- Email: [email protected]
Characterization of the spatial aspects of foraging mycelial cord systems using fractal geometry
Mycol. Res. 97 (6): 762-768 (1993)
762
Prinled in Greal Brilain
Characterization of the spatial aspects of foraging mycelial cord systems using fractal geometry
RORY G. BOL TON AND LYNNE BODDY School of Pure and Applied Biology, University of Wales, Cardiff CFl 3TL UK
The fractal geometry of foraging mycelial systems of Phanerochaete velutina and Hypholoma fasciculare, extending into soil from woody resource bases of varying nutrient status, was determined. The degree of structural heterogeneity and branching of systems, as described by the fractal dimension, was greater when the nutrient status of the resource base was high. H. fasciculare produced more-branched, slower-extending systems, with a greater commitment of mycelial biomass to exploration than P. velutina. The potential use of fractal geometry as a descriptor of foraging strategies of cord-forming, saprotrophic baSidiomycetes, and the possible mechanisms operating to generate fractal growth in these systems are discussed.
Fractal geometry has been applied to the description of many complex objects in natural systems (Gleick, 1987; Kaye, 1989 a; Markx & Davey, 1990; Sugihara & May, 1990), and its potential for describing the growth and branching patterns of fungal mycelia has been recognized (Obert, Pfeifer & Sernetz, 1990; Ritz & Crawford, 1990; Ainsworth & Rayner, 1991). Fractal geometry is applicable to structures that exhibit self-similarity (Mandelbrot, 1982; Kaye, 1989a; Pfeifer & Obert, 1989), that is, they have a geometry that is repeated over magnifications ad infinitum. In practice, such self-similarity only occurs in 'ideal fractal structures', such as Koch's triadic island (Kaye, 1989a). With natural, heterogeneous objects there are limits to the range over which self-similarity applies. Often the heterogeneity of a structure is not identical when viewed under different magnifications, so that any mathematical relation applied to the structure, concerning scale (see below), is sustained only approximately. Such structures are termed 'statistically self-similar' (Kaye, 1989 a), and although fractal geometry is still applicable, there are limitations. The theory, justification and implications of fractal geometry as applied to fungal mycelia have been discussed by Ritz & Crawford (1990). Briefly, the parameter of major interest is the fractal dimension (0). For whole structures embedded in two dimensions, 0 ranges between I and 2, with larger values representing objects of increasing structural irregularity and complexity. Thus, for fungal colonies 0 represents a measure of the heterogeneity and branching of the mycelium (Ritz & Crawford, 1990). When assigning a fractal dimension to complex objects it is assumed that a power law relationship exists for any parameter used to measure a structure (Mandelbrot, 1982; Kaye, 1989 a; Pfeifer & Obert, 1989). Thus in fractal structures the parameter measured is proportional to the units of its measurement, at a rate that is determined by O. To date, two different approaches have
been adopted for the calculation of 0 in fungal colonies grown across two-dimensional surfaces. Firstly, Ritz & Crawford (1990) calculated the mycelial mass contained within a given radius, originating at the centre of a colony, over a range of different radii. Secondly, Obert et al. (1990) employed the 'box-counting method', in which two different types of fractal structure were identified: (I) mass fractals, where the whole mass of the colony is fractal; and (2) surface fractals, where only the colony margin or border is fractal owing to the overlapping of hyphae in the colony centre. According to this terminology, the method of Ritz & Crawford (1990) measures the mass fractal dimension, assuming a colony has a constant dimension across the zone of the search surface investigated. This technique is useful when studying the spatial aspects of foraging systems, since the point of inoculation can be used as the centre of the search surface during calculation, thus defining the search surface as the potential area of exploration for the fungal mycelium. In the present study, fractal geometry was used to investigate spatial aspects of foraging systems of two contrasting mycelial cord-forming, saprotrophic basidiomycetes Phanerochaete velutina (L.: Hook.) Greville and Hypholoma fasciculare (Huds.: Fr.) Kummer as they extended out from a food base into non-sterile soil (d. Dowson et al., 1986, 1988, 1989). The commitment of mycelial biomass to exploration by these systems was also determined and related to their fractal geometry.
