Hierarchical organization -- the recursive composition of sub-modules -- is
ubiquitous in biological networks, including neural, metabolic, ecological, and
genetic regulatory networks, and in human-made systems, such as large
organizations and the Internet. To date, most research on hierarchy in networks
has been limited to quantifying this property. However, an open, important
question in evolutionary biology is why hierarchical organization evolves in
the first place. It has recently been shown that modularity evolves because of
the presence of a cost for network connections. Here we investigate whether
such connection costs also tend to cause a hierarchical organization of such
modules. In computational simulations, we find that networks without a
connection cost do not evolve to be hierarchical, even when the task has a
hierarchical structure. However, with a connection cost, networks evolve to be
both modular and hierarchical, and these networks exhibit higher overall
performance and evolvability (i.e. faster adaptation to new environments).
Additional analyses confirm that hierarchy independently improves adaptability
after controlling for modularity. Overall, our results suggest that the same
force--the cost of connections--promotes the evolution of both hierarchy and
modularity, and that these properties are important drivers of network
performance and adaptability. In addition to shedding light on the emergence of
hierarchy across the many domains in which it appears, these findings will also
accelerate future research into evolving more complex, intelligent
computational brains in the fields of artificial intelligence and robotics.Comment: 32 page