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.

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Summary Loss on ignition (LOI) is one of the most widely used methods for measuring organic matter content in soils but does not have a universal standard protocol. A large number of factors may influence its accuracy, such as furnace type, sample mass, duration and temperature of ignition and clay content of samples. We conducted a series of experiments to quantify these effects, which enabled us to derive (i) guidelines for ignition conditions (sample mass, duration and temperature), (ii) temperature‐specific soil organic matter (SOM) to soil organic carbon (SOC) conversion factors and (iii) clay content‐dependent correction factors for structural water loss (SWL). Bulk samples of a sandy soil (4% clay) and a silt loam soil (25% clay) were used to evaluate the effects of ignition conditions. Samples with a range of clay contents (0–50%) were used to quantify conversion and correction factors. Two furnaces, one without and one with pre‐heated air, did not show significant differences in terms of within‐batch LOI variability. In both furnaces less combustion occurred close to the door, which necessitated tray turning at half‐time as this reduced the standard deviation per batch significantly. Variation in mass loss declined exponentially with sample mass (range, 0.15–20 g). The LOI increased with duration at lower temperatures (≤ 550°C) for the sandy soil. At greater temperatures (600 and 650°C), no effect of duration was found. For the silt loam soil, LOI values increased with duration for each temperature, which was attributed to SWL. The SOM to SOC conversion factor decreased strongly with temperature at an ignition duration of 3 hours from 0.70 (350°C) to 0.57 (500°C) and stabilized around 0.55 between 550 and 650°C, indicating that at temperatures ≥ 550°C all SOM had been removed. The clay correction factor for SWL increased from 0.01 to 0.09 as the temperature of ignition increased from 350 to 650°C. To minimize within‐batch LOI variation we recommend a standard ignition duration of 3 hours, tray turning at half‐time, a sample mass ≥ 20 g and temperatures equal to or greater than 550 °C. To avoid over‐estimates of SOM through structural water loss, the presented SWL correction procedure should always be applied.

Abstract. Grazing cattle exert positive and negative effects on pasture production. It is shown that at a fertilizer nitrogen (N) input of 200 kg N ha -I yc 1 and more, the benefit from N circulation through urine and dung is not of significance for the pasture as a whole. Of the negative effects, poaching has the greatest influence on the response of pasture production to N fertilization.Two one-year experiments are described which showed that there were no significant differences in the response of grassland production to N fertilization between cutting and grazing usage above about 200 kg N ha -I yc 1 •

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In a previous study (Yin et al. 2000. Annals of Botany 85: 579-585), a generic logarithmic equation for leaf area index (L) in relation to canopy nitrogen content (N) was developed: L=(1/ktn)1n(1+ktnN/nb). The equation has two parameters: the minimum leaf nitrogen required to support photosynthesis (nb), and the leaf nitrogen extinction coefficient (ktn). Relative to nb, there is less information in the literature regarding the variation of ktn. We therefore derived an equation to theoretically estimate the value of ktn. The predicted profile of leaf nitrogen in a canopy using this theoretically estimated value of ktn is slightly more uniform than the profile predicted by the optimum nitrogen distribution that maximizes canopy photosynthesis. Relative to the optimum profile, the predicted profile is somewhat closer to the observed one. Based on the L-N logarithmic equation and the theoretical ktn value, we further quantified early leaf area development of a canopy in relation to nitrogen using simulation analysis. In general, there are two types of relations between L and N, which hold for canopies at different developmental phases. For a fully developed canopy where the lowest leaves are senescing due to nitrogen shortage, the relationship between L and N is described well by the logarithmic model above. For a young, unclosed canopy (i.e. L < 1.0), the relation between L and N is nearly linear. This linearity is virtually the special case of the logarithmic model when applied to a young canopy where its total nitrogen content approaches zero and the amount of nitrogen in its lowest leaves is well above nb. The expected patterns of the L-N relationship are discussed for the phase of transition from young to fully developed canopies.

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