MATERIALS AND METHODS Strains and culture media Laboratory stocks of P. velutina and H. fasciculare were used. P. velutina was originally isolated from decaying beech (Fagus
763
R, G, Bolton and Lynne Boddy
sylvatica L.) wood, and H. fasciculare from tissue of a fruit body on a beech log, both collected from the Forest of Dean, Gloucester, U,K, (SO 611145), Cultures were maintained and routinely subcultured on 2 % (w Iv) malt extract agar (MEA; 20 g Munton & Fison spray malt, 15 g Lab M no, 2 agar [-1 distilled water), Growth and photography of mycelial cord systems Foraging mycelial cord systems were grown in 24 x 24 cm lidded bioassay dishes (Nunc: Gibco, Paisley, U.K,), according to the method of Dowson et al. (1986, 1988, 1989), across compressed, non-sterile soil from beech wood block inocula (pre-colonized in agar culture flasks) of different sizes and states of decay (as indicated below). The soil was frozen to - 20°C twice, prior to incorporation into systems, This inhibited the growth of invertebrates such as Collembola spp., which graze fungi and sometimes affect mycelial outgrowth patterns, All cord systems were photographed regularly (see below) using an Olympus OM-2 camera body fitted with a 50 rom OM-system macro lens and Ilford FP4 (125 ASA) 35 mm black and white film, as described in detail by Bolton, Morris & Boddy (1991),
Calculation of fradal dimension (D), rate of mycelial extension, and extra resource mycelial biomass
o was calculated using the method of Ritz & Crawford (1990), except that mycelial area rather than mycelial mass was the parameter measured. Mycelial area has been shown to be directly proportional to mycelial biomass in foraging cord systems of P, velutina, when developing in two dimensions and growing on compressed soil (Bolton et al., 1991), The power law relationship from Ritz & Crawford (1990) may therefore be represented as: A(r)
the image analysis method of Bolton et al. (1991). In addition, a biomass expenditure index of total extra-resource mycelial biomass per total area explored (mg mm- 2 ) was calculated for each P. velutina treatment.
Effed of inoculum resource size, extent of pre-colonization and time on D, rate of mycelial extension, and extra resource mycelial biomass In one experiment, 0 was calculated for mycelial cord systems of P, velutina extending from 0'2, 0'5 and 8 cm 3 wood blocks after 9, 18 and 25 d post-inoculation, and for cord systems of H. fasciculare extending from 0'5 and 8 cm 3 wood blocks after 11, 16 and 37 d post-inoculation, The incubation period for the different-sized inoculum blocks in culture flasks prior to inoculation was staggered, so that the degree of colonization by the test fungus was standardized for each block size, Thus the 0'2, 0-5 and 8 cm 3 wood blocks were incubated for 14, 21 and 35 d respectively, The .relative densities (g cm- 3 ) of the different block sizes were not significantly different (P > 0'05) for each species (Table 1). Table 1. Fractal dimension (0), rate of mycelial extension (rnrn d-'), and extra-resource mycelial biomass (mg) of mycelial cord systems of P, velutina and H. fasciculare extending from inoculum resources of different size with time P, velutina: inoculum volume (ern 3 ) and relative density (g cm- 3 ) in parentheses
Fractal dimension (0)
Biomass (mg)
where A(r) is the area of mycelium contained within radius r, was calculated from photographs of cord systems using the image analysis method of Bolton et al. (1991), Stencils of given radii were used during image capture to define the given area r under investigation. At least five different radii were investigated for each image. Analysis was not taken to the extending mycelial front of colonies owing to boundary effects (Ritz & Crawford, 1990), and differences in branching pattern exhibited by some systems in peripheral zones (see below), Double logarithmic (Robertson) plots of A against r were constructed with r on the x-axis, according to the methodology described by Markx & Davey (1990) and Kaye (1989a). Since A(r) was cumulative over the range of r investigated, the slope of the Robertson plots corresponds to (20 -1) (Kaye, 1989 b). Mycelial extension rate (mm d- 1 ) was estimated from the average of eight radial measurements of mycelial extent for each colony between time of inoculation of trays and sampling time. Extra-resource mycelial biomass (mg) was determined using
