13 Network Organisation of Mycelial Fungi · Network Organisation of Mycelial Fungi 309 ure, summarise and compare such complex net-works. In the 1990s, fractal measures were intro-duced

$Page 1: 13 Network Organisation of Mycelial Fungi · Network Organisation of Mycelial Fungi 309 ure, summarise and compare such complex net-works. In the 1990s, fractal measures were intro-duced$
13 Network Organisation of Mycelial Fungi

M. Fricker1, L. Boddy

2, D. Bebber

1

CONTENTSI. Introduction . . . . . . . . . . . . . . . . . . . . . . . . 307

II. Conceptual Frameworksfor Network Analysis . . . . . . . . . . . . . . . . . . 309A. Experimental Analysis

of Mycelia as Networks . . . . . . . . . . . . . 309B. Common Network Measures . . . . . . . . . 314C. Predicted Transport Characteristics . . . 316D. Predicted Network Resilience . . . . . . . . 317

III. Comparison with Other Representationsof Mycelial Structure and Growth . . . . . . . . 318A. Continuous Models . . . . . . . . . . . . . . . . 318B. Cellular Automata Models . . . . . . . . . . . 319C. Vector Models . . . . . . . . . . . . . . . . . . . . 319D. Abstracted Networks –

Hub and Spoke Models . . . . . . . . . . . . . 320IV. Nutrient Transport Through the Network . 321

A. Transport at the Micronto Millimetre Scale . . . . . . . . . . . . . . . . . 321

B. Transport at the Millimetreto Centimetre Scale . . . . . . . . . . . . . . . . 323

V. Conclusion: Future Prospects . . . . . . . . . . . 324References . . . . . . . . . . . . . . . . . . . . . . . . . . 324

I. Introduction

Filamentous fungi grow out from a spore or an in-oculum, by apical extension of slender hyphae thatthen branch sub-apically to form a fractal, tree-likemycelium. In ascomycetes and basidiomycetes,tangential hyphal fusions or anastomoses occuras the colony develops to form an interconnectedmycelial network (Rayner et al. 1994, 1999; Glasset al. 2000, 2004). The basic sequence of mor-phological events leading to fusion has been welldescribed, most notably by Buller (1931, 1933;summarised by Gregory 1984), and details ofthe underlying cellular and molecular events arebeginning to be elucidated in model systems suchas Neurospora and Colletotrichum (Glass et al.2000, 2004; Hickey et al. 2002; Roca et al. 2003,

1 Department of Plant Sciences, University of Oxford, South ParksRoad, Oxford, OX1 3RB, UK2 Cardiff School of Biosciences, Cardiff University, Cardiff, CF103US, UK

2004, 2005a, b; Fleissner et al. 2005). In the larger,more persistant saprotrophic and ectomycorrhizalbasidiomycetes, the network architecture developsfurther as the colony grows with the formationof specialised high-conductivity channels, termedcords, through aggregation and limited differenti-ation of hyphae (Cairney 2005). Cords tend to bewell insulated from the environment and are ableto translocate nutrients between separate food re-sources or to and from the foraging margin (Boddy1999; Leake et al. 2004). At the same time as cordsform, the intervening regions of the myceliumregress and are presumably recycled to supportnew growth. The resulting structure and scale of thecorded network vary between species, and give riseto qualitatively different, recognisable network ar-chitecture (Fig. 13.1). These networks are not static,but are continuously reconfigured in response tolocal nutritional or environmental cues, damage orpredation, through a combination of new growth,branching, fusion or regression (Boddy 1999; Leakeet al. 2004). Furthermore, a single genetically iden-tical individual network (genetic mycelial unit, orGMU sensu Olsson 2001) can undergo quantumshifts in size through fragmentation, leading toseveral separate functional mycelial units (FMU;Olsson 1999, 2001). Conversely, fusion of separateFMUs in the following growth season can rapidly(re-)generate a more expansive network (Rayneret al. 1994; Boddy 1999; Leake et al. 2004).

Whilst the largest mycelial networks that aretypically grown in laboratory microcosms rangeover 0.1–1.0 m2, in an undisturbed forest ecosys-tem almost all trees and fallen plant parts are in-terconnected by a diverse population of mycelialsystems forming an extensive network over a muchlarger physical scale termed the ‘wood wide web’(WWW; Read 1997; Simard et al. 1997; Simard andDurall 2004). There is considerable evidence for ex-tensive nutrient uptake and exchange through theWWW (Simard et al. 1997; Read and Perez-Moreno2003; Leake et al. 2004; Simard and Durall 2004).

The Mycota VIIIBiology of the Fungal CellHoward/Gow (Eds.)© Springer-Verlag Berlin Heidelberg 2007

308 M. Fricker, L. Boddy, D. Bebber

Fig. 13.1. Colony morphology and network architecturefor different species of saprotrophic basidiomycetes. A–FMycelial systems of Resinicium bicolor (A), Phanerochaetevelutina (B), Hypholoma fasciculare (C), Coprinus picaceous

(D) and Phallus impudicus (E, F) growing from wood blocksof 2 cm side in 24×24 cm trays of compressed non-sterilesoil to illustrate the range of network architecture shown bydifferent species. Photos courtesy of G. Tordoff

Fungi, like any other organisms, must partitionlimited resources among competing requirements.For example, a very dense, highly connected net-work might have high transport capacity and re-silience to damage or attack because of multipletransport pathways. However, it would incur a largematerial cost of construction per unit area of ex-plored space and would cover new ground slowly.Conversely, a sparse system could extend furtherfor the same material cost, but would risk miss-ing resources and have fewer alternate routes tosurvive damage and disconnection (Boddy 1993,1999; Rayner et al. 1994, 1999). We do not knowwhat factors have been most significant in shapingeach strategy in evolutionary terms (Pringle andTaylor 2002) or how organisation and integration ofsuch networks can emerge without centralised con-trol (Rayner 1991; Rayner et al. 1994, 1999). How-ever, as a starting point we might envisage that theresulting networks represent an effective balancebetween cost, exploration, exploitation, transport

efficiency and resilience to damage. Subtle shifts inthe developmental process for different species mayhave effectively weighted the relative importance ofeach these aspects to adapt to different spatial andtemporal patterns of resource availability and envi-ronmental conditions, giving rise to a set of forag-ing strategies for each species (Boddy 1999). How-ever, there has been relatively little explicit analysisof the structure of the networks formed, their dy-namic behaviour and how both impact on theseproposed functions.

