What is Land Resource Management

How does the interaction of ecosystems work in a landscape - from the soil with its countless microorganisms to plants and animals - and how can people live and work in them without destroying their livelihood? Ralf Seppelt is researching these questions at the Helmholtz Center for Environmental Research (UFZ) in Leipzig. The studied mathematician and landscape ecologist relies on mathematical models and simulations. He experiences the best moments when he succeeds in eliciting far-reaching statements about reality from simple models.

Professor Seppelt, you did in the ninetiesStudied technical mathematics. Why did you startto be interested in ecological questions? That was due to the orientation of the course. At the Technical University of Clausthal, we were forced to study computer science and an engineering application subject in addition to a full degree in mathematics. I decided on measurement and control technology. In these lectures, the mathematicians among us immediately looked through the algorithm on the front of the board, but also learned what it means for the application. Because I found these applications so exciting, I looked for a thesis with the engineers.

On a topic from ecology? Yes, I have modeled social-ecological systems. It was about the acceptance of recycling systems and the question of how much subsidies are necessary to keep these systems stable. This brought me to the heart of the environment and, above all, models and simulation applications.

So it was more of a coincidence that they started doing mathto apply to ecological issues? Yes, actually I wanted one thing above all at university: broaden my horizons, deal with other disciplines, but also go deeper. I had a certain affinity for the environment, but the fact that I got a PhD position at the Technical University of Braunschweig, where it was about agro-ecosystems, was again a coincidence.

You have been head of the Landscape Ecology Department atUFZ. Her research area is land resource managementand especially the question of the interactions betweenHuman and nature. What does it mean exactly? Ecosystems are mostly used in some form by humans, be it because we live there, produce food or because we need clean water. Almost everywhere in the world everything that happens in our landscapes is anthropogenic overprinted, influenced by humans. That is one side, the socio-ecological side. On the other hand, we largely do not understand how the ecosystems themselves function. We understand individual processes such as photosynthesis, plant growth or pollination. It looks different when we look at landscapes. For example, which hedges or forests do we need to have enough insects to fight pests or pollinate flowers so that we can produce the food we need - this is partly unknown. We landscape ecologists therefore have to answer two questions: How do ecosystems work and how can we use them in such a way that we achieve sufficient yields without changing ecosystems too much?

Can you explain this with an example? We have a research project in the Philippines about the population dynamics of insects that fight a pest: a small brown beetle that spreads very quickly and attacks the rice fields. Rice farmers believe that the best way to counter this is with pesticides. We think it can be beneficial not to do just that. Because with the pesticides you also catch the insects that fight the pests. From the perspective of dynamic modeling, the question arises as to when the right time is for which measure. Using pesticides can make sense, but it can also be worth waiting a few days because natural pest control will solve the problem, and it will take longer. From a mathematical point of view, these are dynamic process models, differential equations that I have to parameterize. And then they also enable a simulation.

It's about finding the ideal time to use theFind pesticides. Yes, exactly, these are actually non-linear optimization problems.

Since when have ecological processes been modeled at all? It's been a long time. The classic textbooks are from the nineties. Ultimately, the modeling in ecology goes back to considerations in theoretical biology, how one can recognize predator-prey phenomena with coupled systems of differential equations. And since there have been powerful computers for simulations, that is for about thirty years, biologists have also applied mathematics to real processes. This development ran parallel to modeling in climate research.

The climate with its many interactions appearsalready enormously complex. Are models representing ecological systemsrecreate, not much more dynamic and complex? Not necessarily. The reports of the Intergovernmental Panel on Climate Change (IPPC) are also becoming increasingly complex. At the beginning they described the atmosphere, twenty years later also the soil layers and the oceans with the exchange processes that take place there. At some point the vegetation was added. How complex do I have to make the simulation and when do I have to stop? There is a long and ongoing discussion among modelers about this question. And this question is especially important under the aspect that I want and have to communicate results. Because if I build a simple model that is easy to explain and shows decisive patterns that bring important insights, then it might be said: This is too simple! If the model is more complicated and thus perhaps closer to reality, then it says: The predictions are too uncertain.

How do you go about modeling an ecological system? I start by describing it conceptually, then I code the individual processes mathematically. Most of the time, I find that I've done something wrong. From this I learn which ecological processes I should actually have taken into account. And I am learning to better understand individual processes within an ecosystem. In this respect, the development of the model is the decisive phase. This modeling process and then the decision on how complex I make my model, which data and processes I include and which not, that is one step. The other concerns the mathematical methodology.

Where are the math challenges? In statistics, we will need greater competence in the analysis of large and also heterogeneous databases in the future. Because we now also measure landscapes by remote sensing from airplanes or via satellite and thus generate much denser data. The second challenge concerns integration. If we include more and more processes in the models because otherwise we cannot describe ecosystems correctly, then at some point simple differential equations will no longer be sufficient. If I have to deal with discrete processes or disturbances, i.e. non-linear phenomena that are very unpleasant for mathematicians, I can no longer handle them mathematically and analytically, but only numerically.

How do you solve these problems? We are using more and more algorithms here at the UFZ to analyze the existing models. That means, we do optimization runs and use this to look for combinations for an optimal use of land. For this you need a lot of numerics and high-performance computers.

Do you work with mathematicians on this? Two mathematicians are currently working in the Landscape Ecology Department at the UFZ, both of whom are PhD students. They are, so to speak, just like me, on the "wrong track". The other of the thirty colleagues are all environmental scientists with a strong quantitative analytical background.

They also derive recommendations from the simulations for whichRice farmers in the Philippines as well as for fruit growersin Saxony, governments or international organizations.What is involved in communicating these resultsat? Having a solution is one thing, but then explaining what that means for the application is one of the really big challenges. I also had to learn that first. An example: Last year we published a study with which we could mathematically show that not only resources such as crude oil, but also the renewable energy and food resources that we have in the world are limited. To do this, we took a simple basic model from resource economics. The mathematical analysis was comparatively time-consuming, the method part alone in the paper took up several pages. But the content-related discussion of the results was much longer. And it was fine like that. We really got a message across. The study hit the experts and caused a stir in the press. That would not have been possible with mathematics alone, but also not without mathematics. Sometimes you don't even have to do big, complicated math. A very simple model, as in this case, can deliver an incredibly rich treasure trove of results. And that's what ultimately appeals to me about the application of mathematics in environmental sciences.

In this sense, is mathematics an instrument for you ormore? Mathematics is more to me! It's the way I think, how I approach things. This is particularly evident in the phase in which I design the mathematical models. And it is precisely in this approach, in this understanding of the system, that for me the real achievement of mathematics lies.

Would you teach young mathematicianswho are interested in the application area ecology,In addition to the mathematics course, a specialist courserecommend? In principle, a degree in mathematics is sufficient. But you should think outside the box during your studies. It is enough to have a real interest in a practical question. And that doesn't even have to be an ecological question. For example, one of our two mathematicians here analyzed field tests at an agricultural research institute for her diploma thesis and tried out new statistical methods in the process. That was statistically interesting, and what mattered to her was that she could use real data sets. The other took planning and optimization models from the economy as part of a stay abroad in Australia in order to plan nature conservation areas and to optimally show costs. Your working group at the university implemented the entire conservation plan for the Great Barrier Reef off the north coast of Australia. You can use math in so many different areas, not just banking and insurance. But you need a certain openness to get there.

Kristina Vaillant is a freelance journalist in Berlin and works regularly for the media office of the German Association of Mathematicians.