Using Carbon Stable Isotopes to Study C₃ and C₄ Photosynthesis: Models and Calculations

Stable carbon isotopes are a powerful tool to study photosynthesis. Initial applications consisted of determining isotope ratios of plant biomass using mass spectrometry. Subsequently, theoretical models relating C isotope values to gas exchange characteristics were introduced and tested against instantaneous online measurements of ¹³C photosynthetic discrimination. Beginning in the twenty-first century, laser absorption spectroscopes with sufficient precision for determining isotope mixing ratios became commercially available. This has allowed collection of large data sets at lower cost and with unprecedented temporal resolution. More data and accompanying knowledge have permitted refinement of ¹³C discrimination model equations, but often at the expense of increased model complexity and difficult parametrization. This chapter describes instantaneous online measurements of ¹³C photosynthetic discrimination, provides recommendations for experimental setup, and presents a thorough compilation of equations available to researchers. We update our previous 2018 version of this chapter by including recently improved descriptions of (photo)respiratory processes and associated fractionations. We discuss the capabilities and limitations of the diverse ¹³C discrimination model equations and provide guidance for selecting the model complexity needed for different applications.