In this chapter we explore this relatively un-charted middle ground between the microscopiccellular level dominated by discrete tubular hy-phae (reviewed in this series by Trinci et al. 1994)and the macroscopic level of intact colonies (re-viewed in this series by Olsson 2001), to see theextent that it is possible to characterise the net-work aspect of mycelial growth. A few years ago thiswould have been a daunting task as there was nocoherent conceptual framework to describe, meas-

Network Organisation of Mycelial Fungi 309

ure, summarise and compare such complex net-works. In the 1990s, fractal measures were intro-duced as useful tools to capture aspects of thenetwork structure as a metric (Ritz and Crawford1990; Crawford et al. 1993; Donnelly et al. 1995; Mi-hail et al. 1995; Boddy et al. 1999; Crawford et al.1999; Boddy and Donnelly 2006). However, a singlesummary value can only express a small fractionof the complexity in the system, even with sub-sampling of different regions. Recently, consider-able advances have been made in network analysis,using concepts and tools emerging from graph the-ory and statistical mechanics (Strogatz 2001; Albertand Barabasi 2002; Dorogovtsev and Mendes 2002;Newman 2003; Amaral and Ottino 2004). Thesetechniques have been applied to a swathe of com-plex systems, including biological networks suchas protein–protein interactions or food webs, andmay provide a useful conceptual framework forquantitative analysis of fungal mycelia. We there-fore provide an introduction to some of the the-ory and terminology used to analyse networks,translated as far as we are able into mycologicallanguage. We then evaluate its application to ana-lyse the dynamics, efficiency, resilience and adap-tation of self-organised fungal networks at differentspatial scales. We also try to set network analysisin context with other approaches to measure andmodel fungal behaviour, with the expectation thata combination of approaches will be required to un-derstand fungal growth over the enormous rangeof length scales needed.

II. Conceptual Frameworksfor Network Analysis

To use network analysis tools to analyse fungalmycelia, it is necessary to translate the morpho-logical structures observed into an appropriate net-work representation (Bebber et al., submitted). Ourstarting assumption is that the fungal mycelium canbe represented as a graph by classifying junctions(branch-points and anastomoses) as nodes and thehyphae or cords between nodes as links. It is possi-ble to (manually) extract the network from imagesof mycelial systems taken at appropriate resolu-tion. We illustrate the process and results using theclassic microscopic image of Coprinus sterquilinusfrom Buller (1931; Fig. 13.2A) and images of Phane-rochaete velutina from our own work (Fig. 13.2C).We have developed a simple software interface to

simplify extraction of the network that is availableon request.

At the moment nodes have to be manually cho-sen as automated segmentation algorithms that arenot yet sufficiently robust to extract the networkunsupervised. Each node is given a unique identi-fier and stored as a list together with its Cartesian(x, y) co-ordinates. Links are stored interchange-ably either as an adjacency matrix or in a list for-mat that can be imported into a wide range of freelyavailable software packages, such as Pajek (http://vlado.fmf.uni-lj.si/pub/networks/pajek/). As linksvary in length (l) and cross-sectional area (a), thelinks are weighted, i.e. they differ in their connec-tion strength. The diameter and hence area of eachcord can be determined using image analysis tools.The material construction cost of each link canbe estimated from the volume (l × a), i.e. longer,thicker hyphae or cords are more costly to pro-duce in terms of the mass of material requiredto build them. Similarly, the predicted transportflux through the network is expected to increasewith increasing cross-sectional area, but decreasewith link length. The precise relationship betweenflow and area is less clear. For the extreme case oflaminar flow through individual hyphal tubes, flowcan scale with r4 in accordance with the Hagen–Poiseuille equation:

Volume flow rate per hub =πr4

8η∂P

∂x(13.1)

where r is the radius of the tube, η is the viscosityof the fluid, and -−δP/δx is the negative gradientof the hydrostatic pressure. In multi-hyphal aggre-gates such as cords, the structure is more akin toa cylinder packed with individual hyphae in paral-lel. In this case, flow can scale with the area, i.e. r2,although it is recognised that the internal structureof cords can be more complex, with both largervessel hyphae increasing potential flow and fibrehyphae that do not contribute to transport.

A. Experimental Analysisof Mycelia as Networks

The C. sterquilinus colony (Fig. 13.2A) captures theessence of fungal network formation on a micro-scopic scale. A sparse branching tree-like struc-ture forms in the peripheral growth zone fromtip growth and sub-apical branching, whilst sec-ondary growth and fusion of hyphae in the centre ofthe colony forms an interconnected network with


Fig. 13.2. Analysis of mycelial network structures over dif-ferent length scales. A Drawing of a young colony of Co-prinus sterquilinus showing the development of an anasto-mosing network in the colony interior. The colony is around380 μm in diameter (modified from Buller 1931). B Networkrepresentation of the same colony in which the link weight iscolour coded on a rainbow scale, with red representing thethickest hyphae. C Mycelial system of P. velutina grown from4 cm3 beech wood inocula on a 24×24 cm tray of non-sterile

soil with an inert bait (grey circle) after 39 days. Digital im-ages were obtained from photographs taken by R. Bolton.D Network representation of the same colony in which thelink weight is colour coded on a rainbow scale with redrepresenting the thickest cord. E A 75×75 cm portion of anextensive network of the saprotrophic fungus Megacollybiaplatyphylla growing from a log in Wytham Wood, Oxford-shire, UK. F A schematic representation of the P. impudicusnetwork

Fig. 13.3. Establishment of oscillatory phase domains incolonies of P. velutina. Pseudo-colour-coded images show-ing the relative phase of the oscillatory component of la-belled aminoisobutyrate (14C-AIB) transport determinedpixel-by-pixel using Fourier analysis. The colour representsthe phase difference in hours (hrs) according to the adja-cent scale for each image from the oscillation recorded atthe loading site. Only regions with the same frequency arecolour-coded. Regions with a different frequency or wherethe Fourier analysis was not possible, such as the growing

colony margin, are coded in grey-scale. The period of the os-cillation ranged from 18.3 h (A, B) to 14.2 h (C), dependingon the growth temperature with a Q10 of around 2. A Controlcolony grown for 240 h, showing distinct phase domains inthe inoculum and foraging mycelium with ∼7 h phase dif-ference. B Development of an additional phase domain inthe bait of a juvenile colony. The bait lags the inoculum by∼3.5 h. C Phase map of a 35-day-old colony following load-ing at the bait, showing distinct phase domains in the bait,inoculum, connecting cords and foraging mycelium

many cycles (Fig. 13.2A). The extracted networkrepresentation contains 579 nodes and 656 links(Table 13.1), each with an associated measure of itslength and diameter that can be combined to givean estimate of the volume (cost) or predicted resis-tance to flow (Fig. 13.2B). In theory, larger networksthan this can be captured using large-scale mycelialmapping (LSMM; Crawford et al. 1993; Ritz et al.

