2012/12/16 by Irina Kareva, Kareva, Irina, B. Morin +4
Biochemistry, Genetics and Molecular Biology · Medicine · Social Sciences · #Classical Analysis and ODEs (math.CA) #Evolution and Genetic Dynamics #Evolutionary Game Theory and Cooperation #FOS: Biological sciences #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Populations and Evolution (q-bio.PE)
paper · pdf · doi:10.48550/arxiv.1212.3807
openalex publication_date 2012/12/16 · openalex created_date 2022/09/18 · openalex updated_date 2026/07/28
The conditions that can lead to the exploitative depletion of a shared\nresource, i.e, the tragedy of the commons, can be reformulated as a game of\nprisoner's dilemma: while preserving the common resource is in the best\ninterest of the group, over-consumption is in the interest of each particular\nindividual at any given point in time. One way to try and prevent the tragedy\nof the commons is through infliction of punishment for over-consumption and/or\nencouraging under-consumption, thus selecting against over-consumers. Here, the\neffectiveness of various punishment functions in an evolving consumer-resource\nsystem is evaluated within a framework of a parametrically heterogeneous system\nof ordinary differential equations (ODEs). Conditions leading to the\npossibility of sustainable coexistence with the common resource for a subset of\ncases are identified analytically using adaptive dynamics; the effects of\npunishment on heterogeneous populations with different initial composition are\nevaluated using the Reduction theorem for replicator equations. Obtained\nresults suggest that one cannot prevent the tragedy of the commons through\nrewarding of under-consumers alone - there must also be an implementation of\nsome degree of punishment that increases in a non-linear fashion with respect\nto over-consumption and which may vary depending on the initial distribution of\nclones in the population.\n