Models for pasture yield in response to phosphate application

Abstract

Summary. This paper examines the response of total annual dry matter production of pastures to a range of rates of phosphate application supplied in fertilisers from various sources. Data from the National Reactive Phosphate Rock Project were used to compare the goodness-of-fit of 2 non-linear regression models, the Mitscherlich and rational functions models, both of which are convex curves lacking an inflection point. These models were fitted to the data from the 2 ‘core experiments’ and tended to give closely equivalent results, with the Mitscherlich model fitting somewhat better in two-thirds of the cases. Generally, both models fitted the data well, with a test for ‘lack of fit’ being non-significant. The models proved capable of fitting all the various responses observed in the 2 experiments, including: (i) the ‘classic’ asymptotic regression response where dry matter production rises gradually with decreasing slope from a baseline at zero added phosphorus to approach an asymptote at very high rates of phosphate application; (ii) a very rapid rise at a low phosphate rate to an almost constant response value with increasing phosphate application; and (iii) an almost linear growth rate with non-zero slope throughout the phosphate application rate range. The Mitscherlich model was generally more stable for the less classical responses, and its parameters were consistently easy to interpret. Hence, the Mitscherlich model is recommended as suitable for describing pasture yield as a function of phosphate application. A new measure of relative fertiliser performance is proposed, based upon the area below the curved line defined by the fitted Mitscherlich curve, which is simultaneously above the horizontal straight line representing the baseline of no added phosphate. The ratio of this area calculated for a test fertiliser to the similarly defined area calculated for a soluble reference fertiliser such as superphosphate serves as a relative performance index. Also, when the area calculated for the reference fertiliser is less than 10% of the total area under the fitted curve, the site is considered to be unresponsive to phosphate addition.

Homeostatic regulation of elemental stoichiometry by Lemna gibba L. G3 when nutrient interact with toxic metals

“…The growth rate and yield values obtained in this study compare well with our previous studies as well as those reported by other in literature (Finlay et al 1999;Ratkowsky et al 1997). In the first 4-5 days of culture, there was Fig.…”

“…Influence of PO 4 3-on growth rate and biomass turnover reported in this study, have been previously observed and reported elsewhere (Ratkowsky et al 1997). Ratkowsky et al (1997) adopted Mitscherlich's model (Y ¼ a À be Àcx , where Y is yield; a is the maximum yield; b is difference between maximum yield and actual yield at x = 0; c is the rate of approaches maximum yield; and, x is the initial PO 4 3-concentration in the media) to determine the threshold PO 4 3-concentration.…”

“…Ratkowsky et al (1997) adopted Mitscherlich's model (Y ¼ a À be Àcx , where Y is yield; a is the maximum yield; b is difference between maximum yield and actual yield at x = 0; c is the rate of approaches maximum yield; and, x is the initial PO 4 3-concentration in the media) to determine the threshold PO 4 3-concentration. Applying the model to the current data reveals that the influence of PO 4 3-on L. gibba yield reached a threshold was below 1 mg L -1 .…”

Resource manipulation in uranium and arsenic attenuation by Lemna gibba L. (duckweed) in tailing water of a former uranium mine

“…Values are mean of 4 replicates and error bar are standard deviation.off at higher plant phosphorus concentrations. This relationship between L. gibba yield (y) and the PO 3− 4 concentrations fitted into regression based on Mitscherlich model(Ratkowsky et al, 1997) with r 2 = 0.935 and r 2 = 0.897 ( p ≤ 0.001) at 95% confidence interval of goodness of fit for the laboratory and field experimentsTABLE III Growth rates of L. gibba under PO All NH + 4 variation experiments in laboratory were conducted in modified standard Hutner medium. Standard Hutner medium has 40 mg l Control in the field (non-amended tailing water) had 0.013 mg l −1 PO 3− 4 and NH + 4 below detection limits.…”