Networks and neighbors
July 31st, 2007

It seems to me that the new understanding that has emerged in our times has 3 steps: 1) realize everything is connected, 2) notice that the connecting starts with the smallest pieces, 3) know networks rule. When you have these 3 insights, it becomes clear that network rules are the same no matter what the pieces are that a network is connecting. That would mean, for example, that the same network rules are at work in MySpace, in an analog network of friends and in how intestines raise the odds against cancer happening. The following excerpt from a New York Science Times article today explains how neighbors are important—a new discovery: “It’s the simplest possible thing you could have expected, and it’s completely amazing.” Martin Nowak who is quoted is director of the Program for Evolutionary Dynamics at Harvard.

To study cancer, however, Dr. Nowak had to give his models some structure. In the Prisoner’s Dilemma, the players usually just bump into each other randomly. In the human body, on the other hand, cells only interact with cells in their neighborhood.

A striking example of these neighborhoods can be found in the intestines, where the lining is organized into millions of tiny pockets. A single stem cell at the bottom of a pocket divides, and its daughter cells are pushed up the pocket walls. The cells that reach the top get stripped away.

Dr. Nowak adapted a branch of mathematics known as graph theory, which makes it possible to study networks, to analyze how cancer arises in these local neighborhoods. “Our tissue is actually organized to delay the onset of cancer,” he said.

Pockets of intestinal cells, for example, can only hold a few cell generations. That lowers the chances that any one will turn cancerous. All the cells in each pocket are descended from a single stem cell, so that there’s no competition between lineages to take over the pocket.

As Dr. Nowak developed this neighborhood model, he realized it would help him study human cooperation. “The reality is that I’m much more likely to interact with my friends, and they’re much more likely to interact with their friends,” Dr. Nowak said. “So it’s more like a network.”

Dr. Nowak and his colleagues found that when they put players into a network, the Prisoner’s Dilemma played out differently. Tight clusters of cooperators emerge, and defectors elsewhere in the network are not able to undermine their altruism. “Even if outside our network there are cheaters, we still help each other a lot,” Dr. Nowak said. That is not to say that cooperation always emerges. Dr. Nowak identified the conditions when it can arise with a simple equation: B/C>K. That is, cooperation will emerge if the benefit-to-cost (B/C) ratio of cooperation is greater than the average number of neighbors (K).

“It’s the simplest possible thing you could have expected, and it’s completely amazing,” he said.


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