Data from: The evolutionary origins of hierarchy

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.层级结构——即子模块的递归组合——广泛存在于各类生物网络中，包括神经网络、代谢网络、生态网络以及基因调控网络，同时也存在于人工构建的系统中，例如大型组织与互联网。迄今为止，针对网络层级结构的多数研究仅局限于对该特性进行量化表征。然而，进化生物学中一个尚未解决的重要问题是：层级结构究竟为何会演化产生？近期已有研究表明，模块化之所以会演化，是因为网络连接存在成本代价。本研究旨在探究此类连接成本是否同样会促使此类模块形成层级结构。在计算模拟实验中，我们发现，即便任务本身具备层级结构，不存在连接成本的网络也不会演化出层级特性。但当存在连接成本时，网络则会同时演化出模块化与层级结构，且这类网络的整体性能与演化能力（即对新环境的适应速度）均更优。额外的分析结果证实，在控制模块化变量的前提下，层级结构可独立提升网络的适应性。综上，我们的研究结果表明，同一演化动力——连接成本——同时推动了层级结构与模块化的演化，而这两种特性正是提升网络性能与适应性的关键驱动因素。本研究不仅阐明了层级结构在其出现的多个领域中的起源机制，同时也将推动人工智能与机器人学领域中，关于演化出更复杂、智能的计算大脑的后续研究。