BRYOCARB: A process-based model of thallose liverwort carbon isotope fractionation in response to CO2, O2, light and temperature

Evidence from laboratory experiments indicates that fractionation against the heavy stable isotope of carbon (Δ¹³C) by bryophytes (liverworts and mosses) is strongly dependent on atmospheric CO₂. This physiological response may therefore provide the basis for developing a new terrestrial CO₂ proxy [Fletcher, B.J., Beerling, D.J., Brentnall, S.J., Royer, D.L., 2005. Fossil bryophytes as recorders of ancient CO₂ levels: experimental evidence and a Cretaceous case study. Global Biogeochem. Cycles19, GB3012]. Here, we establish a theoretical basis for the proxy by developing an extended model of bryophyte carbon isotope fractionation (BRYOCARB) that integrates the biochemical theory of photosynthetic CO₂ assimilation with controls on CO₂ supply by diffusion from the atmosphere. The BRYOCARB model is evaluated against measurements of the response of liverwort photosynthesis and Δ¹³C to variations in atmospheric O₂, temperature and irradiance at different CO₂ concentrations. We show that the bryophyte proxy is at least as sensitive to variations in atmosphere CO₂ as the two other leading carbon isotope-based approaches to estimating palaeo-CO₂ levels (δ¹³C of phytoplankton and of paleosols). Mathematical inversion of BRYOCARB provides a mechanistic means of estimating atmospheric CO₂ levels from fossil bryophyte carbon that can explicitly account for the effects of past differences in O₂ and climate.