Last week I attended a talk at MIT by Michael Deem, a professor at Rice University who has done some very interesting work on the emergence of modularity in evolution. This is a topic that I have long thought about, as it seems that modularity is intrinsic to many biological phenomena, and it also seems that modular systems would by construction have certain internal structure that can be exploited in computational modeling. My thinking on the topic has been crude and qualitative, and so it was with some delight that I discovered Michael’s work in this area, as his group has placed this problem on very firm quantitative footing. The talk was thought provoking, and left me with genuinely new insights, something that happens with only a small, small fraction of the talks I attend.
His presentation focused mostly on the results and implications of their methodology, as opposed to its mathematical underpinnings (field theory). Suffice it to say that they have developed a theoretical framework for studying evolution, and have, to a first order approximation, shown that modularity can emerge spontaneously in evolved systems. In particular they have identified three properties that, if present, would result in the emergence of modularity. First, the environment must undergo dramatic changes on a regular basis. Second, there must be a mechanism for exchanging large chunks of genetic information between organisms, with “genetic information” here referring abstractly to the material that encodes the evolving unit. In biology this mechanism is horizontal gene transfer, and perhaps gene duplication (he didn’t say anything about gene duplication, and obviously while gene duplication enables large chunks of genetic content to be introduced, it is not the same as having that information directly injected into another organism). Third, the evolutionary landscape must be rugged.
It appears that the first factor is the most important, and it was the main topic of the talk so I will focus on it. Before I get there however I will first describe what he means by modularity. The basic notion is that, given a system of interacting parts, modular systems are structured in a way such that there are a lot of interactions among parts within a group and few interactions between parts in different groups. This is the familiar concept of clusters in unsupervised machine learning. If we represent individual parts by rows and columns in a matrix, and the presence of an interaction by a red entry in the matrix, then this is what modularity would look like:
It is a continuous quantity, with some systems more modular than others. The main result of the talk was that evolved systems tend to a more modular architecture if the environment in which they operate undergoes substantial changes periodically. The intuition behind this result is as follows. When a system is undergoing evolution, it is exploring the space of possible configurations that optimize its fitness in the environment. One can think of the system as exploring the space of all possible matrices pictured above. If there are structural constraints on the space of matrices that it can explore, for example if the system must be modular and thus the matrix roughly block-diagonal, then the system will find the (local) optimum more quickly than if it were exploring the entire space of all possible matrices, because it is searching a constrained and thus smaller space. On the other hand, if the system were unconstrained in its search, then it will find the same or better optimum found by the constrained search, but in a longer time. This is visualized below:
The key feature of the above plot is the time gap during which the fitness of the modular system is higher than that of the non-modular one. If the periodic environmental changes occur on timescales shorter than the gap, then modularity will be preferred, because modular systems could find a better solution in time before a major environmental change occurs and resets the system. Although he didn’t show this, I assume that in the above there is actually a third axis representing modularity, with more modular systems having sharper curves like this:
Then on the resulting two-dimensional surface evolution is optimizing for the level of modularity that yields the best solutions given the expected timescale of environmental changes. In environments that are highly stable, the evolved systems would in fact be less modular, and arguably more fragile and less resistant to change.
A related concept here is the notion of hierarchical modularity. Although he didn’t show the formalism behind this, the idea is that modularity can be defined on multiple levels, presumably by coarse-graining the matrix of interactions and then looking at block-level interactions. Their results suggest that after a system’s modularity at one level has saturated/been optimized, higher-order modularity starts emerging, and it does so right around the time a system’s modularity at one level starts tapering off, as schematized below:
This is of course consistent with our current understanding of biological phenomena and the multiple levels of organization that we observe.
I will finish up with a quick sojourn into a non-biological example that Michael presented. His group also studies other systems, including global trade. He made three interesting observations about what they see there. First, the world as a whole, as a result of globalization and better telecommunication, is getting increasingly less modular. Second, historically speaking the world tends to become more modular in the aftermath of a major financial crisis. Presumably this is because modular systems are able to better insulate disruptions from affecting the entire system, and so the world as a whole tends to tighten up post-crises. Third, since the overall trend has been toward decreasing modularity, the average recovery time from crises has been increasing. This is interesting for many reasons, not least of which is the implication that as we become increasingly more interconnected, our global financial systems are becoming more fragile and slower to recover. On one level this is obvious, as can be evidenced by the fact that floods in Thailand can now have a major impact on supply chains in the US. The drive by some US companies to bring back manufacturing to the US is also driven by similar considerations. But in spite of these measures, the long-term trajectory is clear. Our interconnectedness is potentially making us a more fragile species.