0'5 (0'51 a)
8 (0'55 a)
18
1'21 a 1'22 a
1'81 b 1'62 c
25
1'21 a
1'28 a 1'22 a 1'22 a
9
0'49 a 1'03 a 1'36 a
1'34 a 1'14 a 1'93 a
4'77 a 6'27 a 6'34 a
9
2'53 a
18 25
2'60 a
2'87 a 3'20 a 2'93 a
4'40 a 4'87 a 3'67 a
9
18 25
= K,v
K is a constant, and 0 is the fractal dimension, Mycelial area
0'2 (0'51 a)
Time (d)
Mycelial extension rate (mm d-')
2'00 a
1'62 c
H. fasciculare: inoculum volume (ern 3 ) and relative density (g ern- 3 ) in parentheses 0'5 (0'59 a)
Fractal dimension (0)
11 16
37
Biomass (mg)
11 16 37
Mycelial extension rate (rnrn d-')
11 16 37
8 (0'57 a)
1'68 a 1'70 a 1'59 a
1'93 b 1'92 b 1'84 ab
2'93 a 3'34 a 3'88 a
7'94 ab 13'1 b 25'3 c
1'43 a 1'77 ab 1'70 ab
2'43 ab 2'63 ab 2'67 b
Values for each parameter followed by the same letter are not significantly different (P> 0'05) using one-way ANOVA and S-tests, Comparisons are made within but not between species, for each parameter,
Fractal geometry of mycelial cord systems
764
Figs 1-4. Outgrowth patterns of mycelial cord systems of P. velutina extending from the following. Fig. 1. 0'2 cm 3 inoculum after 18 d. Fig. 2. 0'5 cm 3 inoculum after 25 d. Fig. 3. 8 cm 3 inoculum after 9 d. Fig. 4. 8 cm 3 inoculum after 18 d. The fractal dimensions of the system were 1'25, 1'33, 1'85 and 1'65 respectively. I, inoculum resource block; B, nutritionally inert plastic bait.
In a second experiment, D was calculated for mycelial cord systems of P. velutina extending from wood blocks colonized for different times prior to incorporation in experiments. Thus both 0-5 and 8 cm 3 wood blocks were pre-colonized in culture vessels for 14, 56 and 154 d. Relative density (g cm -3; Table 2) of ten blocks of each inoculum type was determined at the same time as inoculation of blocks into dishes. Four replicates of each treatment were set up.
RESULTS
Effect of inoculum resource size on V, rate of mycelial extension, and extra-resource mycelial biomass In the first experiment, H. fasciculare and P. velutina exhibited different patterns of outgrowth from inocula of different sizes (Figs 1-7). The D exhibited by H. fasciculare were consistently
larger than those of P. velutina for corresponding resources and times (Table 1). With both H. fasciculare and P. velutina, the D was significantly (P < 0'05) larger in systems extending from 8 cm 3 inocula than from smaller resources. D tended to decrease with time, significantly (P < 0'05) with systems of P. velutina extending from 8 cm 3 inocula. Mycelial extension of P. velutina was consistently more rapid than H. fasciculare, for corresponding resources and times (Table 1). D and rate of mycelial extension were significantly positively correlated (P < 0'001) for both P. velutina and H. fasciculare (Fig. 8). The increase in D with mycelial extension rate was more rapid with H. fasciculare compared with P. velutina. Extra-resource mycelial biomass was consistently larger in H. fasciculare compared with P. velutina, for corresponding resources and times (Table 1). Biomass was consistently greater in systems extending from relatively larger resources,
R. G. Bolton and Lynne Boddy
765
~
Figs 5-7. Outgrowth patterns of mycelial cord systems of H. fasciculare. Fig. 5.0'5 em 3 inoculum after 16 d. Fig. 6. 8 em 3 inoculum after 16 d. Fig. 7. 8 cm3 inoculum after 37 d. The fractal dimensions of the systems were 1'59. 1'89 and 1'8 respectively. I. inoculum resource block; B, nutritionally inert plastic bait.
2
0 08
00 0 0
1·8 0
§ c
0 '0;
.,c
•
0
•
0
1·6
•
• •
••
0
.6 'l:l ~ (j
•
0 0
0
1·4
'"...
••
~
1
•
•
1·2
, 0
1
•••
•
•
•
2
•
•
•• • • •
3
4
5
6
Mycelial extension rate (mmd- I ) Fig. 8. Relationship between fractal dimension (D) and rate of
mycelial extension (mm d- 1 ) for foraging mycelial cord systems of P. velufina (.) and H. fasciculare (0).
and consistently increased with time of outgrowth, significantly (P < 0'05) in the case of H. fasciculare.
