Biological solutions to transport network design

Abstract

Transport networks are vital components of multicellular organisms, distributing nutrients and removing waste products. Animal and plant transport systems are branching trees whose architecture is linked to universal scaling laws in these organisms. In contrast, many fungi form reticulated mycelia via the branching and fusion of thread-like hyphae that continuously adapt to the environment. Fungal networks have evolved to explore and exploit a patchy environment, rather than ramify through a three-dimensional organism. However, there has been no explicit analysis of the network structures formed, their dynamic behaviour nor how either impact on their ecological function. Using the woodland saprotroph Phanerochaete velutina, we show that fungal networks can display both high transport capacity and robustness to damage. These properties are enhanced as the network grows, while the relative cost of building the network decreases. Thus, mycelia achieve the seemingly competing goals of efficient transport and robustness, with decreasing relative investment, by selective reinforcement and recycling of transport pathways. Fungal networks demonstrate that indeterminate, decentralized systems can yield highly adaptive networks. Understanding how these relatively simple organisms have found effective transport networks through a process of natural selection may inform the design of man-made networks.

Figure 1

Mycelial network structure. (a–c) Corded mycelium of P. velutina growing from colonized woodblock inoculum (I) over a compressed soil microcosm (22.5×22.5 cm) for 39 days. The mycelium has contacted and colonized a second woodblock (B). (d) Scanning electron micrograph of the fine structure of a cord of P. velutina, showing that cords are composed of a bundle of many parallel fine hyphae. (e) Model of a cord as a bundle of identical hyphae, with cross-sectional area a and length l. The volume of a model cord is la and the predicted transport resistance is la⁻¹. (f–h) Models of a developing mycelial network at 25, 31 and 39 days. Links are pseudo-colour coded by log₁₀(a) on a rainbow scale with red representing thick cords and blue representing thin cords. The positions of woodblocks are highlighted by white squares.

Figure 2

Path lengths in fungal and uniform networks. (a) Functional resistance (mm⁻¹) versus Euclidean distance (mm) from each node to the inoculum for a fungal network (cyan squares), and a network constructed with the same topology and total cost, but uniform cross-sectional area (magenta circles), at 39 days. Lines show smoothed fits. Resistance to added resource (black square) is lower than other nodes at the same Euclidean distance. (b) Smoothed fits of functional resistance (mm⁻¹) versus Euclidean distance (mm) from each node to the inoculum, at 18 days (cyan), 25 days (magenta), 31 days (green) and 39 days (orange). Resistance is greater at the mycelial margins but decreases at a given Euclidean distance over time as the network reinforces links.

Figure 3

Comparison of transport efficiency between weighted fungal and uniform model networks. (a) Global Euclidean efficiency (mm⁻¹) versus network area (mm²) for DT (cyan squares), fungal network (red diamonds) and MST (green triangles). The fungal networks have intermediate global Euclidean efficiency. (b) Root Euclidean efficiency, axes and symbols as in (a). The fungal networks have similar efficiency to the well-connected DTs. (c) Global functional efficiency (mm) versus network area (mm²). Symbols as in (a), except that the fungal weighted (magenta circles) and uniform (red squares) networks are differentiated. The MSTs have the greatest functional efficiency. Fungal networks are intermediate. (d) Root functional efficiency, scales and symbols as in (c). The fungal weighted networks have the greatest root functional efficiency.

Figure 4

Comparison of core size loss between weighted fungal and uniform model networks. (a) Euclidean core size fraction versus fraction of broken links for DTs (cyan squares), fungal networks (red diamonds) and MSTs (green triangles). Fungal networks have intermediate robustness to damage. (b) Functional core size fraction versus fraction of total link a broken. Symbols as in (a), except that the fungal weighted (magenta circles) and uniform (red squares) networks are differentiated. When more than approximately 30% of total link a has been broken, the weighted fungal networks maintain a greater connected core than other types of network.