Fundamental equations for growth in uniform stands of vegetation

Applications of the ‘expolinear’ equation for crop growth described by Goudriaan and Monteith [Goudriaan, J., Monteith, J.L., 1990. Ann. Bot. 66, 695–701] are restricted by the assumption that absolute and specific growth rates are both constant in time. To overcome this constraint, a second-order differential equation is derived that may either be integrated to yield the expolinear equation or used with a daily time-step to simulate growth when absolute and specific growth rates are time-dependent. The expolinear equation fitted the biomass of individual organs in a sorghum trial and related quantities such as leaf area per unit biomass. It predicts that an increase in the variability of weather during early stages of growth will usually reduce biomass production.