A Mathematical Function for Crop Growth Based on Light Interception and Leaf Area Expansion

Abstract

The Richards function is often inappropriate to describe growth for crop stands, in which dry matter characteristically increases at an almost constant rate during the main growth stage. An alternative function with a more physiological basis is developed by assuming that, when light is limiting, growth rate is proportional to intercepted radiation and therefore to an exponential function of leaf area. As the function describes the transition from exponential to linear growth, the name expolinear growth equation is proposed. The parameters of the equation are an initial maximum relative growth rate R_m, a maximum absolute growth rate C_m, and a time t_b at which the stand effectively passes from exponential to linear growth. The ratio R_m/C_m is the product of a light attenuation coefficient K, a specific leaf area s, and a ratio of leaf weight to total plant weight p₁. The time t_b ‘lost’ for growth while the canopy is closing is proportional to the logarithm of fractional light interception at emergence and inversely proportional to R_m. Termination of growth is accounted for by truncation of the expolinear equation. Applications of this type of analysis are given for sorghum and faba bean. The descriptive power of the equation is illustrated for oil palm. Implications for optimum growth strategies are reviewed and caveats are entered.