Effect of extent of pre-colonization of inoculum resources on 0, rate of mycelial extension, and extra-resource mycelial biomass of P. velutina In the second experiment, different patterns of outgrowth occurred from resource bases pre-colonized for varied periods of time (Table 2). However, the relative densities of differentsized inocula pre-colonized for similar periods were only significantly different in 154 d treatments (P < 0'05). The D of systems extending from 8 ems inocula were generally larger than for 0'5 cm 3 inocula for comparable times of pre-colonization and outgrowth (Table 2). For systems developing from both sizes of inocula, precolonized for 14 d, D significantly decreased (P < 0'05) with
time. D also varied depending on the extent of precolonization. With 0'5 ems inocula, significantly (P < 0'05) larger D values were obtained with inocula pre-colonized for 56 d than for 14 or 154 d inocula. at the earlier stages of outgrowth. Significantly lower D values were observed from systems extending from inocula pre-colonized for 154 d. With 8 ems inocula there were no significant differences (P > 0'05) in D associated with the extent of pre-colonization. although the D of systems from 56 d inocula was significantly lower (P < 0'05) than other treatments, after 11 d outgrowth only. With 0'5 em3 inocula, the rate of mycelial extension was significantly different (P < 0'05) between all inoculum precolonization treatments, at the earlier stages of outgrowth, with the 56 and 154 d treatments exhibiting the highest and lowest values respectively. Extra-resource mycelial biomass was significantly larger (P < 0'05) in systems of P. veZutina extending from 8 cm 3 inocula than from 0'5 cm 3 inocula for corresponding times of pre-colonization and outgrowth (Table 2). Biomass was significantly (P < 0'05) greater from 0'5 cm 3 inocula precolonized for 56 d compared with 14 and 154 d inocula. at the earlier stages of outgrowth. With 8 cm 3 inocula, biomass increased with Hme of outgrowth, although not Significantly (P > 0'05) with the 154 d pre-colonized treatment.
Relutionship between D and biomuss expenditure
D was not proportional to the biomass expenditure (mg mm- 2 area explored) of mycelial cord systems of P. veZutina (Fig. 9).
DISCUSSION This study suggests that the D values exhibited by foraging mycelial cord systems of P. velutina and H. fasciculare depend upon the potential of the nutrient base, from which the mycelium is extending. as a carbon/energy source, in that systems emanating from small-sized inocula had the lowest D values. A possible reason may be that whereas a low nutrient base is unable to sustain a complex mycelium with a high
766
Fractal geometry of mycelial cord systems Table 2. Fractal dimension (0), rate of mycelial extension (rom d-'), and extra-resource mycelial biomass (mg) of mycelial cord systems of P. ve/ulina extending from 0'5 and 8 em' inoculum resources of varying states of pre-colonization with time 0'5 em' inoculum size: inoculum pre-colonization time (d) and relative density (g em') in parentheses 14 (0'53 a)
56 (0'52 a)
154 (0'40 b)
IS 27
1'44 (a.l) 1'44 (a,I) 1'24 (a,2)
1'64 (b,l) 1'63 (b,I) 1'22 (ab,2)
1"24 (c,l) 1'21 (c,I) 1'11 (b,I)
11 IS 27
2'02 (a,l) 3'55 (ab,2) 1'15 (a,l)
4'57 (b,I) 6'17 (b,I) 3'18 (a,l)
0'75 (a,I) 1'32 (a,I) 0'53 (a,I)
Mycelial 11 extension IS rate (mm do') 27
3'75 (b,12) 4'00 (b,2) 2'81 (a,l)
6'62 (c,2) 6'62 (c,2) 3'33 (a,l)
1'70 (a,I) 2'05 (a,I) 1'30 (a,l)
Time (d) Fractal dimension (0)
Biomass (mg)
II
8 em3 inoculum size: inoculum pre-colonization time (d) and relative density (g em-') in parentheses 14 (0'57 a)
154 (0'49 a)
l'S8 (b,l) 1'65 (a,I) l'SI (a,l)
1'83 (a,l) 1'77 (a,l) 1'65 (a,I)
5'99 (a,1) 10'53 (a,12) 14'87 (a,2)
6'04 (a,l) 16'18 (a,12) 21'36 (a,2)
20'28 (b,I) 27'68 (a,I) 27'11 (a,l)
4'96 (a,I) 5'71 (a,l) 6'86 (a,l)
4'20 (a,l) 5'02 (a,l) 6'12 (a,l)
6'50 (a,I) 7'52 (a,I) 7'56 (a,I)
Fractal dimension (0)
II
IS 27
1'90 (a,l) 1'79 (a,12) 1'48 (a,2)
Biomass (mg)
11 15 27
Mycelial 11 extension IS rate (mm d-') 27
56 (0'54 a)
Data in the same column followed by the same number, and data in the same row followed by the same letter, for each different inoculum size and parameter, are not significantly different (P > 0'05) using one-way ANOYA and S-tests,
