Identifying Neural Network Topologies That Foster Dynamical Complexity

We use an ecosystem simulator capable of evolving arbitrary neural network topologies to explore the relationship between an information theoretic measure of the complexity of neural dynamics and several graph theoretical metrics calculated for the underlying network topologies. Evolutionary trends confirm and extend previous results demonstrating an evolutionary selection for complexity and small-world network properties during periods of behavioral adaptation. The resultant mapping of the space of network topologies occupied by the most complex networks yields new insights into the relationship between network structure and function. The highest complexity networks are found within limited numerical ranges of clustering coefficient, characteristic path length, small-world index, and global efficiency. The widths of these ranges vary from quite narrow to modest, and provide a guide to the most productive regions of the space of neural topologies in which to search for complexity. Our demonstration that evolution selects for complex dynamics and small-world networks helps explain biological evidence for these trends and provides evidence for selection of these characteristics based purely on network function—with no physical constraints on network structure—thus suggesting that functional and structural evolutionary pressures cooperate to produce brains optimized for adaptation to a complex, variable world.