*Lewi Stone explains how Alan Roberts brought physics and mathematics to bear on understanding complex ecological systems.*

It is important to realize that the renaissance in biologically inspired physics that we see today is probably in a large part due to the few brave physicists like Alan who broke away from the Los Alamos paradigm of modelling atomic bombs. These pioneers in the 70s and 80s tried to find a new way, where physics could also help understand the “Laws of Nature” and their biological underpinnings.

Unfortunately I am unable to attendtoday’s event celebrating Alan’s life [held 3 February, 2018 in the University of Melbourne]. But thank you for giving me the opportunity to share some of my experiences working with Alan as one of his PhD students. I first met Alan in 1984 at his office in the Monash University Physics Department to discuss beginning a PhD. Alan appeared on crutches, and explained with an unforgettably big grin that he had just come back from San Diego where he had broken his now plastered leg in a motor-bike accident. From the outset, I sensed immediately that this was definitely not the ivory-tower university professor I was expecting to meet.

Alan quickly launched into a discussion about his research interests. With great enthusiasm, he proceeded to show how he could set up mathematical equations to investigate large complex **living** ecosystems. If you think about it, this sounds an almost impossible thing to do. But Alan made use of an ingenious framework that by means of an almost “magical reduction”, he was able to transform incredibly complex systems into relatively simple and elegant equations. In all seriousness, it left the impression that we would be working with, not Newton’s “Laws of motion,” not Einstein’s equations of relativity, but something akin to Roberts “Laws of Nature.” And I think this is where Alan was heading, although he would never describe it that way.

More amazingly, Alan could rigorously prove that this “magical reduction” holds accurately in important circumstances, so that the simplified ecosystem equations were rigorously valid. Alan attempted to use the equations to understand how ecosystems sustained themselves, and to explore their instability thresholds. For Alan, the “golden egg” was to find an answer to the abstract question: *“Does the complexity of living systems give them robustness, or does complexity endow living systems with inherent fragility?” *

For example, diverse tropical ecosystems are characterised by millions of species interactions. You might suspect that because of this massive complexity, the break-down of only one ort wo interaction links in the system would have minimal impact. Yet the mathematics shows that the more complex these systems are, the more unusually fragile they become to interactions dropping out, and could even result in large-scale species extinctions.

Alan spent years studying these sorts of phenomena.

Alan’s goal was to borrow ideas from statistical physics to understand the processes that explain ecological stability. Differential equations, eigen values, nonlinear dynamical systems, chaos, random matrices – all the things we learnt about in our university maths courses, Alan was applying to help him study the living world. It was truly an inspirational introduction and I was pretty much hooked into beginning a PhD with Alan, right on the spot. I would be joining the ranks of his other PhD students, Ken Tregonning and George Nassios.

Alan clearly knew this material from every angle – from the angle of a theoretical physicist; from the angle of a mathematician; from the angle of an ecologist with a great love for the natural world; and from the angle of a remarkable individual interested in how complex societies can structure themselves in ways that allows them to persist sustainably.

At the time, theoretical ecology was a young experimental discipline. There were only a few small scientific groups around the world grappling with these problems. In this respect, Alan was extremely brave and taking a substantial academic career risk. He dangerously moved away from his established career in theoretical atomic physics, and moved into the science of modelling ecosystems, which he himself was almost single-handedly pioneering in Australia.

In the end, today, it has become a huge flourishing discipline. Most modern universities around the world have a working research group in theoretical ecology. Every math department, and many physics departments, have a faculty member, or research group that connects with this work. Mathematical biology is now one of the hottest research areas in Science. And Life Science departments are crawling with physicists studying bioinformatics, and the dynamics of living systems.

So Alan was there at the start. But back then in Australia in the 80s he was pretty much alone and at the centre o fit. Moreover, he was making quite a name for himself on the international scene. Alan was publishing articles in top journals. Maybe every 1-2 years he had a publication in “*Nature*”, the most prestigious science journal on the planet, and the journal that most scientists usually can only dream to publish in. I doubt, at the time, if there were many other scientists at Monash with Alan’s publication success in top-tier journals.

It is important to realise that the renaissance in biologically inspired physics that we see today is probably in a large part due to the few brave physicists like Alan who broke away from the Los Alamos paradigm of modelling atomic bombs. These pioneers in the 70s and 80s tried to find a new way, where physics could also help understand the “Laws of Nature” and their biological underpinnings. I should also mention that now, some 30+ years later, there is a renewed interest specifically in Alan’s publications. Works with Ken Tregonning, George Nassios and myself (Alan’s students), on the feasibility and stability of ecosystems are being rediscovered and Alan’s studies which advocate analyses of large random matrices from 30 years ago, are now viewed as cutting-edge science. They also form a central part of the new discipline of “Network Science” which applies similar theory to the internet, terrorist networks, and even financial markets and global banking networks.

As a physicist, Alan was a“problem solver.” Maths and physics present a whole universe of equations waiting to be solved. But Alan was also very involved in solving real human problems. In World War II he served in the Australian airforce in the New Guinea campaign, and as he often told us, this whole period opened his eyes to international politics and contributed to the evolution of his own political ideas and worldview, and certainly the physicists contributions to this. I’m sure many of you will be discussing Alan’s political interests and contributions today.

Having Alan as a supervisor, over many years proved to be an invaluable and unforgettable education, that often went well beyond physics. The weekly PhD meetings covered vast amounts of intellectual terrain. They exposed us to so many new ways of viewing the world, as we learnt to follow and appreciate Alan’s complex analytical thinking processes, which he so loved to share with us. Whether it beMonash University politics (he was president of Monash Staff AssociationFAUSA), analysing the nuclear arms race as the Cold War was dragging to an end, or deciphering Umberto Eco’s latest novel *The Name of the Rose*, Alan was there on top of it all, challenging us and explaining it to us. Although Alan’s different interests and activities took a great deal of his time, he was always pushing us through the PhD, and all his doctoral students ended up doing very well for themselves.

Alan was a deep thinker and multi-dimensional personality who, as a physicist, not only spent most of his career mathematically modelling “complexity,” but he was also revelling in it in his own real life. He is greatly missed.

**Lewi Stone teaches at RMIT University and Tel Aviv University**