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On Species Preservation and NonCooperative Exploiters Lone Grønbæk Kronbak University of Southern Denmark Marko Lindroos University of Helsinki Outline Motivation Model Results Motivation Combining two-species models with the game theory What are the driving force for species extinction in a twospecies model with biological dependency? Does ‘Comedy of the Commons’ occur in two-species fisheries? What are the ecosystem consequences of economic competition? Modelling approach Two-species n symmetric competitive exploiters with non-selective harvesting technology Fish stocks may be biologically independent or dependent What is the critical number of exploiters? Analytical independent species model S-G model Derive first E* as the optimal effort, it depends on the relevant economic and biological parameters An n-player equilibrium is then derived as a function of E*and n. Relate then the equilibrium to the weakest stock’s size to compute critical n*, over which ecosystem is not sustained. Dependent vs independent species Driving force of extinction: Independent species Biotechnical productivity Economic parameters Dependent species Biological parameters must be considered Gives rise to a complex set of conditions For example: Natural equilibrium does not exist ‘The Comedy of the Commons’ Numerical dependent species model Cases illustrated: Biological competition, symbiosis and predator-prey Case 1: Both stocks having low intrinsic growth rate Case 2: Both stocks having a high intrinsic growth rate Case 3: Low valued stock has a low intrinsic growth rate, high value stock has a high intrinsic growth rate. Case 4: Low valued stock has a high intrinsic growth rate, high value stock has a low intrinsic growth rate. Parameter values applied for simulation p1 p2 Rlow Rhigh K1= K2 c q OA MS θ1 θ2 1 2 0.3 0.9 50 7 0.5 60 60 [-0.2;0.2] [-0.2;0.2] Case 1: low intrinsic growth rate 60 ncrit 40 20 0 -0.2 -0.1 0.2 0.1 0 0 0.1 theta1(alpha) -0.1 0.2 -0.2 theta2(beta) Case 2: High growth 60 50 ncrit 40 30 20 10 0 -0.2 -0.1 0.2 0.1 0 0 0.1 -0.1 0.2 theta1(alpha) -0.2 theta2(beta) Case 4: Low valued stock has a high intrinsic growth rate, high value stock has a low intrinsic growth rate. 60 ncrit 40 20 0 -0.2 0.2 -0.1 0.1 0 0 0.1 theta1(alpha) -0.1 0.2 -0.2 theta2(beta) Opposite case 3 Conclusion ‘Tragedy of the Commons’ does not always apply A small change in the interdependency can lead to big changes in the critical number of non-cooperative players With competition among species a higher intrinsic growth rate tend to extend the range of parameters for which restricted open access is sustained Discussion From single-species models to ecosystem models Ecosystem approach vs. socio-economic approach Agreements and multi-species
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