Evolution of modularity in regulatory networks

Ten Tusscher and Hogeweg (2011) studied evolved body plan networks. They scored architectural modularity with two algorithms, one using Newman's leading eigenvector method and one using random walks, so that results would not depend on one heuristic.² They also scored random networks, architecturally modular networks and neutrally evolved networks. The neutral networks served as the benchmark for asking whether selection favoured modularity.² Krakauer and colleagues (2020) describe the general network approach. Quantitative measures look for partitions of nodes and edges that are overrepresented in the data compared with a null model.⁶ They add that developmental definitions, such as those for limbs or body segments, have not been given as quantitative measures.⁶

Ten Tusscher and Hogeweg (2011) criticised the architectural algorithms. They suspected that even a small overlap in genes shared between functional modules stops those modules being recognised as architectural ones.¹ Their alternative method counted a network as more modular when fewer overlaps were found between its minimum segment networks and its domain networks.¹ In their account, wiring-based scores can therefore miss modules that are defined by what the genes do.

Kriegman, Cheney and Bongard (2018) argued that modular systems are more evolvable, because evolution can improve one subsystem without disrupting others.⁴ They noted that modularity can come from how a system is built or can itself evolve. In their evolved robots, genes for morphology were independent of genes for control. The more successful lineages with development evolved a further form, which the authors call differential canalization. Some plastic traits became integrated and canalized while others stayed plastic.⁵ Sengupta, Stemmler and Friston (2013) make a related point for neuronal networks. They report hierarchical modularity that trades physical cost against topological complexity.³

Recent studies still use modules as working units. Timsit and Grégoire (2021) describe ribosomal protein networks in which each new extension and connection gradually relates functional modules.⁷ Pai and colleagues (2025) clustered gene expression and interaction data from Xenobots and found 10 enriched clusters, many resembling the functional enrichment results.⁹ Bongard and Levin (2023) question the category. If a system polycomputes, different observers may see different functions, so some will judge it more modular than others.⁸ They argue the classical distinction should be abandoned in its original form.⁸