1996) and analysed at the level of an individual hy-pha. However, it becomes increasingly difficult todistinguish fusions from overlapping hyphae as thecolonies become denser; and the sheer number of

Table. 13.1. A summary of common network measures andtheir application to fungal mycelia

Network Organisation of Mycelial Fungi 311To

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nodes and links makes manual extraction of thenetwork prohibitively time-consuming. In the fu-ture it may be possible to sub-sample segments ofthe entire colony if suitable methods are developedto deal with the connectedness of nodes and linksat the artificial boundaries that this introduces.

The next appropriate level of resolution in prac-tical terms are microcosms in the centimetre to me-tre range where the dominant structure is a cordedmycelium (Figs. 13.1, 13.2C,D). In the case of theP. velutina grown in a 24-cm square microcosm, thesize of the corded experimental networks reachesaround 500–1500 nodes (Fig. 13.2C; Bebber et al.,submitted). It might be appropriate to consider thelinks to be directed on the basis of their initialgrowth direction. However, in practice, the physi-ological direction of nutrient fluxes is more impor-tant and does not have to follow the developmen-tal connection sequence. Unfortunately, we cannotpredict a priori which direction the flux may movein and, indeed, we expect it to vary dependingon the source–sink relationships within the net-work. In the future, the techniques to map fluxesdescribed below (Sect. IV.) may provide this infor-mation, but at this stage it is simpler to assumethat links are undirected and capable of movingnutrients in either direction. The reader is referredto the chapter by Ashford and Allaway (Chap. 2 inthis volume) for a discussion of the possible role ofvacuolar transport mechanisms for trans-cellularmovement of materials over long distances.

In theory, the same approaches can be usedfor networks in the field. However, the structure ismore difficult to capture from simple photographs(Fig. 13.2E) as the network requires careful excava-tion and additional on-site notes to define contigu-ous cords. Thus, at this stage it is relatively easy toextract a schematic representation of the network(Fig. 13.2F), but rather more difficult to performa robust quantitative analysis.

B. Common Network Measures

Once the weighted network has been digitised,a wide range of network parameters can be calcu-lated. Some of the most common ones are given inTable 13.1. These values either have a straightfor-ward biological meaning in their own right or theyprovide a comparison with network structuresin other domains. As the data are embedded inEuclidean space, a number of basic morphologicalmeasures can be readily derived. An insight into

the behaviour of the mycelial network can thenbe gleaned by following the trajectory for eachparameter over time (Bebber et al., submitted). Forexample, the area covered by the colony can be esti-mated from the convex hull (effectively the polygonformed by stretching an elastic band around theoutermost points), provided the network is nottoo sparse (Fig. 13.4A). The sum of the linklengths gives the total length of mycelium present(Fig. 13.4B), whilst including the cross-sectionalarea of the links gives an estimate of the volume ofthe fungus that, with appropriate calibration, canbe related to the wet or dry weight. Early develop-ment in P. velutina is characterised by initial diffusegrowth and branching of individual hyphae, whichthen resolve into cords as the growing front movesoutward (Fig. 13.2C). Thus global network sizemeasures, such as area, number of nodes andnumber of links, increase through time (Fig. 13.4A,B). However, the local scale network evolutionis characterised by selective loss of connectionsand thinning out of the fine mycelium and weakercords that gives rise to a decrease in the networkdensity (cost per unit area) with increasing colonyarea (Fig. 13.4C). Although these measures providea compact summary of the whole colony, theydisguise any local variations in structure. There area number of spatial averaging techniques, such asKriging (Isaaks and Srivastava 1989), to interpolatebetween the very fine information at the level ofeach node and the overall colony metrics; and thisapproach may also facilitate comparison betweendifferent replicates and treatments.

A number of different quantities are typicallymeasured for a network to understand its proper-ties better. The degree (k) of each node is given bythe number of links associated with that node. Thustips have a degree of 1 as they are only connectedto the previous node and branch points typicallyhave a degree of 3, because the growth processesforming the network tend to give a single branch ora single fusion at each point. Initially overlappingcords often subsequently fuse, which generates k =4 nodes. It is unlikely that there will be any loopswhere a link curls back around on itself to re-jointhe same node, although multiple parallel links be-tween two nodes are possible. As the fine structureof the mycelium within a food resource, such as anagar inoculum or wood block, cannot be resolved,each of these is represented as a node with manylinks, resembling a hub in other network systems.

Considerable emphasis has been placed onthe frequency distribution of node degree in other


Fig. 13.4. Network measures for colonies of P. velutina.Mycelial systems of P. velutina were grown from 4 cm3 beechwood blocks in 24×24 cm trays of non-sterile soil and pho-tographed at intervals up to 39 days. The weighted networkwas manually extracted from digitised images and a rangeof network parameters calculated for three independenttime-series. A The change in area, measured as the convexhull, with growth of the colonies. B The change in myceliumtotal length as the area increases. C The mass density takinginto account the varying diameter of the cords. D The prob-ability distribution of log10 node strength. E The change inthe proportion of fundamental cycles (α) with increasingarea. F Comparison of the shortest path (in 1000s) fromthe inoculum to every node for the weighted network plot-ted against the same network with the weights distributedevenly across the links. Points below the diagonal indicate

that the fungus is performing better than expected for thisnull model. G Average shortest path distances (in 1000s)plotted against the Euclidean distance from the inoculumfor all nodes at the time points indicated. Only means fittedby Friedman’s smoother are shown for clarity. Mean val-ues for later stages are smaller than those for earlier stagesat a given Euclidean distance, showing that the networkincreases transport capacity as it develops. H The centralpoint dominance (CPD) gives a measure of the decrease inthe importance of the inoculum as the network becomesbetter connected. I Change in the reachability of all nodesin the network with progressive removal of links to sim-ulate the effect of grazing. The resilience of the weightednetwork (open circles) is greater than the same networkwith the weights distributed evenly as a null model (opensquares)

networks, following the discovery of scale-freedistributions in networks from many differentdomains (Barabasi and Albert 1999). However,the degree distributions for fungal networks arenot very informative because of the constraintsimposed by the developmental process and crowd-ing effects restricting the maximum number of

possible connections, as with other spatial net-works (Barrat et al. 2005). In weighted networks,the weighted degree distribution of node strength,measured as the sum of link cross-sectional areasper node, is regarded as a more informative meas-ure to take into account the varying importance ofthe connections to each node (Barrat et al. 2004).


For the P. velutina networks, the frequency distri-bution of node strength follows an approximatelylog-normal distribution (Fig. 13.4D).

