Laboratory-based gas exchange measurements to parameterize the Ball et al. (1987) model of gs were made on nine dates between 15 August and 12 September. At pre-dawn on each date, an uppermost fully expanded leaf was selected at random from one field plot of each treatment. The petioles were cut, recut underwater and kept in water for the duration of the measurements. Leaves collected in this manner achieve light-saturated rates of photosynthesis (Ainsworth et al. 2004; Morgan et al. 2004) that equal or exceed rates observed in the field (Rogers et al. 2004). Leaf gas exchange was measured using two open-path gas exchange systems incorporating infrared CO2 and water vapour analysers and a 2 cm2 leaf chamber (LI-6400; Li-Cor, Lincoln, NE, USA). The two systems were calibrated against a standard known concentration of CO2 in air (21.4% O2/balance N2; CO2 503 µmol mol−1; SJ Smith Welding Supply, Decatur, IL, USA) and known h from a precision water vapour generator (LI-610, Li-Cor). Leaf A and gs were calculated according to von Caemmerer & Farquhar 1981). All measurements were performed at a common leaf temperature of 25 ± 1 °C. Photosynthesis was initiated with an incident photosynthetic photon flux density (PPFD) of 1500 µmol m−2 s−1, [CO2] of 370 µmol mol−1 and atmospheric saturation vapour pressure deficit (D) of < 1 kPa. Once photosynthesis had attained steady-state rates, the effects of varying [CO2], PPFD and D were tested in three consecutive phases (Fig. 1a), across ranges representative of growing conditions for G. max at SoyFACE (Rogers et al. 2004). Firstly, the [CO2] of air entering the chamber was varied stepwise (370, 150, 250, 350, 450, 650, 850, 1200, 1500 µmol mol−1) as PPFD was held constant at 1500 µmol m−2 s−1. Changes in leaf transpiration with [CO2] caused variation in D, but this was minimized (D < 1 kPa) by manually adjusting the flow of air through a desiccant column to control the water vapour pressure of air entering the chamber. Secondly, PPFD incident on the leaf was varied stepwise (1500, 1000, 700, 400, 200, 100, 75, 50 µmol m−2 s−1) as [CO2] of air entering the chamber was held constant at growth [CO2] (370 or 550 µmol mol−1). Again, variation in D with transpiration was minimized by manual adjustments. Thirdly, vapour pressure was varied stepwise in six increments from ~ 0.5–1.0 kPa to 2.5–3.5 kPa while PPFD was held constant at 1500 µmol m−2 s−1, and [CO2] of air entering the chamber was maintained at growth [CO2] (370 or 550 µmol mol−1). The shift from wetter to drier air was characterized in D because the deficit in vapour pressure from the intercellular leaf space to the atmosphere is a direct determinant of transpiration. In turn, changes in the rate of transpiration impact gs (Mott & Parkhurst 1991). However, the Ball et al. (1987) model does not deal with this response mechanistically. Therefore, for the purposes of model parameterization, the progressive increase in D imposed on the leaf related to a progressive decrease in h. Throughout the measurements, gas exchange was allowed to reach steady state before the results were recorded and the next stepwise change initiated. The intercept (go) & slope (m) of the Ball et al. (1987) model were determined by linear least squares regression. Parameterization was performed with gas exchange data from each individual leaf measured. Two leaves were measured from each of four ambient [CO2] plots and four elevated [CO2] plots. The effect of growth [CO2] on the intercept and slope of the Ball et al. (1987) model was tested with the plot averages (n = 4), using a mixed model analysis of variance in the MIXED procedure of SAS (SAS Institute, Cary, NC, USA). Growth [CO2] was treated as a fixed effect, while block was a random effect. Because of the low true replicate size and to avoid Type II errors, a probability level of P = 0.1 was set as the threshold for significance.