  Earth's modern atmosphere is highly oxygenated and is a remotely detectable
signal of its surface biosphere. However, the lifespan of oxygen-based
biosignatures in Earth's atmosphere remains uncertain, particularly for the
distant future. Here we use a combined biogeochemistry and climate model to
examine the likely timescale of oxygen-rich atmospheric conditions on Earth.
Using a stochastic approach, we find that the mean future lifespan of Earth's
atmosphere with oxygen levels more than 1% of the present atmospheric level is
1.08+-0.14 billion years. The model projects that a deoxygenation of the
atmosphere, with atmospheric oxygen dropping sharply to levels reminiscnet of
the Archaean Earth, will most probably be triggered before the inception of
moist greenhouse conditions in Earth's climate system and before the extensive
loss of surface water from the atmosphere. We find that future deoxygenation is
an inevitable consequence of increasing solar fluxes, whereas its precise
timing is modulated by the exchange flux of reducing power between the mantle
and the ocean-atmosphere-crust system. Our results suggest that the planetary
carbonate-silicate cycle will tend to lead to terminally CO2-limited biospheres
and rapid atmospheric deoxygenation, emphasizing the need for robust
atmospheric biosignatures applicable to weakly oxygenated and anoxic exoplanet
atmospheres and highlighting the potential importance of atmospheric organic
haze during the terminal stages of planetary habitability.
