Ternary effects on the gas exchange of isotopologues of carbon dioxide

The ternary effects of transpiration rate on the rate of assimilation of carbon dioxide through stomata, and on the calculation of the intercellular concentration of carbon dioxide, are now included in standard gas exchange studies. However, the equations for carbon isotope discrimination and for the exchange of oxygen isotopologues of carbon dioxide ignore ternary effects. Here we introduce equations to take them into account. The ternary effect is greatest when the leaf-to-air vapour mole fraction difference is greatest, and its impact is greatest on parameters derived by difference, such as the mesophyll resistance to CO ₂ assimilation, r _m. We show that the mesophyll resistance to CO ₂ assimilation has been underestimated in the past. The impact is also large when there is a large difference in isotopic composition between the CO ₂ inside the leaf and that in the air. We show that this partially reconciles estimates of the oxygen isotopic composition of CO ₂ in the chloroplast and mitochondria in the light and in the dark, with values close to equilibrium with the estimated oxygen isotopic composition of water at the sites of evaporation within the leaf. The manuscript describes corrections to standard equations for carbon and oxygen isotope discrimination (in CO2) that take into account ternary corrections that are already made to standard gas exchange equations. We show that when the corrections are applied to gas exchange of water and light CO2, but not to the heavy isotopologues of CO2, errors arise. These errors are often small but can be large when the leaf-to-air vapour pressure difference is large, and when the isotopic composition of CO2 inside the leaf is quite different from that in the air. This substantially reconciles apparent differences between estimates of the oxygen isotope composition of CO2 in leaves in the dark and in the light. The ternary correction increases the calculated mesophyll resistance to CO2 transfer. Its magnitude also means that values of fractionation factors for photorespiration and day respiration probably need to be reassessed.