You Let Me Complicate You - Complexity Theory and Natural Selection (Part I)

The theory of natural selection has never lacked for critics. One of the more recent tweakings is coming from a new branch of mathematics.
Complexity theory addresses…well, complexity, in systems from computer networks to corporate structure, the stock market and biology. Complexity theory encompasses chaos theory and systems theory, and may soon change the way we study biological systems. While the original application is computers and mathematical systems, complexity may be applied to natural systems such as evolution.

One of the biggest handicaps in biology is study by reduction. We learn about a system (an organism, an ecosystem) by breaking it down into its composite parts and studying them.
While this may teach us about the structures, it teaches us precious little about the dynamics of intact systems, and affords us almost no predictions about system outcomes. We can learn much from the separate parts of a tree, but less about the functioning of all these parts together, still less about the tree’s dynamic role in an ecosystem.
This is a problem which has more significance as the scientific order of study increases. Physics feels this pinch less so, chemistry perhaps a bit more. Biology perhaps most of all, as it contains such complex structures as ecosystems, human bodies, and the history of species.

Enter complexity. A mathematical modeling of complex systems, it discerns holistic patterns in the growth and change of systems over time. Complexity theory suggests that systems can be inherently self-organizing and self-directing, given the proper parameters.
If a system is too chaotic, it will break down – if it is too static, it will never change. The most efficient point to be at, called the Edge of Chaos, is right before the system disintegrates into chaos. At this point, new properties of the system emerge, such as the ability to self-organize, sharply increased productivity and gradual, measured growth and change. These features seem to be common to many kinds of systems. It is the implied universality that is most surprising, fundamentally adjusting how we think about the terms “random” and “chance”.
To take an example from the natural world, schools of fish darting about reefs in perfect (or near-perfect) synchronization appear to be the very pinnacle of order, perhaps under the directive of an extremely talented head fish, or born with an ability to perform underwater choreography that would shame the Riverdance troupe. But each fish seems to follow only one directional directive; go in the average direction of your neighbors. From this one imprecise rule, comes the overall order we see in the schools – order from chaos.

The existence in nature of these self-organizing complex properties in any form is thought provoking. Such self-organizing forms may be the most beneficial. This widespread occurrence of properties is one of the strongest arguments for natural selection to accommodate complexity: It is a system. It does exhibit this self-organizing property of other systems found at the edge of chaos. Are these system properties responsible for the order we see in the living world today?

So can we apply complexity theory to natural selection?
Complexity theory has been postulated to apply to such chaos-defying events as the origin of life, extinctions, and speciations, shoring up the holes in the theory of natural selection as it applies to questions of order and chaos.
The major criticism of complexity theory is also its main drawback in the natural sciences: it is essentially useless in many situations because of the lack of data to model initial conditions. It’s fine and good to simulate the evolution of species, but we don’t have all the required data for those species yet.
It is a new branch of math, which has not stood the tests of time or falsifiable experiments. In the case of biological applications, it still lives largely in the realm of theory, albeit one holding much promise.

Next time, the conclusion of our 2-part debut: Your intrepid guide will offer up some examples; Kaufmann’s autocatalytic sets, the origin of life, and some concrete math for fellow eggheads.