A new empirical equation for the sigmoid pattern of determinate growth, 'the beta growth function', is presented. It calculates weight (w) in dependence of time, using the following three parameters: t(m), the time at which the maximum growth rate is obtained; t(e), the time at the end of growth; and w(max), the maximal value for w, which is achieved at t(e). The beta growth function was compared with four classical (logistic, Richards, Gompertz and Weibull) growth equations, and two expolinear equations. All equations described successfully the sigmoid dynamics of seed filling, plant growth and crop biomass production. However, differences were found in estimating w(max). Features of the beta function are: (1) like the Richards equation it is flexible in describing various asymmetrical sigmoid patterns (its symmetrical form is a cubic polynomial); (2) like the logistic and the Gompertz equations its parameters are numerically stable in statistical estimation; (3) like the Weibull function it predicts zero mass at time zero, but its extension to deal with various initial conditions can be easily obtained; (4) relative to the truncated expolinear equation it provides more reasonable estimates of final quantity and duration of a growth process. In addition, the new function predicts a zero growth rate at both the start and end of a precisely defined growth period. Therefore, it is unique for dealing with determinate growth, and is more suitable than other functions for embedding in process-based crop simulation models to describe the dynamics of organs as sinks to absorb assimilates. Because its parameters correspond to growth traits of interest to crop scientists, the beta growth function is suitable for characterization of environmental and genotypic influences on growth processes. However, it is not suitable for estimating maximum relative growth rate to characterize early growth that is expected to be close to exponential.

We appraised the literature and described an approach to estimate the parameters of the Farquhar, von Caemmerer and Berry model using measured CO2 assimilation rate (A) and photosystem II (PSII) electron transport efficiency (F2). The approach uses curve fitting to data of A and F2 at various levels of incident irradiance (Iinc), intercellular CO2 (Ci) and O2. Estimated parameters include day respiration (Rd), conversion efficiency of Iinc into linear electron transport of PSII under limiting light [k2(LL)], electron transport capacity (Jmax), curvature factor (q) for the non-rectangular hyperbolic response of electron flux to Iinc, ribulose 1·5-bisphosphate carboxylase/oxygenase (Rubisco) CO2/O2 specificity (Sc/o), Rubisco carboxylation capacity (Vcmax), rate of triose phosphate utilization (Tp) and mesophyll conductance (gm). The method is used to analyse combined gas exchange and chlorophyll fluorescence measurements on leaves of various ages and positions in wheat plants grown at two nitrogen levels. Estimated Sc/o (25°C) was 3.13 mbar mbar -1 ; Rd was lower than respiration in the dark; Jmax was lower and q was higher at 2% than at 21% O2; k2(LL), Vcmax, Jmax and Tp correlated to leaf nitrogen content; and gm decreased with increasing Ci and with decreasing Iinc. Based on the parameter estimates, we surmised that there was some alternative electron transport.

Plants react to their environment and to management interventions by adjusting physiological functions and structure. Functional-structural plant models (FSPM), combine the representation of three-dimensional (3D) plant structure with selected physiological functions. An FSPM consists of an architectural part (plant structure) and a process part (plant functioning). The first deals with (i) the types of organs that are initiated and the way these are connected (topology), (ii) co-ordination in organ expansion dynamics, and (iii) geometrical variables (e.g. leaf angles, leaf curvature). The process part may include any physiological or physical process that affects plant growth and development (e.g. photosynthesis, carbon allocation). This paper addresses the following questions: (i) how are FSPM constructed, and (ii) for what purposes are they useful? Static, architectural models are distinguished from dynamic models. Static models are useful in order to study the significance of plant structure, such as light distribution in the canopy, gas exchange, remote sensing, pesticide spraying studies, and interactions between plants and biotic agents. Dynamic models serve quantitatively to integrate knowledge on plant functions and morphology as modulated by environment. Applications are in the domain of plant sciences, for example the study of plant plasticity as related to changes in the red:far red ratio of light in the canopy. With increasing availability of genetic information, FSPM will play a role in the assessment of the significance towards plant performance of variation in genetic traits across environments. In many crops, growers actively manipulate plant structure. FSPM is a promising tool to explore divergent management strategies.

Tillering ceases at specific light conditions within the wheat canopy, independent of population density, and to a lesser extent independent of light intensity. It is suggested that cessation of tillering is induced when the fraction of PAR intercepted by the canopy exceeds a specific threshold (0.40-0.45) and red : far-red ratio drops below 0.35-0.40.

SummaryInterspecific differences in functional traits are a key factor for explaining the positive diversity-productivity relationship in plant communities. However, the role of intraspecific variation attributable to phenotypic plasticity in diversity-productivity relationships has largely been overlooked. By taking a wheat (Triticum aestivum)-maize (Zea mays) intercrop as an elementary example of mixed vegetation, we show that plasticity in plant traits is an important factor contributing to complementary light capture in species mixtures.We conceptually separated net biodiversity effect into the effect attributable to interspecific trait differences and species distribution (community structure effect), and the effect attributable to phenotypic plasticity. Using a novel plant architectural modelling approach, wholevegetation light capture was simulated for scenarios with and without plasticity based on empirical plant trait data.Light capture was 23% higher in the intercrop with plasticity than the expected value from monocultures, of which 36% was attributable to community structure and 64% was attributable to plasticity. For wheat, plasticity in tillering was the main reason for increased light capture, whereas for intercropped maize, plasticity induced a major reduction in light capture.The results illustrate the potential of plasticity for enhancing resource acquisition in mixed stands, and indicate the importance of plasticity in the performance of species-diverse plant communities.