The next level of organisation up, from a con-sideration of individual nodes and their summarystatistics, is a consideration of the propertiesof their local neighbourhood. There are severalmeasures that describe how well each node andits neighbours are interconnected. One of themost common is the mean clustering coefficient,C (Watts and Strogatz 1998), defined as theproportion of links connecting a node’s immediateneighbours out of the maximum possible numberof links. However, C is restricted to the case ofcycles with three links forming triads, which isnot appropriate to all classes of network, includingfungal mycelia, as their construction effectivelyprecludes formation of triads. In practice, thenetwork forms an interconnected reticulate systemwith many 4-, 5- or 6-node rings spreading awayfrom the central inoculum. Thus more generalmeasures have been proposed to capture thestructure of larger cycles (Alon et al. 1997; Cal-darelli et al. 2004). The meshedness coefficient wasrecently introduced to address this point for planargraphs of ant galleries (Buhl et al. 2004; Cardilloet al. 2006). However, the meshedness coefficientis actually a re-discovery of the alpha coefficientoriginally proposed by the geography communityin the 1960s (Haggett and Chorley 1969). Thus weprefer this latter original terminology and measureof closed loops as it has a historical precedent overmeshedness (Fig. 13.4E). The shift from essentiallya radial tree during early growth to a morereticulate network with increased cross-linking isreflected in an increasing value of the alpha index(Fig. 13.4E). Thus these fungal networks progressfrom a branching tree to a weakly connected lattice-like network behind the growing margin througha process of fusion and reinforcement to formloops and selective removal and recycling of excessredundant material (Bebber et al., submitted).

C. Predicted Transport Characteristics

To determine the efficiency of nutrient transloca-tion in the mycelial network, the predicted trans-port performance was assessed. The typical metricused in network analysis is based on the shortestdistance between any two nodes and is summarisedeither as the average, to give the average shortestpath through the network, or as the longest shortest

path which is termed the diameter of the network.A small average shortest path or a low diameter im-plies that it is easy to transport material anywherein the network. However, in weighted mycelial net-works, the network diameter is a highly unstablemeasure of network size as it is extremely sensi-tive to thin links with very high resistance at themycelial margin. Thus we have not yet found thisa useful network statistic, even for comparison withnetworks from other domains.

In a spatial graph, the average shortest pathand the network diameter is expected to increase asthe colony gets bigger, simply because they are de-fined by the physical distances between the nodes.However, including the predicted consequences ofthe varying cross-sectional area can significantlyalter this view. Thus, thickening of some routes,effectively increasing their transport capacity,reduces the apparent shortest transport path(Bebber et al., submitted). In isolation, it is difficultto attribute meaning directly to this measure.However, one way to assess the significance of theorganisation of the weighted links is to comparethe actual network with one in which the weightshave been either randomised between the links ordistributed evenly across all links. Although resultsfrom such an analysis can be summarised as themean shortest path or the diameter, it has provedmore informative to consider how the performancechanges with radius, not least because this mapsonto the developmental sequence of networkformation. Thus, over most of the physical radiusof the colony, the structure built by the fungus hasa lower shortest path than the equivalent structurewith the same total material spread evenly acrossthe network (Fig. 13.4F). Near the boundary thetwo systems become equivalent and right at themargin, where the very fine hyphae are located,the real colony performs much worse than thehomogeneous network. As the network grows,previously peripheral nodes, which originally hada long shortest path, become better connectedto the inoculum by the development of strongerlinks (Fig. 13.4G). Thus the branching marginresolves down to a more efficient transport systemthrough thinning out of some links, coupled withreinforcement of retained routes and an increase intheir transport capacity (Bebber et al., submitted).

The importance of any node, as a transport hub,can be estimated from the proportion of shortestpaths that pass through it, in a measure termed thebetweenness centrality that was originally used inthe social sciences (Freeman 1977). A more specific


measure derived from the betweenness centrality isthe central point dependence (CPD), which focusessolely on the relative importance of the node withthe greatest betweenness centrality. In fungal net-works this corresponds typically to the inoculum.Thus the CPD declines from ∼90% to ∼70% in con-trol networks (Fig. 13.4H) and to∼55% in networkswith an additional added wood resource (Bebberet al., submitted). This suggests that the networkbecomes more decentralised as it grows, formingcross-links that bypass the original inoculum.

Although these network measures providesome indication of the predicted transport effi-ciency of the mycelial systems, network analysisbased on graph theory does not readily capture theimportance of many potential parallel pathways forflux through the network, as they are dominatedby measures that highlight single (shortest) paths.We have also examined alternative approachesusing well developed tools for solving current flowthrough complex resistor networks (e.g. Hankin2006). The weighted adjacency matrix from themycelial network is already in an appropriateform to be recast as an electrical circuit analogue,with the additional constraint that flux (current)through the network can only be calculated ifa driving force (voltage) is applied to certainpoints in the network. This allows what-if typeexaminations of the expected flux as source–sinkpatterns change. For example, a map of thepredicted current flow from the inoculum to thehyphal tips can be calculated if a voltage is appliedat the inoculum and all the tips are grounded.

D. Predicted Network Resilience

Whilst the architecture of the weighted networkclearly improved transport efficiency, in nature thesame system also has to resist accidental damageor targeted attack by grazers.

In many networks, the probability of node orlink removal is unlikely to be random, and may alsoshow a high degree of correlation between adjacentnodes. For example, in the case of fungi, grazing bysoil invertebrates may occur at specific locations inthe network (Harold et al. 2005). This is becausesome regions are more palatable or accessible thanothers. One measure to characterise the vulnera-bility of the network is to examine the effect of linkbreakage on global efficiency (E), where E is mea-sured as the sum of the inverse of all shortest paths(Latora and Marchiori 2001). This measure is more

appropriate than just changes in the mean short-est path as it can handle disconnection of parts ofthe network. In other network analyses it is oftenthe nodes that are attacked. However, for fungalmycelia we believe that discussion of link breakagehas more biological relevance. Thus, in a targetedattack, we assume that the probability of link break-age is proportional to length and inversely propor-tional to area [P(b) ∼ l/a], i.e. longer, thinner cordsare more likely to break. To highlight the impor-tance of the organisation of the weighted links inthe network, this can be compared with a model inwhich the breakage probability is proportional tolength alone. The relative global efficiency, E/Emax,where Emax is the efficiency of the unbroken net-work, is consistently greater for a given proportionof links broken, when link weighting is taken intoaccount. Thus the distribution of link diametersin the fungal networks significantly increases theirresilience to attack. One disadvantage of the vul-nerability measure for a weighted network is thatconsistent removal of the weakest links naturallybiases the measure of efficiency, so the decrease innetwork performance is perhaps not as marked asexpected. An alternative measure, termed reacha-bility (Ball and Provan 1983), provides an unbiasedmeasure as it only considers the proportion of pathsremaining, without reference to their transport ca-pacity (Fig. 13.4H).

