Table 1.
Variables, parameters and functions used in the game.
Fig 1.
The best responses of the fish and of the manager.
The ESS size of the fish (solid line) and the best response of the manager (dotted line) for two different values of the juvenile growth rate: g = 3 (orange) and g = 5 (blue). For this example, R = 4, z = 3, d = 0.2, c = 5 and s = 1. The ESS size of the fish increases with juvenile growth rate and decreases with harvesting rate, the optimal harvesting rate for the manager increases with juvenile growth rate. The Nash equilibrium lies at the intersection of the ESS curve of the fish and the best response curve of the manager, the Stackelberg equilibrium and the pristine lie on the ESS curve of the fish but not on the best response curve of the manager, while the team optimum lies on the best response curve of the manager, but not on the ESS curve of the fish.
Fig 2.
The effect of harvesting rate on the profit for three management strategies: Ecologically enlightened, evolutionarily enlightened and domestication.
Each panel corresponds to increasing net size: z = 3, z = 6 and z = 10. In all three cases: R = 4, s = 1, d = 0.2, g = 5 and c = 5. The ecologically enlightened manager considers the size of fish at maturation as fixed (uECO) and selects the harvesting rate HECO that maximizes the profit with this in mind. The evolutionarily enlightened manager assumes that the size of fish at maturation is the ESS u* and selects a harvesting rate HEVO that maximizes the profit accordingly. The profit curve for the evolutionarily enlightened management intersects the profit curve for the ecologically enlightened management at its maximum. The evolutionarily enlightened approach leads to higher profits with a lower harvesting rate than the ecologically enlightened one, but is susceptible to the tragedy of the commons. The curve “Tragedy of the commons” shows how the profit varies with H when the size of the fish is fixed at uEVO. The profit curve for domestication lies above all the others.
Fig 3.
The effect of net size on the profit for three management strategies: Ecologically enlightened, evolutionarily enlightened and domestication.
In this example R = 4, s = 1, d = 0.2, g = 5 and c = 5. The evolutionarily enlightened (Stackelberg) curve reaches a higher peak at a higher net size than the ecologically enlightened (Nash) curve. The evolutionarily enlightened profit curve intersects the ecologically enlightened one from above and they coincide from that point onwards. Domestication leads to substantially higher profits and a large optimal net size.
Fig 4.
Sensitivity analysis of the three equilibria for the case where the manager can set only the harvesting rate.
Sensitivity analysis showing how profit and harvesting rates change with the intensity of density dependence R, the maximum fecundity rate s, the natural mortality rate d, the growth rate of juveniles g and the cost of fishing c (z = 6). Arrows pointing up (down) indicate that the profit is increasing (decreasing) when the corresponding parameter increases, arrows pointing to the right (left) indicate that the harvesting rate at the equilibrium is increasing (decreasing) when the corresponding parameter increases. The profit at the ecologically enlightened and evolutionarily enlightened equilibria are directly proportional to s, R and g and inversely proportional to c and d. The harvesting rate at both equilibria increases when s, g or R increase and decreases when c or d increase. The profit at domestication equilibrium increases with s, R and g and decreases with c and d. The corresponding harvesting rate increases with R and s and decreases with c.
Fig 5.
Sensitivity analysis of the three equilibria for the case where the manager can set both the harvesting rate and the net size.
Sensitivity analysis showing how how profit and net sizes change with respect to the intensity of density dependence R, the maximum fecundity rate s, the natural mortality rate d, the growth rate of juveniles g and the cost of fishing c. The profit of the ecologically enlightened (Nash) manager and of the evolutionarily enlightened (Stackelberg) manager are directly proportional to s, R and g and inversely proportional to c and d. The optimal net size of both managers increases when g or R increase and decreases when s increases. Moreover, the optimal net size of both managers decreases with c and d. The profit from domestication and the corresponding optimal net size increase with s, R and g and decrease with c and d.
Table 2.
The possible approaches of the manager, the corresponding game-theoretic concepts and the strategies of the manager and the fish.