Geodesic
Is it possible to prevent the ``Tragedy of Common Resource''?
Matematičeskaâ biologiâ i bioinformatika, Tome 7 (2012) no. 1, pp. 30-44.

Voir la notice de l'article provenant de la source Math-Net.Ru

We analyze a “resource-consumer” type system, where consumers can not only deplete the common renewable resource but are also capable of contributing to its restoration. Within the frameworks of this model, consumers are defined as clones which are characterized by their intrinsic (parametric) rate of interaction with the resource, from producers up to over-consumers. The exploitive depletion of a shared resource is known as the “tragedy of the commons”. We first study the dynamics of parametrically homogeneous system, identifying a series of basic and transitional regimes with respect to parameter variations. In order to analyze the parametrically heterogeneous population and its evolution over time we apply the Reduction theorem, reducing an otherwise infinitely dimensional system of ODEs to finite dimensionality. We show that collapse of the heterogeneous system is still possible with the same set of initial conditions but the heterogeneous population survives longer than a homogeneous one. We also analyze the possibility of preventing the tragedy of the commons through external regulation, i.e., by inflicting punishment upon over-consumers and/or encouraging under-consumers. We observe that the most effective mode of regulation requires both punishment and reward, which need to be adjusted depending on the initial distribution of clones in the population, and “non-linear” punishment of over-consumers is required to prevent the tragedy of the commons. 
@article{MBB_2012_7_1_a10,
     author = {F. S. Berezovskaya and I. G. Kareva and G. P. Karev},
     title = {Is it possible to prevent the {``Tragedy} of {Common} {Resource''?}},
     journal = {Matemati\v{c}eska\^a biologi\^a i bioinformatika},
     pages = {30--44},
     publisher = {mathdoc},
     volume = {7},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MBB_2012_7_1_a10/}
}
TY  - JOUR
AU  - F. S. Berezovskaya
AU  - I. G. Kareva
AU  - G. P. Karev
TI  - Is it possible to prevent the ``Tragedy of Common Resource''?
JO  - Matematičeskaâ biologiâ i bioinformatika
PY  - 2012
SP  - 30
EP  - 44
VL  - 7
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MBB_2012_7_1_a10/
LA  - ru
ID  - MBB_2012_7_1_a10
ER  - 
%0 Journal Article
%A F. S. Berezovskaya
%A I. G. Kareva
%A G. P. Karev
%T Is it possible to prevent the ``Tragedy of Common Resource''?
%J Matematičeskaâ biologiâ i bioinformatika
%D 2012
%P 30-44
%V 7
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MBB_2012_7_1_a10/
%G ru
%F MBB_2012_7_1_a10
F. S. Berezovskaya; I. G. Kareva; G. P. Karev. Is it possible to prevent the ``Tragedy of Common Resource''?. Matematičeskaâ biologiâ i bioinformatika, Tome 7 (2012) no. 1, pp. 30-44. http://geodesic.mathdoc.fr/item/MBB_2012_7_1_a10/

[1] Hardin G., “The tragedy of the Commons”, Science, 162 (1968), 1243–1248 | DOI

[2] Ostrom E., Governing the commons. The evolution of institution for collective action, Cambridge University Press, 1990

[3] Odling-Smee F.J., Laland K.N., Feldman M.W., Niche construction: the neglected process in evolution, Princeton University Press, 2003

[4] Krakauer D.C., Karen M.P., Douglas H.E., “Diversity, dilemmas, and monopolies of niche construction”, The Amer. Nat., 173:1 (2009), 26–40 | DOI

[5] Kareva I., Berezovskaya F., Castillo-Chavez C., “Niche Construction and Sustainability in Resource-Dependent Competition Models”, J. of Math. Biosci (to appear)

[6] Berezovskaya F., Novozhilov A., Karev G., “Population models with singular equilibrium”, J. of Math. Biosci., 208:1 (2007), 270–299 | DOI | MR | Zbl

[7] Bautin H.H., Leontovich, E.A., Metody i priemy kachestvennogo issledovaniya dinamicheskikh sistem na ploskosti, Nauka, Moskva, 1976

[8] Kuznetsov Yu., Elements of applied bifurcation theory, Springer, New York, 1998 | MR

[9] Karev G.P., “On mathematical theory of selection: continuous time population dynamics”, J. of Math. Biol., 60:1 (2010), 107–129 | DOI | MR

[10] Fisher R.A., The Genetical Theory of Natural Selection: A Complete Variorum Edition, Oxford University Press, Oxford, 1999 | MR | Zbl

[11] Kapur J.N., Maximum entropy models in science and engineering, John Wiley Sons, 1989 | MR | Zbl