Games Nature Plays

“To me game theory is the coolest area of mathematics that exists,” said Joel Brown, professor in the Department of Biological Sciences, co-founder of Project Squirrel and one of a small cohort of evolutionary biologists currently using game theory in cancer research.

Professor Joel Brown and Rowdy the squirrel

Joel Brown and Rowdy. Photo by Jean Powlesland

“Basically, game theory is the study of strategic decision making. It uses mathematics to both create models of that decision making and to predict behaviors. It was born in 1944 with the publication of a totally unreadable book, Theory of Games and Economic Behavior, in which John von Neumann and Oskar Morgenstern systematized the math and formalized game theory.”

Games permeate our existence. They are in politics and diplomacy, military strategy, technology—and our everyday lives.

“The most obvious games are win/lose, but in fact a game is any time when your best move depends on the moves of others. Most are relatively easy to solve. Let’s say you are walking down the sidewalk and someone is walking toward you taking up all the space. What do you do? What do they do? Who drops back or moves aside, ceding the space? At what point does the move take place? That’s a game in its most basic form,” explained Brown.

After Neumann and Morgenstern, the next big advance in GT was in 1951 when mathematician John Forbes Nash, and game theorists Reinhard Selten and John Harsanyi proved the Nash Equilibrium. In this model, each person or group is doing the best they can given existing conditions. There is no benefit from changing strategy unless every player changes. In the Nash Equilibrium, players are locked in a game of “no regrets strategy” in conditions that are very stable and may often be quite bad—and the dynamic can be seen in everything from family systems to political dictatorships. The GT trio shared the 1994 Nobel Prize in Economics for this work.

Evolutionary Game Theory emerged in 1973 with the work of George R. Price and John Maynard Smith, in which game theory was applied to biology, specifically Darwinian evolutionary biology. “Evolution by natural selection seems to have a large number of games, particularly predator/prey games in which any adaptation of an organism is probably partially or wholly in response to the adaptation of another,” explained Brown.

“My favorite example—and this is what I first teach students who have no game theory—is,‘Why is there wood?’ I will get a human-centric response such as ‘So we can have houses and furniture’,” he said. “But everything in nature is for itself and wood exists because of competition for light. ‘How high can I get my leaves?’ says the tree. Well, how tall does the tree want to be as an adaptation? Taller than its neighbor. Those 350-foot-tall redwoods in California are simply monuments to an evolutionary game for light. No more, no less. Of course there are all the things associated with wood: woodpeckers have a place to live, beavers build things. But ultimately the explanation for why there are woody plants is a Nash Equilibrium—everyone tries to be a bit taller until getting taller in that particular poker game isn’t worth it and then we call that the canopy height.

Joel Brown and Rowdy

Joel Brown and Rowdy. Photo by Jean Powlesland

“I first became interested in game theory in economics. I thought it was cool that people could actually try to solve diplomacy problems mathematically,” said Brown. “Then I got into grad school at the University of Arizona and wanted to study population interactions. I chose desert rodents—kangaroo rats and pocket mice were my PhD animals. They were my road to squirreldom. I was applying adaptations to ecological systems in which natural selection comes into play and I wanted to apply EGT to this work. No one in our department was working with game theory so I sought out Thomas L. Vincent, who was an aerospace mechanical engineer and the closest thing to a GT expert on campus. He became my mentor and from that day until shortly before he died of pancreatic cancer in October 2009 we met or talked weekly. Our goal was to develop a more comprehensive theory for natural selection using game theory. We published papers together and had a good time.”

Brown joined the biological sciences faculty at UIC in 1987. He established his lab to continue his research using foraging theory and game theory to study predator-prey interactions and urban wildlife locally and globally. Enter the squirrels.

A fox squirrel and a gray squirrel

Fox squirrel (left) and grey squirrel co-exist in the western suburbs. Photo by Con Buckley

“I thought it was really important that grad students get to see research happening. Not everyone gets to zip off to exotic places and come back with data. I was looking around here and, of course, the most conspicuous beasts were squirrels and no one was studying them. We have a living laboratory right here in which we gather data and build the theory and models that we can then apply to mapping the behaviors and adaptations of more exotic or endangered creatures. Urbanites should understand that the squirrels and the possums and the robins are just as wild as the mountain lions and springboks. We have our own urban game park that is very exciting if you just look.”

Using EGT, scientist may be able to model and predict the behavior of various cancers… 

As Brown was teaching, researching and publishing, Tom Vincent began working with Robert Gatenby, who was then the director of radiology at the University of Arizona Medical Center. They were exploring the idea that cancer is an evolutionary game in which individual tumor cells are engaged in a game with each other, not with the patient.

“Tom’s partnership with Gatenby, who now runs the program on Integrative Mathematical Oncology at Moffitt Cancer Center and Research Institute, began in 2003. In 2005 I met Gatenby at Tom’s house,” said Brown. “I was very interested in the work but I was spread pretty thin. I just didn’t have time to get involved; Tom kept gently pushing. We got together at the International Society of Dynamical Games in Poland in June of 2008. Over conversation and beer I agreed to join the project. We published our first joint paper in 2009.

A breast cancer cell

Breast cancer cell image. Courtesy of Mark Lloyd, Moffitt Cancer Center

“In cancer, once you get past cancer initiation, the developing tumor is made up of populations that are now single-cell protists. Often people think of cancer as being a disease of the genes, a failure in the signaling systems in which the cells are going rogue, but really our body has spun off a new single-cell life form and once that life form has initiated it is a disease of Darwinian evolution. The patient is the world, the environment, the habitat. The tumor cells are the individuals that then begin to have an ecology. The tumor is their ecosystem. They adapt to their circumstances, they evolve to their habitat. Like beavers, they may engineer their environment, build things up and tear things down. They are really quite amazing in what they evolve to do. With this view, they are an evolutionary game.”

Brown and collaborators from Moffitt are focusing on breast cancer and in April presented their research on “Using Evolutionary Principles and Mathematical Modeling to Prolong Remission Response in Metastatic Breast Cancer” at the National Cancer Institute’s Office of Physical Sciences-Oncology Network Investigator’s Meeting.

Applying EGT to cancer research and treatment is not the current orthodoxy. Brown notes that there are a fair number of oncologists “trying to think about evolution, but there are only a handful of labs and people fully trained in evolution and natural selection who are focusing their expertise on cancer.”

Evolutionary Game Theorists who are focusing on cancer see great promise for treatment in the long term. Using EGT, scientists may be able to model and predict the behavior of various cancers and develop more individualized therapies and management strategies.

Martin Nowak at Harvard has done some good work and Dr. John Pepper at the National Cancer Institute is wonderful—an evolutionary biologist who has dedicated himself to cancer research. Our recent PhD alumnus, Paul Orlando (biological sciences 2012), has been recruited to work with him at NCI,” said Brown. “It’s definitely a big part of my work now, but it is one part. I do still love my squirrels.”

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