We study the dynamics of modularization in a minimal substrate. A module is a functional unit relatively separable from its surrounding structure. Although it is known that modularity is useful both for robustness and for evolvability (Wagner 1996), there is no quantitative model describing how such modularity might originally emerge. Here we suggest, using simple computer simulations, that modularity arises spontaneously in evolutionary systems in response to variation, and that the amount of modular separation is logarithmically proportional to the rate of variation. Consequently, we predict that modular architectures would appear in correlation with high environmental change rates. Because this quantitative model does not require any special substrate to occur, it may also shed light on the origin of modular variation in nature. This observed relationship also indicates that modular design is a generic phenomenon that might be applicable to other fields, such as engineering: Engineering design methods based on evolutionary simulation would benefit from evolving to variable, rather than stationary, fitness criteria, as a weak and problem-independent method for inducing modularity.
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