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 Rm, a maximum absolute growth rate Cm, and a time tb at which the stand effectively passes from exponential to linear growth. The ratio Rm/ Cm is the product of a light attenuation coefficient K, a specific leaf area s, and a ratio of leaf weight to total plant weight p 1 • The time tb 'lost' for growth while the canopy is closing is proportional to the logarithm of fractional light interception at emergence and inversely proportional to Rm. 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.

A high seed yield and associated attributes of dry matter production achieved by recent Japanese soybean cultivars

“…Hence, we developed the present study to focus on light interception and utilization by soybean plants because both are key constituents for dry matter accumulation. Ball et al (2000) argued that having a short duration before the full canopy cover is achieved (>90% light interception) may increase yield because it shortens the time required after emergence to begin linear biomass accumulation, which Goudriaan and Monteith (1990) is considered to be lost time. Lee et al (2008) showed that achieving complete ground cover by the R1 [stage in the classification of Fehr and Caviness (1977)] or shortly thereafter is required to achieve maximum yield.…”

An alternative approach in hydrograph decomposition and separation of the baseflow

“…The Goudriaan and Monteith (1990) expo-linear model was adapted for hydrological purposes. The expo-linear model allowed to characterize the RC as two change ratios, the maximum runoff ratio (C) which discriminated the phase associated with the direct flow (linear), and a relative runoff ratio (k) associated to the baseflow (exponential).…”

Modelling Visible Foliar Injury Effects on Canopy Photosynthesis and Potential Crop Yield Losses Resulting from Fluoride Exposure

“…The responses of the rate of photosynthesis to variations in environmental factors can be described in terms of the biochemical processes of electron transport and carbon dioxide fixation [27], or carbon dioxide assimilation by leaves and plant canopies [16,28,29], or by dry matter accumulation at the crop level [30,31]. The modelling approaches differ in the way in which this conversion is expressed, and the interactions with other processes that are incorporated into the energy conversion coefficient.…”

“…In spite of the theoretical superiority of the biochemical model and because detailed biochemical and physiological information is lacking for many crop species, empirical leaf and canopy models still provide satisfactory empirical predictions of the relative effects of environmental factors on crop yield or forest production [29,31,34,35]. Where variations in plant condition or soil or atmospheric water deficits [16,17,20] may influence carbon dioxide assimilation and dry matter production, it is necessary to extend the model beyond the effects of the factors considered in Table 1.…”