The game theory of life

Human genome
Computerised image of a fragment of the human genome. Photograph: AP

Original story reprinted with permission from Quanta magazine, an editorially independent division of, whose mission is to enhance public understanding of science by covering research developments and trends in mathematics and the physical and life sciences.







"If you do this day after day, at the end of the year, you will do almost as well as if you had followed the best expert from the beginning," said Christos Papadimitriou, a computer scientist at the University of California, Berkeley. "It's as if you were omniscient in the beginning, singling out the best expert and following their advice day after day."



Umesh Vazirani science


Traditional applications of game theory to evolution examine how evolutionary processes shape an individual's behavior. They have also been used to study the evolution of altruism and other properties. "But here, we're talking about something completely different," said Adi Livnat, a biologist at Virginia Polytechnic Institute in Blacksburg, Va., who collaborated on the study.  The new study focuses on genes rather than individual organisms, and on the genetic makeup of the population instead of behavior.

The approach could illuminate a long-standing mystery in population biology. Just as in the financial world, where it's best to keep a diversified portfolio, Vazirani and his collaborators found that the algorithm values both fitness and diversity. You might be tempted to place all your money on a soaring stock. But if circumstances change and that stock starts to tank, you're better off having invested in a more balanced selection. Similarly, an organism's genes may be perfectly tailored to a particular set of environmental conditions, but if those conditions change, a genetically diverse population is more likely to survive.

"Evolution is, of course, interested in performance," Papadimitriou said.

"But it's also interested in hedging its bets, keeping around a lot of genetic diversity because who knows what will come next."


The findings provide a "speculative suggestion" for how this might happen, though the authors don't propose a specific mechanism, said Nick Barton, a biologist at the Institute of Science and Technology in Austria who was not involved in the study. "I don't think it gives us the algorithm that can achieve the diversity we see on Earth in 3.5 billion years, when life first began," he said.

Stearns and others in the field say it's too soon to assess how the findings will affect our understanding of evolution. Even though the connection between different fields is interesting, "it does not actually help us understand biological evolution," said Chris Adami, a physicist and computational biologist at Michigan State University, who was not involved in the study. "Unless such a relationship allows you to say something new either in computer science or biology, it's just an observation."

Evolutionary biologists are often skeptical of mathematical insights from outsiders. Although mathematicians and computer scientists regularly publish in the field, biologists disagree over how much their contributions have done to shape it. "I think it will take some time to figure out how the paper plays out," Stearns said. "If this doesn't cause any new data to be gathered, then it won't be very important." Even if the findings don't prove relevant in the short-term, they might prove important over the long –term. Sometimes it can take decades before the right technology or approach arises to test a new theory, Stearns said.

The equations in the study are based on certain assumptions that may limit their applicability to the real world. For example, the equations don't account for mutations, which would introduce new alleles, or strategies, into the game. (Adding this factor makes the mathematics much more complex.) Some say this simplification is a serious drawback, while others maintain that it is not so important in the short term, when existing variations have the strongest impact. "What happens when you move away from the assumptions?" said Lee Altenberg, a senior fellow at the Konrad Lorenz Institute in Austria. "They have pinned a single point on the map. But to know whether that means anything, you have to start departing from that point."

One outcome of the analysis is likely to puzzle biologists. According to the standard view of evolution, the further a generation lies in the past, the less impact it has on the present — your ancestors from 1,000 years ago probably had less effect on your fitness than your grandparents. But if the Berkeley team's insights hold up, "it shows us that every past generation contributes equally to what happens in the next generation," Stearns said. "That's an intriguing and wildly implausible claim from the standpoint of regular evolution." Papadimitriou said his team was also perplexed by that outcome. "It is something that hopefully will make researchers rethink, revisit and interpret," he said.

"You can't really test these theorems in relation to real life," Barton said. "They are tools for getting intuition about how to understand evolution."

Evolution and entropy

One of the surprising discoveries of Papadimitriou's study is that natural selection values not just fitness, but also genetic diversity, which in more technical terms is referred to as entropy. This view that evolution optimizes not just mean fitness but mean fitness and entropy is not well known, "but I think it's a deep observation," Adami said.


"Applications of entropy in evolution have had a bad name, because they were very ill-defined," Barton said. "More recently, there have been some interesting, and much sounder, ideas, which make a link between fields that are addressing a similar issue: statistical physics and evolutionary biology both try to understand the overall properties of a complicated system, independent of the microscopic details."

These more recent results are mathematically sound, but they still don't connect well with existing biological understanding, he said. "So it's not clear to biologists how [the results] might help explain their open questions."
