A REVISED FRANKS MODEL FOR ESTIMATING CO2 CONCENTRATIONS IN DEEP TIME USING GINKGO FROM THE FOSSIL ATMOSPHERES EXPERIMENT

Ginkgo is a morphologically conservative plant lineage with abundant Mesozoic and Cenozoic fossil leaves that frequently preserve cuticle recording epidermal cell patterns including stomatal features. These attributes have made Ginkgo popular for reconstructing atmospheric CO₂ (pCO₂) in deep time, but many potential proxies remain poorly calibrated because of few long-term growth studies of living Ginkgo biloba under elevated pCO₂. Here we report the efforts of the Fossil Atmospheres project to estimate pCO₂ in deep time from a modeling standpoint. We grew Ginkgo biloba plants (from seed and male clones) for up to seven years under pCO₂ concentrations ranging from 425-1000 ppm. The Franks Model was designed to estimate pCO₂ easily from fossils using a simplified photosynthetic model that requires a few morphological measurements (stomatal density, pore size, pore depth) and δ¹³C values, combined with several generalized parameters typical of modern plants. This approach allows for easy data collection on fossil material, with the rest of the generalized inputs strongly supported by a mechanistic understanding of plant physiology. We applied the Franks gas exchange model to estimate pCO₂ from ginkgos grown under known pCO₂ in the Fossil Atmospheres experiment. Using default values for Ginkgo prescribed in the original model produced poor results, as the resulting estimates were both variable (39% error rate) and biased. These default settings overestimate pCO₂ at low concentrations and underestimate pCO₂ at elevated CO₂ concentrations. Model estimates were greatly improved with the input of assimilation rate values (An) measured directly on the plants in the experiment instead of using the default CO₂ compensation point equation. With this modification, we find much higher correspondence between model estimates and known pCO₂ values. The addition of An values brings our error rate down to 28%, a typical error rate in other applications of the Franks model. Measured An values improve the fitness of the model because, at least for Ginkgo, the CO₂ compensation point equation that governs how the Franks Model allows pCO₂ estimates to increase is a poor fit to the An vs. pCO₂ relationship for Ginkgo. We recommend that either a more generalized mechanistic equation be developed, or that measured An values from modern analogs be utilized when estimating paleo-pCO₂ from fossils.