Journal of Applied Mathematics and Decision Sciences
Volume 1 (1997), Issue 1, Pages 27-43

Dynamical systems modelling of the interactions of animal stocking density and soil fertility in grazed pasture

I. D. Wickham,1 G. C. Wake,1 S. J. R. Woodward,2 and B. S. Thorrold2

1Department of Mathematics, University of Auckland, Auckland, New Zealand
2AgResearch, Whatawhata Research Center, Private Bag 3089, Hamilton, New Zealand

Copyright © 1997 I. D. Wickham et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


To examine the long-term effects of fertiliser application on pasture growth under grazing, a mathematical representation of the pasture ecosystem is created and analysed mathematically. From this the nutrient application level needed to maintain a given stocking rate can be determined, along with its profitability. Feasible stocking levels and fertiliser application rates are investigated and the optimal combination found, along with the sensitivity of this combination. It is shown that profitability is relatively insensitive to fertiliser level compared with stocking rate.