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