Whilst a single metric, such as 50% of the maxi-mum efficiency or number of paths, provides a suc-cinct summary of the resilience of the network, itdisguises much of the subtlety in the full responseof the fungal systems to attack. Thus the reacha-bility of the weighted network does not decay witha simple function, but is eroded down to a corethat is very much harder to destroy than equivalentnetworks with evenly distributed weights or ran-domised weights. This suggests that the same corearchitecture that gives the network good predictedtransport properties (see Sect. C.) also gives it goodresilience. Interestingly, the predicted pattern fol-lowing this type of simulated attack closely matchesthe observed pattern for real mycelial systems ofP. velutina under attack by particular species ofCollembola (Fig. 13.5A, B). It is also worth not-ing that part of the resilience of such a biologicalnetwork may not be just the architecture of the net-work prior to damage, but the ease and efficiencywith which the network can reconnect itself follow-ing attack. In this respect, a self-organising spatialnetwork may have considerable advantages overa random network in the cost, consistency and effi-


Fig. 13.5. The effect of Collembola grazing on networks of P.velutina. Mycelial systems of P. velutina grown from 4 cm3

beech wood inocula on 24×24 cm trays of non-sterile soilafter 21 days in the absence (A) and presence (B) of Collem-bola. In the presence of grazing, the network is trimmed

down to a central core and the frequency of circumferentiallinks increases. In addition there is a profusion of newfine mycelia from the damaged tips. Digital images wereobtained from photographs taken by G. Tordoff

cacy of the rewiring process needed to re-establisha functioning system.

III. Comparisonwith Other Representationsof Mycelial Structure and Growth

Network analysis provides a compact descriptionof the fungal mycelium drawn from experimentalsystems and may provide insights into the under-lying developmental processes. However, it is nota mathematical model of the fungal growth processper se. In an ideal world it might be possible to infernetwork construction algorithms from the networkstructure which would be of use to biologists andmay also inform the design and construction of an-thropogenic infrastructure networks. Whilst this isstill an aspiration, it is instructive to compare theresults and expectations of the experimentally de-rived network representation with other models ofcolony growth.

A. Continuous Models

There is an extensive literature describing both thecell biology of hyphal tip growth (see the chapters

by Bourett et al., Fischer, and Sudbery and Court;respectively Chaps. 1, 5 and 6 in this volume) cou-pled with increasingly sophisticated mathemati-cal models based around the vesicle supply cen-tre (VSC) model (Bartnicki-Garcia et al. 1989; re-viewed by Prosser 1995a, b; Geitmann 2006; seealso Sudbery and Court, Chap. 6 in this volume),including extension to three-dimensional models(Gierz and Bartnicki-Garcia 2001; Tindemans et al.2006). These models provide the raw material fordeveloping models of colony branching patterns,but do not yet include anastomoses. Furthermore,they are probably pitched at too fine a resolution toconsider scaling-up to a working model of networkformation.

At the level of the colony, a range of differ-ent modelling approaches have been applied (Bezziand Ciliberto 2004). There are several ‘continuousmodels’ that seek to model the collective attributesof the mycelium, rather than the growth of indi-vidual hyphae, but include morphological featuressuch as tip growth, branching, anastomosis and celldeath within the equations (Edelstein 1982; Edel-stein and Segel 1983; Edelstein et al. 1983; Edelstein-Keshet and Ermentrout 1989; Davidson et al. 1996,1997; Davidson and Park 1998; Davidson and Ols-son 2000; Boswell et al. 2002, 2003a; Jacobs et al.


2004). In such models growth is driven by nutri-ent concentration derived from uptake and inter-nal passive or active transport. The most advancedpartial differential equation (PDE) model has beendeveloped for Rhizoctonia solani and has been cal-ibrated against experimental measurements of keyparameters (Davidson et al. 1997; Davidson 1998;Davidson and Olsson 2000; Boswell et al. 2002,2003a). Predictions from the model match experi-mental observations for systems growing on tessel-lated heterogeneous resources (Jacobs et al. 2004),but the equations are difficult to solve mathemat-ically (Boswell et al. 2003b) and effectively limitcomputation to a simulation of growth over a fewcentimetres and a few hours. Nevertheless, thesemodels provide good descriptions of mass andsubstrate distributions for growth in both homoge-neous and heterogeneous environments. One of thedisadvantages of this basic PDE approach is that itcan only describe the architecture of the myceliumthrough its average properties, such as branchesand fusions per unit area, since it does not have anexplicit morphological representation of the colonystructure. This makes it more difficult to under-stand the impact that the network structure mighthave on transport properties and colony growth.

B. Cellular Automata Models

The first attempts to capture a direct representa-tion of the morphology of the colony were basedon cellular automata (CA) operating in discretetime, space and state. Although CA models

Fig. 13.6. Morphological models of colony growth. A Thetypical output from a cellular automaton model running ona hexagonal grid in which the growth direction and branch-ing probability have a limited degree of stochasticity (M.D.Fricker, unpublished data). B Visualizations produced bythe neighbour-sensing model of hyphal growth, assum-ing a negative autotropic reaction and density-dependentbranching (branching probability 40% per iteration), withthe density field being generated by all of the mycelium.

An additional horizontal plane tropism restricts growth toa thin horizontal zone analogous to a circular colony grownon agar (viewed from above, upper visualization) with a nar-row profile (side view, lower visualization; Meškauskas et al.2004a). C An analytically solvable model showing radialconnections from peripheral nodes to an effective hub. Theaverage shortest path can be calculated with varying cost-functions for systems with multiple concentric rings (Jarrettet al. 2006)

are discredited, ‘growth’ is typically controlledthrough interaction with continuous fields ofnutrients or signalling molecules (Ermentrout andEdelstein-Keshet 1993; Liddell and Hansen 1993;Regalado et al. 1996; Lopez and Jensen 2002). CAmodels can generate crude spatial representationsof mycelial structure (Fig. 13.6A), but are heavilyconstrained by the regular, often two-dimensionallattice used in the simulation. One more recentapproach to unite the aspirations of the differenttypes of modelling is to make a hybrid model thatcaptures the most pertinent biological behaviourrin a PDE model, but allows the PDE model torun on a discrete framework that simulates thediscrete behavior of individual hyphae and thenetwork structure of the mycelium. This approachhas been pioneered by Davidson and colleagueswith impressive results (Boswell et al. 2006).

