Functional and physical constraints for evolving small-world structure in embodied networks

The human brain contains a huge number of neurons (~10¹¹ neurons) and a huge number of interconnections (~10¹⁴ synapses). The ontogenetic process that forms this structure is believed to be ruled primarily by optimizing principles of resource allocation and constraint minimization [1], [2]. These evolutionary and developmental processes lead to brain structures that are known to have certain interesting macroscopic properties, such as small-world behavior [3], [4], [5]. However, the nature of these constraints to building neural structure, and the relationship of such structure to cognitive performance remain important questions. Connectivity structure might be the result of wiring optimization; at least this appears to be a plausible assumption as wiring is expensive, thus evolution would prefer structures that minimize wiring and the cost of building it [6]. However, this must be balanced with factors for optimizing information processing performance, as a minimally wired network may not be adequate to integrate information and support sufficient dynamics for controlling the organism. It is therefore plausible that real brain network development has both physical constraints and functional information processing constraints that guide the development of structural elements and functional dynamics [7], [8]. In this paper we present an embodied model of a brain network that uses both spatial and functional constraints in its evolutionary and developmental processes. We show that small-world organization can develop in such embodied systems when both constraints are present. And we compare the performance of the embodied agent to evolutionary systems that use only functional constraints to guide the systems development.