Model-based optimisation of agricultural profitability and nutrient management: a practical approach for dealing with issues of scale

To manage agricultural landscapes more sustainably we must understand and quantify the synergies and trade-offs between environmental impact, production and ecosystem services. Models play an important role in this type of analysis as generally it is infeasible to achieve this using experiments alone. Here we link a relatively detailed, agricultural landscape model with a multiple-objective optimisation algorithm to determine solutions that maximise on both profitability and minimise greenhouse gas emissions in response to fertilizer application. Optimisation of landscapes for multiple objectives can be complex, particularly when there are a large number of control variables. We explore some practical solutions to such a problem, and show the advantages of using an hierarchical approach to the optimisation, whereby it is applied to finer scale units first, and then the solutions from each optimisation are combined in a second step. We show that if there is no interaction between units then the solution derived using such an approach will be the same as the one obtained if the landscape is optimised in one step. However, if there is spatial interaction, or if there are constraints on the allowable sets of solutions then outcomes can be quite different. In these cases, other approaches to increase the efficiency of the optimisation may be more appropriate – such as partially seeding the population with near optimal solutions.