Complexity theory, power laws, bears and honey

Following from my comment on Laszlo's last post, I looked up one of the topics that always burns in the back of my mind: complexity theory.

As a first stab, I read this article from 2001. Old, so perhaps you have heard about it already?

In a nutshell, paleontologists are puzzled by the dramatic discontinuities in the extinction patterns of life on earth over its history. Occasionally there are cataclysmic episodes that causes mass extinctions. Physicists call this phenomenon Self-Organized Criticality (SOC).

"In recent years, some physicists and other adherents of a new field called complexity have argued that the answer involves a simple mathematical theory -- the same one that may explain the collapse of a sand pile or a crash in the stock market. But their suggestions have drawn fire from paleontologists, the group traditionally charged with investigating life's past."

The SOC physicists traced the lengths of time that ancient groups of animals had survived, and found (surprise!) a power-law behaviour: most of the time, things were quiescent, but occasionally there was a mass extinction--the same behaviour typically seen with earthquakes, volcanic eruptions, and solar flares. This didn't have to do with external events (like an asteroid hitting the earth), but evolved as a consequence of how the different species interacted with each other. The complexity theorists say that the power-law "fingerprint" is indicative of a system in a critical state.

The main jam was that the paleontologists re-analyzed the data "with the appropriate statistical tests", and no power-law behaviour emerged. They again tested it with a new database of 36,000 genera showing when the groups appeared and when they vanished ("the best data set that is available at this point in time"), and still no evidence of a power-law pattern was found.

Another complexity theorist put it this way: "It's not enough to say that self-organized critical models give power laws, and we see power laws in the fossil record, and therefore they must be self-organized critical. That's logic on the same level as saying, 'Bears like honey, my wife likes honey, therefore my wife is a bear.'"

As a result, Richard Sole, one of the SOC physicists, has modified his ideas and decided to collaborate with Douglas H. Erwin, a paleontologist at the Smithsonian Institution, to see if complexity theory can help explain the appearance of new species after major biological crises.

I doubt this is the last we hear of complexity theory bashing heads with other fields--perhaps this happens on a power-law basis??--and i'm sure there is a lot of interesting stuff to mine...