degree of branching, an increase in nutrient status affords a more space-filling, branched mycelium, This possibility is supported by the consistently increased extra-resource mycelial biomass observed in systems extending from resources of higher nutrient status. Furthermore, as exploratory growth proceeds, Le. where the nutrient base has not become exhausted, mycelial outgrowth becomes less complex, as represented by lower D. This reduction in D may be symptomatic of a biomass-conserving strategy, through reabsorption of nutrients from autolysed cord branches, such as is implied by the regression of remote cord branches observed during resource capture by these fungi (Dowson et al., 1986, 1988, 1989). The results also suggest that P. velutina may exhibit a base-line D of about 1'2, that represents the most affordable fractal-producing biomass expenditure when nutrients are limited. The effect of relative density/time of pre-colonization is less clear. With the 0'5 cm 3 resource, the peak D found in
systems growing from 56 d pre-colonized blocks may be attributable to: (1) greater fungal establishment than in the blocks pre-colonized for 14 d; (2) less depletion of nutrients than in the 154 d (0'40 g cm- 3 ) pre-colonized blocks. The generally higher D values for systems growing from 8 cm 3 compared with 0'5 cm 3 resources probably result from greater nutrient sources in the former, which in tum is a result of less decay (higher densities) and/or large size of resource. It is of interest that although prolonged pre-colonization of 8 cm 3 resources did not result in significant changes in D, there were consistent increases in extra-resource mycelial biomass and rate of mycelial extension. Again, this may be attributable to greater fungal establishment within the more pre-colonised resources. The observed increase in biomass expenditure without a consequent benefit from increased D indicates a relatively less efficient utilization of exploratory effort. This point demonstrates that D provides information concerning the spatial distribution of foraging biomass in mycelial cord systems that cannot be given by biomass expenditure measurements alone. The scatter of values on the plot of D against a biomass expenditure index (mg cm- 2 area explored) (Fig. 9) indicates the variability in the efficiency of spatial distribution of mycelial biomass, and demonstrates that foraging cord systems of P. velutina are not optimal in this respect. Systems that exhibited relatively higher D and lower biomass expenditure were more efficient in occupying the area that had been explored. Care must, however, be taken in interpreting the fractal data in terms of foraging efficiency. Clearly D, as calculated here, describes the spatial characteristics of colonies occupying an area already explored, In the context of foraging efficiency, the zone of mycelium at the periphery of the foraging mycelial front may be of greater importance with regard to resource capture, although it is important to note that resources may be distributed heterogeneously in time as well as space. Differences in branching pattern between the extending mycelial front and regions closer to the centre of foraging cord systems were clearly exhibited by H. fasciculare (Fig. 7). The method of Obert et al. (1990) is more suitable for investigating the fractal nature of this zone, since the current method of analysis breaks down in the peripheral regions of structures (Ritz & Crawford, 1990).
In contrast to the study of Ritz & Crawford (1990), where an unlimited supply of nutrient was distributed homogeneously throughout the substratum, differences in mycelial cord outgrowth patterns do not directly reflect the balance between exploratory and exploitative growth. In cord-forming fungi, these two conflicting modes of growth can be said to be spatially separated, with exploitative growth limited to discontinuous resource packages. Therefore the space-filling efficiency of exploratory mycelial cord systems, as described here by D, affects the probability with which spatially discontinuous resource packages may be encountered. Exploratory fronts with high D would be more effective in locating resource units of small size, essentially blanketing the foraging area. Thus the strategy employed by a fungus may be indicative of its resource specificity, its tolerance to stressful microenvironmental conditions, and its combative ability (Cooke & Rayner, 1984; Dowson et aI., 1988). These
R. G. Bolton and Lynne Boddy
767
2
• • 1·8 -
S t::
.2
•
1·6
l-
.5 "0 ]
<>
....o:l
1-4
1·2
I
••
l-
• •• • ••• • -:.
••
r-.P: •• •
0
• •
•
"
•
• •
.\
• • •
•
•
••
•
-
•
•
• •
• •
• • • ••
•
•
•
• • • • • • • • •• • • •• •• •
I.l.
