Geometric Series-Steady State (GSSS) Model: A New Protocol for Interpreting Compound-Specific Δ¹⁴C Data

A model system developed to understand the complicated history of general organic matter in soil using its carbon isotopic data such as Δ¹⁴C and δ¹³C is described. The system, named the geometric series-steady state (GSSS) model, is mathematically described as when the geometric series reaches a steady state in infinite time. This model assumes that molecules of photosynthetic origin are continuously supplied as well as decaying at constant rates. Consideration of the model leads to the following general remarks: (1) the GSSS model defines the unique undisturbed line on the Δ¹⁴C age-abundance plane, along which any molecules supplied exclusively by photosynthesis may fall; (2) the model defines the disturbed regions on the plane: molecules supplied by not only photosynthesis but also biotic/abiotic synthetic reactions may give plots on the disturbed regions; (3) the δ¹³C value of a molecule cannot be fractionated by Rayleigh distillation type-fractionation. As an exercise, the GSSS model has been applied to the reported data of several fatty acids of different carbon number from soil. A protocol is presented which applies the GSSS model to the natural system, whose Δ¹⁴C value was greatly altered by the bomb effect. By the combination of the GSSS consideration and model simulation using real atmospheric ¹⁴C data during the last half century, the author investigated the behavior of fatty acids within the assumptions of the model. Assuming that fatty acids with carbon number greater than or equal to 26 are undisturbed, the GSSS model concludes that fatty acids in soil with carbon number less than 26 are not directly supplied from leaf litter, but should be synthesized continually from other less labile molecules in the soil. The proportion of synthesized molecules to those supplied originally from leaves is greater for the smaller carbon numbered fatty acids. The GSSS model should be applicable to any system, in which a molecule is regularly supplied from atmospheric CO₂ via photosynthesis.