The evolution of modularity

Jeff Clune, a computer scientist interested in artificial life, has a paper out about how tuning evolutionary pressure in a certain way evolves networks with a high modularity. Let’s debunk this.

  • tuning evolutionary pressure: emphasize cost of connections. This makes intuitive sense for networks in which there is a physical distance to cover (like a railway network); there are arguments for applying to more abstract networks like genetic and metabolic pathways. In online social networks, however, there is no physical distance; creating a new link is very cheap; maintaining a live social connection, however, is typically costly – and even, if we are to take the Dunbar number argument seriously, constrained by a hard ceiling.
  • evolves: Clune’s model starts from random neural networks that need to perform a certain task. They receive stimuli from eight inputs (think an 8-pixel retina) and evolve to answer whether a pattern of interest is present, based on the stimuli. Patterns are perceived by two blocks of 4 pixels each; those considered (exogenously) of interest are slightly different for the two blocks (dubbed “left” and “right”). Evolution happens by simulating networks that reproduce according to a fitness measure (more fit networks have more offspring) and with random mutation. Two alternative measures of fitness are considered: maximizing performance only (PA) and maximizing performance while minimizing connection costs (P&CC). Performance is measured against two tasks: determine whether a pattern is present in both the right and the left pixel clusters (L-AND-R); or whether it is present in either the right or the left pixel clusters (L-OR-R). Which patterns count as an object differs in the left and right halves of the retina. Notice that the task assigned to the networks is itself modular, as a partition between “right” and “left” pixels is postulated. The results of the paper carry through for nonmodular problems, albeit in attenuated form.
  • modularity: measured by Q (distance from the random-null). This simulation evolves left-right modularity, which means that left inputs and right inputs are routed through different components (= classes of the modularity-maximizing partition). This occurs in 56% of cases with P&CC and never with PA after 25,000 generations.

This setup produces two very interesting conclusions.

  1. Highly modular networks perform better. The additional constraint of minimizing connection costs produces a population of networks that, on average performs better in a P&CC setting than in a less constrained PA setting. This is driven by the true engine of the paper: if you take only high-performing network, you will notice that they tend to have an inverse correlation between cost and modularity. Non-modular high performing networks also evolve: in a P&CC environment, the evolutionary pressure on cost combines to that on performance and kills those off. The result is that, on average, high-performing networks (which are also high modularity, hence low cost) perform better in P&CC than in PA.
  2. Highly modular networks are more evolvable. Clure took perfect performance networks from an environment where the task is L-AND-R to one where it is L-OR-R (simulating mutated environmental conditions). At the same time, he did not change the PA/P&CC evolutionary constraints, letting networks evolved under one set of constraints continue to be subject to the same set of constraints, but under new environmental conditions. Result: modular networks evolved under P&CC took a smaller number of generations to adapt to the new task.

The question here is what this means for networks representing online communities. We have a structural conclusion, “modular networks are more efficient”, that makes intuitive sense because you might get clusters of people working on a subset of a problem, receiving inputs and passing outputs to other clusters through only few edges. We have also an evolutionary conclusion, “evolution produces modularity” that is unlikely to carry through. In the social world, the effect of evolutionary forces is weak, if not negligible: costs are low, and natural selection too slow. You might conceivably turn the problem around and instruct public authorities to somehow emulate evolution, supporting communities with more efficient configuration of users and dropping out of the less efficient ones. Alternatively, you could take a during-life learning perspective rather than an evolutionary one, and ask community managers and moderators (not funding agencies!) to “teach” networks efficient configurations.

Another note is important for me, though very marginal for the paper: levels of Q around 0.4 are considered “high”. And the Edgeryders induced conversation network is up at 0.47!

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