Simple equations for dynamic models of the effects of CO sub(2) and O sub(3) on light-use efficiency and growth of crops

Atmospheric concentrations of CO sub(2) and O sub(3) are increasing, which is expected to affect light-use efficiency (LUE) and yield of crops. We derive a mathematical formula for crop LUE as a function of CO sub(2), temperature, light intensity and the Rubisco content of upper leaves. A corollary formula is derived that expresses the sensitivity of crop growth rate to changes in Rubisco, under various conditions. Both formulas were incorporated in an existing wheat model, together with new equations that represent the effects of O sub(3). Five parameters were defined that quantify O sub(3) relations: (1) the amount of Rubisco damaged per unit O sub(3), (2, 3) rate and metabolic costs of O sub(3) detoxification, (4, 5) rate and costs of repair. For quantification of the damage coefficient and repair rate, equations were developed that can be applied to gas exchange measurements in plants subjected to stepwise increase in ambient ozone concentration. The model was parameterised for spring wheat using literature data. Model simulations were carried out for various time courses of O sub(3), CO sub(2), temperature, light intensity, to explain reports in the literature on variation in crop response to elevated CO sub(2) and O sub(3) under different climatic conditions. In spite of model simplicity, simulations explained much of reported variation in crop response to elevated levels of CO sub(2) and O sub(3). The need and use of additional experimentation is discussed, as is the scope for analysing plant defence strategies in terms of investment in detoxification and repair.