Data from: The relative efficiency of modular and non-modular networks of different size

Most biological networks are modular but previous work with small model networks has indicated that modularity does not necessarily lead to increased functional efficiency. Most biological networks are large, however, and here we examine the relative functional efficiency of modular and non-modular neural networks at a range of sizes. We conduct a detailed analysis of efficiency in networks of two size classes: ‘small’ and ‘large’, and a less detailed analysis across a range of network sizes. The former analysis reveals that while the modular network is less efficient than one of the two non-modular networks considered when networks are small, it is usually equally or more efficient than both non-modular networks when networks are large. The latter analysis shows that in networks of small to intermediate size, modular networks are much more efficient that non-modular networks of the same (low) connective density. If connective density must be kept low to reduce energy needs for example, this could promote modularity. We have shown how relative functionality/performance scales with network size, but the precise nature of evolutionary relationship between network size and prevalence of modularity will depend on the costs of connectivity.

绝大多数生物网络均具备模块化特征，但此前针对小型模型网络的研究表明，模块化未必能提升功能效率。然而，多数生物网络的规模庞大，因此本研究针对不同规模的模块化与非模块化神经网络，探究二者的相对功能效率。我们针对两类规模等级——“小型”与“大型”网络的效率展开详细分析，并对全范围网络规模进行了粗略分析。前述详细分析结果显示：当网络规模较小时，模块化网络的效率低于所考察的两类非模块化网络之一；但当网络规模扩大后，模块化网络通常与两类非模块化网络效率相当，甚至更优。后述粗略分析则表明，在中小规模的网络中，当连接密度相同时（均为较低水平），模块化网络的效率远高于非模块化网络。例如，若需通过降低连接密度以减少能量消耗，这一条件将可能推动模块化特征的演化。本研究已阐明相对功能/性能随网络规模的变化规律，但网络规模与模块化的普遍性之间的确切演化关系，仍取决于连接成本的具体情况。