Scoring the evolution of network features. a. Schematic of the path scoring scheme. In this subset of networks (blocks) fold-changes in the feature to be scored are denoted by x. The observed networks in this path are connected by blue arrows and indexed with the o subscript. Networks not connected by these arrows are networks resulting from the available alternative evolutionary changes at each intermediate network, indexed with the a subscript. Red outlines indicate networks which optimize the feature at each stage. Each evolutionary change in a path is penalized by the logarithm of the ratio of the observed feature score to the best alternative feature score at each intermediate network. The total path score is the sum of the penalties for the five evolutionary changes (see Methods for a detailed explanation of the scoring scheme). b. Distribution of evolutionary path scores for the three scored features. Paths with higher scores perform better in optimizing that network feature.