The Evolutionary Origins of Hierarchy
Fig 2
A cost for network connections produces networks that are significantly more hierarchical, modular, high-performing, and likely to functionally decompose a problem.
The algorithms for quantifying hierarchy and modularity are described in Methods. The bars below plots indicate at which generation a significant difference exists between the two treatments. (A) The hierarchical AND-XOR-AND problem (the default for our experiments). The top eight nodes are inputs to the problem and the bottom node is an output. (B) P&CC networks are significantly more hierarchical than PA networks. p-values are from the Mann-Whitney-Wilcoxon rank-sum test, which is the default statistical test throughout the paper unless otherwise stated. (C) P&CC networks are also significantly more modular than PA networks, confirming a previous finding [17, 38]. (D) P&CC networks evolve a solution to the problem significantly faster. (E) Evolved networks from the 16 highest-performing replicates in the PA treatment. The networks are non-hierarchical, non-modular, and do not tend to decompose the problem. Each network panel reports fitness/performance (F), hierarchy (H), and modularity (M). Nodes are colored if they solve one of the logic sub-functions in (A). S1 Fig shows networks from all 30 replicates for both treatments. (F) Evolved networks from the 16 highest-performing replicates in the P&CC treatment. The networks are hierarchical, modular, and decompose the problem. (G) A comparison of P&CC and PA networks from the final generation. P&CC networks are significantly more hierarchical, modular, and solve significantly more sub-problems.