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 other ecosystem services. Models play an important role in this type of analysis as generally it is infeasible to test multiple scenarios by experiment. These models can be linked with algorithms that optimise for multiple objectives by searching a space of allowable management interventions (the control variables). Optimisation of landscapes for multiple objectives can be computationally challenging, however, particularly if the scale of management is typically smaller (e.g. field scale) than the scale at which the objective is quantified (landscape scale) resulting in a large number of control variables whose impacts do not necessarily scale linearly. In this paper, we explore some practical solutions to this problem through a case study. In our case study, we link a relatively detailed, agricultural landscape model with a multiple-objective optimisation algorithm to determine solutions that both maximise profitability and minimise greenhouse gas emissions in response to management. The optimisation algorithm combines a non-dominated sorting routine with differential evolution, whereby a ‘population’ of 100 solutions evolves over time to a Pareto optimal front. We show the advantages of using a hierarchical approach to the optimisation, whereby it is applied to finer-scale units first (i.e. fields), and then the solutions from each optimisation are combined in a second step to produce landscape-scale outcomes. 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 initialising the control variables for half of the population of solutions with values expected to be near optimal. Our analysis shows the importance of aligning a policy or management recommendation with the appropriate scale.