On Species Preservation and Non- Cooperative 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 two- species 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 p1p1 p2p2 R low R high K1=K2K1=K2 cqOAMSθ1θ1 θ2θ [-0.2;0.2]

Case 1: low intrinsic growth rate

Case 2: High growth

Case 4: Low valued stock has a high intrinsic growth rate, high value stock has a low intrinsic growth rate. 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