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 simulationp1 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

-0.2

-0.1

0

0.1

0.2 -0.2

-0.1

0

0.1

0.2

0

20

40

60

theta2(beta)theta1(alpha)

ncrit

Case 2: High growth

-0.2

-0.1

0

0.1

0.2 -0.2-0.1

00.1

0.2

0

10

20

30

40

50

60

theta2(beta)theta1(alpha)

ncrit

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

-0.2

-0.1

0

0.1

0.2 -0.2

-0.1

0

0.1

0.2

0

20

40

60

theta2(beta)theta1(alpha)

ncrit

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