  The Anthropocene is characterized by close interdependencies between the
natural Earth system and the human society, posing novel challenges to model
development. Here we present a conceptual model describing the long-term
coevolution of natural and socioeconomic subsystems of Earth. While the climate
is represented via a global carbon cycle, we use economic concepts to model
socio-metabolic flows of biomass and fossil fuels between nature and society. A
wellbeing-dependent parametrization of fertility and mortality governs human
population dynamics. Our analysis focuses on assessing possible asymptotic
states of the Earth system for a qualitative understanding of its complex
dynamics rather than quantitative predictions. Low dimension and simple
equations enable a parameter-space analysis allowing us to identify
preconditions of several asymptotic states and hence fates of humanity and
planet. These include a sustainable co-evolution of nature and society, a
global collapse and everlasting oscillations. We consider scenarios
corresponding to different socio-cultural stages of human history. The
necessity of accounting for the "human factor" in Earth system models is
highlighted by the fact that carbon stocks during the past centuries evolved
opposing to what would "naturally" be expected on a planet without humans. The
intensity of biomass use and the contribution of ecosystem services to human
well-being are found to be crucial determinants of the asymptotic state in a
biomass-only scenario. The capitalistic, fossil-based scenario reveals that
trajectories with fundamentally different asymptotic states might still be
almost indistinguishable during a very long transient phase. Given current
population levels, our study also supports the claim that besides reducing the
global demand for energy, only the extensive use of renewable energies may pave
the way into a sustainable future.
