Insights from the Landscape Decisions Programme’s maths modelling working group

The Landscape Decisions Programme Coordination Team (PCT) have set up a working group to examine the role of mathematical modelling in informing landscape decisions. Sergei Petrovskii explains the value of the working group and details some insights from the discussions.

Modern landscapes are complex systems where many environmental, economic, political and cultural factors, processes and constraints come together. Whatever the incentive may be for a change in landscape use, it is rarely possible to identify a ‘best case’ scenario or solution using traditional semi-intuitive approaches alone, such as courtroom style panel decisions based on expert opinions.

Thus, one reason why we decided to set up a maths modelling working group is to try to make use of modern mathematical techniques that allow us to consider landscapes as a formal optimisation problem. Although this idea is not entirely new, previous attempts to use optimisation methods have tended to fall below the required level of systems complexity and hence have largely failed to provide consistent advice to decision-makers.

One particularly relevant context in which standard optimisation techniques fail dramatically is when dealing with systems featuring multiple levels of decision-making where an optimum (in some sense) needs to be reached between the interests of national, regional and local authorities. This, however, can be resolved by using more advanced mathematical methods of multi-criteria multi-level optimisation.

Key insights

The maths modelling working group has focused on a variety of issues and made considerable progress. Several points are worth highlighting from the discussions so far.

First, in relation to land use change, decision-makers do use optimisation routinely, but this is often done intuitively rather than formally. Although decision-makers themselves may not use the word ‘optimisation’, the whole idea of looking for a ‘best possible’ solution is in fact an attempt to optimise. However, intuitive – that is, informal, not rigorous – approaches are bound to fail as they are incapable of coping with the inherent systems complexity that underpins decisions.

Second, there are many examples where intuitive approaches have failed to find the ‘best’ solution to a land use problem. The maths modelling working group has identified some of these examples. These cases may benefit from the use of advanced mathematical optimisation methods.

Third, the working group has conducted a revision of modern optimisation methods and the methods that are particularly relevant for landscape decisions, such as NSGA2 algorithms, have been identified.

Fourth, two case studies have been identified to demonstrate the power of modern mathematical optimisation methods. These are the farmers-pollinators system, and the carbon offsetting system. Work has started on developing a hybrid modelling-optimisation approach for these systems. Finally, although there is no chance that formal optimisation techniques will replace humans in decision-making, the use of optimisation methods can provide efficient and consistent advice to relevant authorities to enable an informed decision on land use to be made. This will help ensure that modern multifunctional landscapes are used in an efficient and sustainable way.


Sergei Petrovskii is the Landscape Decision Programme’s Lead expert in Environmental Mathematics and a Professor at the University of Leicester. He is a mathematician with 30 years of experience in the modelling of natural phenomena. His research focuses on nonlinear dynamics, dynamical systems’ application to ecology and ecological complexity.