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.

Predicting rice (Oryza sativa) productivity under future climates is important for global food security. Ecophysiological crop models in combination with climate model outputs are commonly used in yield prediction, but uncertainties associated with crop models remain largely unquantified. We evaluated 13 rice models against multi-year experimental yield data at four sites with diverse climatic conditions in Asia and examined whether different modeling approaches on major physiological processes attribute to the uncertainties of prediction to field measured yields and to the uncertainties of sensitivity to changes in temperature and CO 2 concentration [CO 2 ]. We also examined whether a use of an ensemble of crop models can reduce the uncertainties. Individual models did not consistently reproduce both experimental and regional yields well, and uncertainty was larger at the warmest and coolest sites. The variation in yield projections was larger among crop models than variation resulting from 16 global climate model-based scenarios. However, the mean of predictions of all crop models reproduced experimental data, with an uncertainty of less than 10% of measured yields. Using an ensemble of eight models calibrated only for phenology or five models calibrated in detail resulted in the uncertainty equivalent to that of the measured yield in well-controlled agronomic field experiments. Sensitivity analysis indicates the necessity to improve the accuracy in predicting both biomass and harvest index in response to increasing [CO 2 ] and temperature.

The Beta function, commonly used as a skewed probability density function in statistics, was introduced to describe the effect of temperature on the rate of crop development. The framework is set by three cardinal temperatures, namely the base (Tb), the optimum (T 0 ) and the ceiling (T,) temperature. The model parameters T b and 7;; and three other coefficients JJ., a and {3 can be used to derive the value of T 0 and the maximum developmem rate. Parameter a also characterizes the curvature of the relationship with temperatures between Tb and T 0 , and parameter {3 describes the curvature between T 0 and T..,. The model has one parameter less than the Rice Clock Model (RCM); and in contrast to the RCM, it ensures that the maximum development rate occurs exactly at 7;,. The model accurately described the response to temperature of several developmental processes, and was superior to two widely used thermal time approaches in predicting rice flowering time.

a b s t r a c tNearly three decades ago Farquhar, von Caemmerer and Berry published a biochemical model for C 3 photosynthetic rates (the FvCB model). The model predicts net photosynthesis (A) as the minimum of the Rubisco-limited rate of CO 2 assimilation (A c ) and the electron transport-limited rate of CO 2 assimilation (A j ). Given its simplicity and the growing availability of the required enzyme kinetic constants, the FvCB model has been used for a wide range of studies, from analysing underlying C 3 leaf biochemistry to predicting photosynthetic fluxes of ecosystems in response to global warming. However, surprisingly, this model has seen limited use in existing crop growth models. Here we highlight the elegance, simplicity, and robustness of this model. In the light of some uncertainties with photosynthetic electron transport pathways, a recently extended FvCB model to calculate A j is summarized.Applying the FvCB-type model in crop growth models for predicting leaf photosynthesis requires a stomatal conductance (g s ) model to be incorporated, so that intercellular CO 2 concentration (C i ) can be estimated. In recent years great emphasis has been put on the significant drawdown of Rubisco carboxylation-site CO 2 concentration (C c ) relative to C i . To account for this drawdown, mesophyll conductance (g m ) for CO 2 transfer can be added. We present an analytical algorithm that incorporates a g s model and uses g m as a temperature-dependent parameter for calculating A under various environmental scenarios.Finally we discuss a C 4 -equivalent version of the FvCB model. In addition to the algorithms already elaborated for C 3 photosynthesis, most important algorithms for C 4 photosynthesis are those that capture the CO 2 concentrating mechanism and the extra ATP requirement by the C 4 cycle. Although the current estimation of the C 4 enzyme kinetic constants is less certain, applying FvCB-type models to both C 3 and C 4 crops is recommended to accurately predict the response of crop photosynthesis to multiple, interactive environmental variables.

Elevated CO2 and temperature strongly affect crop production, but understanding of the crop response to combined CO2 and temperature increases under field conditions is still limited while data are scarce. We grew wheat (Triticum aestivum L.) and rice (Oryza sativa L.) under two levels of CO2 (ambient and enriched up to 500 μmol mol(-1) ) and two levels of canopy temperature (ambient and increased by 1.5-2.0 °C) in free-air CO2 enrichment (FACE) systems and carried out a detailed growth and yield component analysis during two growing seasons for both crops. An increase in CO2 resulted in higher grain yield, whereas an increase in temperature reduced grain yield, in both crops. An increase in CO2 was unable to compensate for the negative impact of an increase in temperature on biomass and yield of wheat and rice. Yields of wheat and rice were decreased by 10-12% and 17-35%, respectively, under the combination of elevated CO2 and temperature. The number of filled grains per unit area was the most important yield component accounting for the effects of elevated CO2 and temperature in wheat and rice. Our data showed complex treatment effects on the interplay between preheading duration, nitrogen uptake, tillering, leaf area index, and radiation-use efficiency, and thus on yield components and yield. Nitrogen uptake before heading was crucial in minimizing yield loss due to climate change in both crops. For rice, however, a breeding strategy to increase grain number per m(2) and % filled grains (or to reduce spikelet sterility) at high temperature is also required to prevent yield reduction under conditions of global change.

Day respiration (Rd) is an important parameter in leaf ecophysiology. It is difficult to measure directly and is indirectly estimated from gas exchange (GE) measurements of the net photosynthetic rate (A), commonly using the Laisk method or the Kok method. Recently a new method was proposed to estimate Rd indirectly from combined GE and chlorophyll fluorescence (CF) measurements across a range of low irradiances. Here this method is tested for estimating Rd in five C3 and one C4 crop species. Values estimated by this new method agreed with those by the Laisk method for the C3 species. The Laisk method, however, is only valid for C3 species and requires measurements at very low CO2 levels. In contrast, the new method can be applied to both C3 and C4 plants and at any CO2 level. The Rd estimates by the new method were consistently somewhat higher than those by the Kok method, because using CF data corrects for errors due to any non-linearity between A and irradiance of the used data range. Like the Kok and Laisk methods, the new method is based on the assumption that Rd varies little with light intensity, which is still subject to debate. Theoretically, the new method, like the Kok method, works best for non-photorespiratory conditions. As CF information is required, data for the new method are usually collected using a small leaf chamber, whereas the Kok and Laisk methods use only GE data, allowing the use of a larger chamber to reduce the noise-to-signal ratio of GE measurements.

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