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The Anthropocene is characterized by close interdependencies between thenatural Earth system and the human society, posing novel challenges to modeldevelopment. Here we present a conceptual model describing the long-termcoevolution of natural and socioeconomic subsystems of Earth. While the climateis represented via a global carbon cycle, we use economic concepts to modelsocio-metabolic flows of biomass and fossil fuels between nature and society. Awellbeing-dependent parametrization of fertility and mortality governs humanpopulation dynamics. Our analysis focuses on assessing possible asymptoticstates of the Earth system for a qualitative understanding of its complexdynamics rather than quantitative predictions. Low dimension and simpleequations enable a parameter-space analysis allowing us to identifypreconditions of several asymptotic states and hence fates of humanity andplanet. These include a sustainable co-evolution of nature and society, aglobal collapse and everlasting oscillations. We consider scenarioscorresponding to different socio-cultural stages of human history. Thenecessity of accounting for the "human factor" in Earth system models ishighlighted by the fact that carbon stocks during the past centuries evolvedopposing to what would "naturally" be expected on a planet without humans. Theintensity of biomass use and the contribution of ecosystem services to humanwell-being are found to be crucial determinants of the asymptotic state in abiomass-only scenario. The capitalistic, fossil-based scenario reveals thattrajectories with fundamentally different asymptotic states might still bealmost indistinguishable during a very long transient phase. Given currentpopulation levels, our study also supports the claim that besides reducing theglobal demand for energy, only the extensive use of renewable energies may pavethe way into a sustainable future.

Sustainability, collapse and oscillations of global climate, population and economy in a simple World-Earth model