So, water-use efficiency (and carbon assimilation rate) is correlated with ambient CO₂ concentration (Ca), and carbon isotope discrimination Δ is correlated with Pi/Pa (partial CO₂ pressure, intercellular and atmospheric, respectively) in C3 species. If the Ca increased, would that result in decreasing Δ? In other words, would increasing ambient CO₂ levels result in less discrimination towards the ¹³C isotope, in C3 species? And if that's true, is my math sound?
After more research, I've found this to be true and the reason why. Discrimination against ¹³CO₂ isotope comes from two reasons; kinetic effects (diffusion and enzyme fractionation), and thermodynamic effects (1). ¹²CO₂ and ¹³CO₂'s diffusion rates are different, carboxylation reaction's discrimination value is 30 per million, and the diffusivity of ¹³CO₂ is 4.4 per million less than that of ¹²CO₂ (2).
When stomata are fully open
they place no place no limitation on diffusion of CO₂, C3 leaves should discriminate against ¹³CO₂ by 30 per million, with respect to the atmosphere. When stomata are sufficiently closed that they become the sole source of limitation, the discrimination should be 4 per million. Intermediate cases give intermediate discriminations. (2)
It's known that when CO₂ is abundant in the atmosphere, stomata start to close because their job is to balance the CO₂ uptake and water loss by transpiration. This, combined with the previously mentioned information, to my understanding, means that, when they are more closed, CO₂ in the intercellular space gets consumed more. This lessens the carboxylation reaction's effect on the ¹³CO₂ discrimination because the CO₂ in intercellular space becomes more limited compared to the free diffusion of fully open stomata. In other words, carboxylation reaction has less CO₂ molecules to choose from intercellular space because free diffusion doesn't supply a constant flow of CO₂ molecules, making it use more ¹³CO₂.
(1) Farquhar et al., 1989, Annual Rev. Plant Physiol, Carbon Isotope Discrimination and Photosynthesis
(2) Farquhar et al., 1982, Aust. J. Plant Physiol, On the Relationship between Carbon Isotope Discrimination and the Intercellular Carbon Dioxide Concentration in Leaves