shifts in abundance exhibited by some marine fish populations can be driven by the fishing fleet behaving like generalist predators. Here we develop a population dynamic model with negative feedback in the fish stock and a sigmoid functional response of the fishing effort, we assume that the rate of change in effort from year to year is a positive function of fishery revenue, but is negatively influenced by fishing costs which are proportional to the annual ratio between fishing effort/stock size. We use this model to consider how changes in the fishing effort driven by ecological and economic forces can generate the observed large abrupt shifts in the abundance of the jack mackerel (Trachurus murphyi) stock at south-eastern Pacific. Our model predict that jack-mackerel stock dynamics can have alternate stable states. Our simple bio-economic model allows us to explore some management responses in a heuristic manner, where the most critical element seems to be the combination of an n-shaped isocline for fish stock growth and a slanted isocline of fishing effort whose slope is highly sensitive to changes in the profitability of the fishery.