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Distribution networks -- from vasculature to urban transportation systems --are prevalent in both the natural and consumer worlds. These systems areintrinsically physical in composition and are embedded into real space,properties that lead to constraints on their topological organization. In thisstudy, we compare and contrast two types of biological distribution networks:mycelial fungi and the vasculature system on the surface of rodent brains. Bothsystems are alike in that they must route resources efficiently, but they arealso inherently distinct in terms of their growth mechanisms, and in that fungiare not attached to a larger organism and must often function in unregulatedand varied environments. We begin by uncovering a common organizationalprinciple -- Rentian scaling -- that manifests as hierarchical network layoutin both physical and topological space. Simulated models of distributionnetworks optimized for transport in the presence of fluctuations are also shownto exhibit this feature in their embedding, with similar scaling exponents.However, we also find clear differences in how the fungi and vasculaturebalance tradeoffs in material cost, efficiency, and robustness. While thevasculature appear well optimized for low cost, but relatively high efficiency,the fungi tend to form more expensive but in turn more robust networks. Thesedifferences may be driven by the distinct functions that each system mustperform, and the different habitats in which they reside. As a whole, this workdemonstrates that distribution networks contain a set of common, emergentdesign features, as well as tailored optimizations.

Embedding of biological distribution networks with differing environmental constraints