Models for pasture yield in response to phosphate application Academic Article uri icon


  • 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.


  • Ratkowsky, DA
  • Sale, PWG
  • Tennakoon, SB
  • Johnson, D
  • Simpson, PG

publication date

  • 1997