C. Vector Models

An alternative approach to achieve greater mor-phological realism is to develop models based upon(empirical) rules that govern the growth rate andbranching characteristics of vectors representingthe hyphae. The rules may include stochastic sam-pling of experimentally determined parameter dis-tributions of, for example, tip and branch angles,branching frequency or internode length (Hutchin-son et al. 1980; Yang et al. 1992a, b; Lejeune andBaron 1995, 1997, 1998; Lejeune et al. 1995). Ratherthan prescribe these growth and branching param-eters, Meškauskas and colleagues (2004a, b) devel-


oped a Neighbour Sensing (NS) model in whichthe growth vector of each virtual hyphal tip is cal-culated taking into account the potential influenceof the surrounding virtual mycelium (Fig. 13.6B).Thus in this model branching probability, posi-tion and orientation are determined directly byevaluation of local density-dependent fields, ratherthan through random stochastic processes. Themodel outputs various colony statistics, such astotal mycelial length and internode length, thatassist in comparison with real experimental data(Meškauskas et al. 2004a, b).

Other visually realistic simulations have beenproduced using ‘Lindenmayer’ (or L) systems.L-Systems are string rewriting rules (productions)operating on a component (predecessor) and con-verting it to a successor according to the rule(s),so that a complex object can be developed bysuccessive replacement of parts of a simpler object.They were formulated by Lindenmayer (1968) asan axiomatic theory of biological development.L-Systems operate with a string notation whichhas been given increasing levels of complexity andsimulation power over the years (Prusinkiewiczand Lindenmayer 1990; Prusinkiewicz 2004;Prusinkiewicz and Rolland-Lagan 2006; see alsothe ‘visual models of morphogenesis’ website athttp://www.cpsc.ucalgary.ca/Research/bmv/vmm-deluxe/index.html).

Although branching fungal mycelia fit wellwith the L-system framework, there has beenlittle application of L-systems to modelling fungi(Liddell and Hansen 1993; Soddell et al. 1995;Tunbridge and Jones 1995). The most sophisticatedstochastic context-sensitive parametric L-systemso far developed (Tunbridge and Jones 1995) imple-ments the underlying cellular processes originallyput forward by Prosser and Trinci (1979). Thustip growth is dependent on vesicle supply fromsub-apical compartments. Once sufficient growthoccurs, nuclear division and septum formationtake place. If sufficient vesicles subsequently accu-mulate in subapical segments, branch formation isinitiated. Iteration of these rules generates a stringdescribing the branching structure, but with noexplicit two- or three-dimensional representation.To produce realistic two-dimensional images,additional stochastic operations are includedduring visualisation of the structure, such asrandom selection of branching direction, variationin branching angle, curved hyphal shape andpreferential radial growth. The authors note thatmore realistic graphical depiction would require

the introduction of geometrical information intothe simulation so that the stochastic elementsform part of the developmental rules rather thanjust affecting visualisation of the structure.

These models all produce branching trees,where the emphasis is to achieve a representativesimulation of the structure formed or to investigateplausible mechanisms based on the underlyingphysiological processes that may control growth.However, none of the vector models includeanastomoses, not least because hyphal contactis difficult to calculate in three-dimensionalspace and cycles are difficult to capture withinthe hierarchical data structure of either theNS-model or L-model. Thus, none of the currentmorphological models help to provide any insightinto the importance of the network structure.Furthermore, it is not possible to perform muchquantitative comparison between the extractednetwork representations described here and themodel simulations in the absence of anastomoses.

D. Abstracted Networks –Hub and Spoke Models

An alternative approach to understand the be-haviour of fungal networks is to abstract theessence of a mycelial network and re-cast it ina form that permits more rigorous mathematicalanalysis. Thus the interplay between radial expan-sion and lateral connections can be captured ina ‘hub and spoke’ model of the developing fungalmycelium (Ashton et al. 2005; Jarrett et al. 2006; seeFig. 13.6C). This is a generalised topology applica-ble to several different (non-biological) transportsystems and allows exactly solvable solutions toquestions of nutrient flows under different costscenarios (Ashton et al. 2005; Jarrett et al. 2006).The formula for the average shortest path lengthacross the network comprising a central hub withvarying connections (spokes) to a ring of nodes canbe calculated and exhibits non-trivial behaviourwhen different cost functions are imposed ontransport through the hub, for example. It is possi-ble to extend this model further to consider a morecomplicated model of a biological system whichcontain a ring and hub embedded within anotherring, with the original ring–hub motif functioningnow as a hub. This process may then be repeatedto whatever extent is required by ‘re-normalising’each ring–hub combination as a hub for the nextouter ring, with a cost for using this hub equivalent


to the average shortest path of the original ring–hub motif (Jarrett et al. 2006). This enables analysisof increasingly complex networks by collapsingmultiple rings around a very central hub into onestructure albeit with a complicated cost function.

IV. Nutrient TransportThrough the Network

Although the network architecture is of consider-able interest, it only defines which connections arepossible at any given time, but not the strength ordirection of nutrient transport or signalling fluxesflowing on the network. The precise mechanismsunderlying nutrient translocation in fungi are notyet characterised in detail, but are thought to in-clude mass flow, diffusion, generalised cytoplasmicstreaming and specific vesicular transport (Jen-nings 1987; Olsson and Jennings 1991; Olsson andGray 1998; Cairney 2005; Darrah et al. 2006; see alsothe chapter by Ashford and Allaway, Chap. 2 in thisvolume).

A. Transport at the Micron to Millimetre Scale

At the cellular level, many organelles are knownto move by motor-driven transport predominantlyalong the microtubule cytoskeleton, primarily tokeep pace with the extending hyphal tip in the api-cal septal compartment (Fischer 1999; Steinberg2000; Suelmann and Fischer 2000; Westermann andProkisch 2002; Hickey et al. 2005; see also the chap-ters by Fischer and by Sudbery and Court, respec-tively Chaps. 5 and 6 in this volume). Occasionallymuch more rapid movements can be observed andmay be driven by association with different classesof motor protein (Suelmann and Fischer 2000).For example, during normal growth, migration ofthe most apical nuclei follows tip elongation, atspeeds of 0.1–1.2 μm min−1, with progressive slow-ing and eventually arrest sub-apically (Suelmannet al. 1997; Fischer 1999). However, during forma-tion of a dikaryon, nuclear migration can be or-ders of magnitude higher (Suelmann and Fischer2000) and nuclei can spread over long distancesthroughout the whole mycelium of the compatiblepartner. Whilst the nucleus is not normally con-sidered in discussion of nutrient movement, it hasbeen suggested that mobilisation of N and P fromDNA can act as a valuable source of nutrients froman osmotically inactive precursor that can be ex-

ploited under resource limitation or during sec-ondary branch formation in more mature hyphae(Maheshwari 2005).

