In order to assess observational evidence for potential atmospheric biosignatures on exoplanets, it will be essential to test whether spectral fingerprints from multiple gases can be explained by abiotic or biotic-only processes. Here, we develop and apply a coupled 1D atmosphere-ocean-ecosystem model to understand how primitive biospheres, which exploit abiotic sources of H$_2$, CO, and O$_2$, could influence the atmospheric composition of rocky terrestrial exoplanets. We apply this to the Earth at 3.8 Ga and to TRAPPIST-1e. We focus on metabolisms that evolved before the evolution of oxygenic photosynthesis, which consume H$_2$ and CO and produce potentially detectable levels of CH$_4$. O$_2$-consuming metabolisms are also considered for TRAPPIST-1e, as abiotic O$_2$ production is predicted on M-dwarf orbiting planets. We show that these biospheres can lead to high levels of surface O$_2$ (approximately 1-5 per cent) as a result of CO consumption, which could allow high O$_2$ scenarios, by removing the main loss mechanisms of atomic oxygen. Increasing stratospheric temperatures, which increases atmospheric OH can reduce the likelihood of such a state forming. O$_2$-consuming metabolisms could also lower O$_2$ levels to around 10 ppm and support a productive biosphere at low reductant inputs. Using predicted transmission spectral features from CH$_4$, CO, O$_2$/O$_3$, and CO$_2$ across the hypothesis space for tectonic reductant input, we show that biotically produced CH$_4$ may only be detectable at high reductant inputs. CO is also likely to be a dominant feature in transmission spectra for planets orbiting M-dwarfs, which could reduce the confidence in any potential biosignature observations linked to these biospheres.
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