Evolutionary Networks

In response to the previous post, here's a story from Guardian UK/America about ongoing research on networks. It features the work of Lieberman and Nowak on evolutionary graph theory. This mathematics, arranged in a grid network, shows the particular ways that networks evolve over time, be they cancer cells or human social networks. Lieberman's evolutionary graph theory [Harvard.edu] describes several features of dynamic networks. It is a general theory of how population structure affects evolutionary dynamics:

• "random" vs. "scale-free" networks [scale-free networks develop larger inequalities]

• the fixation-probability of mutants [evolutionary agents]

• graphs as suppressors or amplifiers of [evolutionary] selection

• frequency-dependent evolution

• the outcome of evolutionary games [scenarios] is dependent on the structure of the graph

• in small populations, "drift" dominates, i.e. random mutations don't trigger an evolutionary path, while

• large populations are sensitive to small changes in selection values

• the higher the correlation between the mutant's fitness and fixation, the stronger the effect of natural selection

Lieberman and Nowak's theories involve replicators. [GDUK] A replicator is an entity that makes copies of itself; it could be a virus or an idea. Network theory predicts where that replicator will go, how successfully it will propagate.

Human organizations have complicated network structures25−27. Evolutionary graph theory offers an appropriate tool to study selection on such networks. We can ask, for example, which networks are well suited to ensure the spread of favorable concepts. If a company is strictly one-rooted, then only those ideas will prevail that originate from the root (the CEO). A selection amplifier, like a star structure or a scalefree network, will enhance the spread of favorable ideas arising from any one individual. Notably, scientific collaboration graphs tend to be scalefree28.

One of the more interesting things that Lieberman notes is that individuals don't evolve, populations do:

Evolutionary dynamics act on populations. Neither genes, nor cells, nor individu- als but populations evolve.

Historically, this concept has been applied to the biological evolution of species. But through graph theory, we can also show that social networks evolve, but not individuals. This supports Luhmann's idea that social systems are systems that take shape beyond the individual level.

Lieberman's paper on evolutionary graphs is short and not hard to understand. Just read the sentences between the mathematical equations and it's fairly clear.