Movement of material in vesicles along a cy-toskeletal system is perhaps a more traditionalmechanism to translocate nutrients over longdistances. However, at this stage there is littlequantitative information documenting the role ofvesicle movement in sub-apical compartments, asmost research has focussed on vesicle traffickingevents at the tip, particularly the evidence for(or against) endocytosis (e.g. Cole et al. 1997;Hoffmann and Mendgen 1998; Fischer-Partonet al. 2000; Atkinson et al. 2002; Torralba and Heath2002; Read and Kalkman 2003; Steinberg and Fuchs2004; Harris and Kwang 2006; see also the chapterby Bourett et al., Chap. 1 in this volume). Motor-driven transport along microtubules can operate atspeeds of 1–3 μm s−1 (Steinberg 1998, 2000), whichis more than sufficient velocity to bring materialto an elongating tip, although the flux depends onthe volume of the vesicles and the concentration ofthe nutrients. To be an effective transport systemover several septal compartments or even overa whole colony, a microtubule-based system wouldrequire persistent polarised arrays extending overa considerable physical distance. Although thereis increasing evidence of a role for microtubules inorganelle movement (Xiang and Plamann 2003),only a few studies have documented microtubulearrays over the physical scales needed to explainnutrient transport throughout a colony (see, forexample Timonen et al. 2001). Likewise, actin mi-crofilaments are essential for polarised growth andseptation, and are involved in organelle movementin apical cells (Steinberg 1998, 2000; Czymmek et al.2005; Harris and Kwang 2006; see also the chapterby Sudbery and Court, Chap. 6 in this volume), buttheir role has not been studied in the long-distancetransport of vesicles on a millimetre scale or higher.

In addition to small vesicle transport, ithas been proposed that the highly dynamicpleiomorphic vacuolar system might have a rolein long-distance nutrient translocation (Ashford1998; Ashford and Allaway 2002; Chap. 2 in this vol-ume). This extensive organelle system is present infilamentous fungi of all the major fungal taxonomicgroups so far examined (Ashford 1998; Ashfordand Allaway 2002). Several mechanisms have beensuggested, including diffusion through connectedvacuole compartments, directed transport of smallvesicles, ‘crawling’ of large vacuoles and evenperistaltic-like contractions (Ashford 1998; Cole


et al. 1998; Bago et al. 2001; Ashford and Allaway2002; Cairney 2005; see the chapter by Ashford andAllaway, Chap. 2 in this volume). We recently usedconfocal fluorescence recovery after photobleach-ing (FRAP) of an internalised fluorescent markerto quantify diffusive transport for different levelsof vacuolar organisation moving away from thetip, in combination with a predictive simulationmodel from these data to determine the transportcharacteristics of the system over an extendedlength scale (Darrah et al. 2006). This combinedimaging and modelling approach reveals thatthe vacuole system can have a major impact onsolute transport on a millimetre-to-centimetrescale. There is also a strong predicted interactionbetween vacuolar organisation, available nutrientlevels, the predicted diffusion transport distancesand the architecture of the branching colonymargin. For example, an unbranched hyphapossessing a continuous tubular vacuole systemcan sustain growth over a transport distance ∼12–24 mm solely by diffusion through the vacuolesystem. Conversely, diffusion alone in a maximallybranched system would only be sufficient to supplyenough resources to the tip over a few millimetres(Darrah et al. 2006).

This poise between translocation being suffi-cient or insufficient depending on the amount of hy-phal branching and status of the vacuolar networksuggests that nutrient supply through the vacuolarsystem could be an important route to co-ordinatetip growth and branching. It is possible that reg-

Fig. 13.7. Schematic diagram of possible transportpathways operating in corded mycelial systems. (i) Water(open arrows) and nutrients (dashed line) are initiallytaken up at the inoculum. (ii) An osmotically active solute(solid arrows) is loaded into a vessel hypha with a cord togenerate an acropetal pressure-driven mass flow that alsocarries other solutes towards the tips. (iii) The osmoticgradient is maintained by solute unloading at the baseof the peripheral growth zone. (iv) Nutrients needed forgrowth move towards the tip through a combination of

cytoplasmic diffusion, mass flow, vesicle transport and/ordiffusion through the vacuole system. Nutrients taken upat the tip have to move backwards against the prevailingdirection of mass flow, possibly through the vacuolesystem (v). (vi) The majority of the osmotically activesolute is loaded into a second vessel hypha to generatea mass flow in the opposite direction to facilitate basipetaltransport. (vii) Unloading of the solute at the inoculumcompletes the cycle needed for rapid bi-directional solutemovement

ulation of the connectivity of the vacuolar systemcould change its translocation capacity accordingto the local nutrient demand. The system could thusshift between increasing transport to tips, to pre-venting unnecessary nutrient mobility by isolatingtips. Alternatively, and equally likely, is that the vac-uolar system translocates material acquired by thetips back into the main colony, against the massflow component in the cytoplasm needed for tipextension, particularly when growing over an inertsubstrate (Fig. 13.7). This problem becomes pro-gressively more acute moving basipetally from thetip, as the acropetal flow through the parent hyphahas to increase with the number of tips supported.Some reduction in the flow velocity can be achievedby increasing the diameter of the hypha, particu-larly as volume flow scales with r4 (see Eq. 13.1).However, fluorescence labelling of the vacuoles andmitochondria in these regions shows that they areanchored in place and buffeted by a cytoplasmicflow (Ashford 1998; Darrah et al. 2006).

It should be noted that the vacuole model doesnot preclude additional solute translocation path-ways that may operate in parallel in the cytoplasm.We are currently working on the measurement andmodelling of cytoplasmic and apoplastic diffusionand mass flow pathways, with a view to buildingan extended model with all compartments rep-resented. It is expected that this will yield usefulpredictive results for relatively simple branchedmycelial systems in the peripheral growth zone.However, there is still remarkably little understand-


ing on how these might interface with the develop-ing sub-marginal anastomosis network and cordformation behind the growth front. Clearly an areafor future research is to provide detailed anatomi-cal descriptions of the hyphal organisation in thesekey areas of the colony, to link cell biological inves-tigations at the hyphal level to flux-based measure-ments at the colony level.

B. Transport at the Millimetreto Centimetre Scale

Detailed temporal and spatial analysis of nutrientfluxes in individual mycelia uses non-invasive map-ping of radioisotopes, mainly 14C and 32P. Typically,the final radiolabel distribution is visualised usingautoradiography techniques, phosphor-imaging oranalysis by destructive harvesting of the tissues fol-lowed by scintillation counting. The emerging pic-ture for C and P dynamics is complex, with evidencefrom studies in microcosms for highly responsiveshifts in nutrient allocation depending upon thesize and quality of resource units, the sequence oftheir encounter and the presence of other compet-ing organisms (Boddy 1999). In general, substan-tial levels of isotope are taken up, but with vary-ing amounts retained at the loading site (Clipsonet al. 1987; Olsson and Gray 1998). Net allocationof the remainder through the network is a com-plex function of multiple competing source–sinkrelationships (Wells et al. 1995, 1998, 1999). Move-ment can be bi-directional (Granlund et al. 1985;Olsson and Gray 1998; Lindahl et al. 2001; Nielsenet al. 2002), with features similar to the operationof a circulatory system (Wells et al. 1998).

Absolute rates of translocation vary over at leasttwo orders of magnitude, from 1.8 mm h−1 (Ols-son and Gray 1998) to 200 mm h−1 (Brownlee andJennings 1982), depending upon the degree thatspecific transport pathways, such as cords and rhi-zomorphs, have developed. The most likely systemdriving transport over these length scales is massflow, although how the driving force is establishedand the precise anatomy, connectivity and controlof flux through the conduits are not clear. Unlikea cytoskeletal/motor-driven system, the velocity ofmovement in a mass flow system is relatively un-informative per se, as it is a function of the relativecross-sectional area of the different pipes at eachlevel in the branching hierarchy. For example, thewater flow rate through a single cord growing outacross an inert surface has to scale linearly with the

number of growing tips supported and inverselywith the cross-sectional area of conducting tissuein the cord in relation to the cross-sectional area ofthe individual hyphae. In other branching systemsthere is typically conservation of cross-sectionalarea at all levels of the branching hierarchy, giv-ing a constant flow rate (West et al. 1997, 2001).We infer that this is not the case in fungal net-works, as the diameter of the cords increases ata lower rate than predicted by an area-preservingrelationship and conversely the measured (nutri-ent) velocities are all significantly greater than thetip extension rate. There is also a major concep-tual difficulty in setting up a plausible mass flowmodel that can accommodate bi-directional move-ment without extremely tight coupling between in-flow and outflow at each end of the system. Onesolution might be to have specialised cells cyclingan osmotically active molecule, such as trehalose,at both ends of two adjacent but insulated con-duits to generate anti-parallel mass flow (Fig. 13.7).Other nutrients could be loaded and unloaded atany point of the circulating stream as local source–sink patterns change. Interestingly, the rate of so-lute movement in the cords in such a circulatorymass flow model could be completely uncoupledfrom the rate of tip growth.

In comparison to C and P, even less informationis available for N dynamics, as there is no suitableradioisotope tracer. However, some progress hasbeen made using 14C-aminoisobutyrate (14C-AIB)as a non-metabolised marker for soluble aminoacids (Kim and Roon 1982; Watkinson 1984; Lillyet al. 1990; Olsson and Gray 1998; Tlalka et al. 2002,2003). 14C-AIB shows rapid uptake, bi-directionaltransport and movement through specific trans-port pathways in undifferentiated mycelia onagar (Olsson and Gray 1998). Recently, usingphoton-counting scintillation imaging (PCSI), weshowed that N allocation is extremely dynamic,with rapid, preferential N-resource allocation toC-rich sinks, induction of bi-directional transporton cord formation and abrupt switching betweendifferent pre-existing transport routes (Tlalkaet al. 2002, 2003). These results suggested that ourpredictions of transport based solely on the net-work architecture (see Sect. C.) are too simplistic.However, we believe that the mismatch betweenpredictions from the simple network model andthe experimental data will be a productive areafor future research and may give much greaterinsights into the strategy used by the fungus tocontrol fluxes.


Whilst indeterminate growth and flexible re-source allocation are of great benefit in exploitinga patchy resource environment (Boddy 1999; Et-tema and Wardle 2002; Watkinson et al. 2006), co-ordination of these activities poses a considerablechallenge within an interconnected, but locally re-sponsive, network (Rayner et al. 1994). In this con-text, it is interesting to note that there is a significantpulsatile component to N-transport, with evidencefor differential behaviour between the assimilatoryand foraging mycelia. The pulsatile component canbe analysed using Fourier techniques to show thatsignals from the assimilatory hyphae in the inocu-lum, new resources and the foraging hyphae alloscillate as distinct domains that are locally syn-chronised, but are out of phase with each other(Fig. 13.3, see page 310; Tlalka et al., submitted).At this stage we do not know what significance toattribute to the emergence of oscillatory phase do-mains in terms of global co-ordination within thecolony. However, there is an extensive literatureon the emergent properties of coupled oscillatorysystems (see, for example Strogatz 2001) and it istempting to speculate that coupled oscillatory be-haviour may reflect underlying pattern formationin basidiomycete fungi, as with other simple micro-bial systems (Gerisch 1987; Dormann et al. 2002;Ueda 2005). This may represent a general princi-ple used by self-organising biological systems toachieve global co-ordination and solve complexrouting problems (Nakagaki et al. 2000, 2004; Teroet al. 2006).

V. Conclusion: Future Prospects

The past few years have seen massive advancesin the technology available to address fundamen-tal questions in fungal biology. Live cell imaging,molecular techniques and green fluorescent pro-tein fusions are set to revolutionise our understand-ing of sub-cellular dynamics in a similar mannerto results in the plant field (Brandizzi et al. 2002;Fricker et al. 2006; see also the chapters by Ash-ford and Allaway, and Bourett et al., respectivelyChaps. 1 and 2 in this volume). New radioisotopeimaging techniques are adding dynamics to ourunderstanding of nutrient fluxes at the colony level(Gray et al. 1995; Timonen et al. 1996; Olsson andGray 1998; Lindahl et al. 2001; Tlalka et al. 2002,2003), whilst tools from graph theory may start toprovide insights into the crucial network organi-

sation and behaviour within the colony. Indeed, itis not impossible that detailed characterisation ofsuch self-organised, adaptive networks and theirdynamical behaviour may inform strategies to im-prove the design of anthropogenic infrastructurenetworks. Finally, a range of mathematical modelsis being developed that have the potential to drawtogether results from all these disparate strandsand synthesise a coherent picture of colony growthand function for the first time.

Acknowledgements. Research in the authors’ laborato-ries has been supported by BBSRC (43/P19284), NERC(GR3/12946, NER/A/S/2002/882), EPSRC (GR/S63090/01),EU Framework 6 (STREP No. 12999), the Oxford UniversityResearch Infrastructure Fund and the University DunstonBequest. We thank A. Ashford, K. Burton, P.R. Darrah,D.P. Donnelly, D. Eastwood, J. Efstathiou, J. Hynes,N. Johnson, F. Reed-Tsochas, M. Tlalka, G.M. Tordoff,S.C. Watkinson and members of CABDyN for stimulatingdiscussion.

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13 Network Organisation of Mycelial Fungi · Network Organisation of Mycelial Fungi 309 ure, summarise and compare such complex net-works. In the 1990s, fractal measures were intro-duced