•
•••
•
~ ll)
•
• I
20
I
I
40 60 80 Biomass expenditure (mg mm-2 area explored x 10-5)
100
120
Fig. 9. Relationship between fractal dimension (D) and extra-resource mycelial biomass expenditure (mg mm- 2 area explored) for foraging mycelial cord systems of P. velutina.
factors, as well as the status of the resource base from which the mycelium is extending, will detennine D. Thus H. fasciculare, associated with unspecialized resource and microenvironmental requirements, and high attacking combative ability (Dowson ef al., 1988), exhibited relatively high D, indicative of a short-range foraging strategy. In contrast, the greater resource specificity exhibited by P. velufina, and consequent longer-range foraging strategy, was illustrated by its relatively low D, faster rate of mycelial extension, and smaller commitment to extra-resource mycelial biomass. Although D provides a valuable description of the branching patterns of mycelial cord systems, it does not elucidate the underlying processes generating the differences in structural complexity observed. Rayner (1991) has proposed a theory of hydraulic pressure distribution and differential insulation, whereby the pressure generated through uptake of solutes and subsequent osmosis of water is distributed through mycelial systems according to the degree of hyphal insulation. An increase in ratio between pressure and insulation would result in an increased tendency to branch. Such hydraulic pressure has been proposed to drive the translocation of nutrients in mycelium of Serpuia Iacrimans Gennings, 1991). The results presented here are congruent with hydraulic pressure-generated branching patterns. Clearly, resource bases of relatively higher nutrient status can generate a greater potential. Since mycelial cords extending through soil are located in a relatively hostile environment, the foraging mycelium is largely non-assimilative, and so the degree of insulation might be expected to be constitutively high. Thus, the increased D observed in systems extending from resources of high nutrient status may have more to do with increased hydraulic pressure than reduced insulation. The differences
observed in outgrowth pattern between systems of H. fasciculare and P. velufina extending from resources of comparable nutrient status, however, may be attributable to differences in how these fungi insulate their hyphae. The more-branched systems of H. fasciculare may be constitutively less insulated to internal pressure. The faster extension rates exhibited by P. velufina could be generated in a more insulated system, with pressure being directed to hyphal apices rather than being dispersed through branching. Note, however, that within-species comparisons indicate faster extension rates associated with higher D (Fig. 8). If the degree of insulation remains constitutively constant for each species, the increased internal pressure generated in systems extending from high nutrient bases may be sufficient to increase both branching and mycelial extension. Thus it is possible that the different correlations between D and the extension rate exhibited by the different species may provide a profile of insulation for different species. In conclusion, fractal geometry offers a valuable instrument for describing the space-filling characteristics and foraging idiosyncrasies of cord-fonning fungi. The structural complexity exhibited by these fungi allows for a high degree of functional co-ordination that is necessary for adaptation within an uncertain environment. This complexity may be generated through simple mechanisms that could be driven by the physical constraints of nutrient availability and source-sink relationships.
We acknowledge the Natural Environment Research Council for financial support during this study. We would also like to thank Steven Hendry and Dr A. D. M. Rayner for
Fractal geometry of mycelial cord systems useful discussion, the referees for their comments on the original manuscript, and Dr Julian Wimpenny for the use of his image analysis system.
768 Dowson, C. G., Springham, P., Rayner, A. D. M. &; Boddy, L. (1989). Resource relationships of foraging mycelial systems of Phanerochaete velutina and Hypholoma fascicular< in soil. New Phytologist 111, 501-509. Gleick, j. (1987). Chaos. Heinemann: London. jennings, D. H. (1991). The spatial aspects of fungal growth. Science Progress 75, 141-156.
REFERENCES Ainsworth, A. M. & Rayner, A. D. M. (1991). Ontogenetic stages from coenocyte to basidiome and their relation to phenoloxidase activity and colonization processes in Phanerochaele magnoliae. Mycological Research 95, 1414-1422.
Bolton, R. G., Morris, C. W. & Boddy, L. (1991). Non-destructive quantification of growth and regression of mycelial cords using image analysis. Binary 3, 127-132. Cooke, R. C. & Rayner, A. D. M. (1984). Ecology of Saprotrophic Fungi. Longman: London. Dowson, C. G., Rayner, A. D. M. & Boddy, L. (1986). Outgrowth patterns of mycelial cord-forming basidiomycetes from and between woody resource units in soil. Journal of General Microbiology 132, 203-211. Dowson, C. G., Rayner, A. D. M. & Boddy, L. (1988). Foraging patterns of Phallus impudicus, Phanerochaete laevis and Steccherinum fimbria tum between discontinuous resource units in soil. FEMS Microbiology Ecology 53, 291-298.
(Accepted 3 November 1992)
Kaye, B. H. (1989a). A Random Walk Through Fractal Dimensions. VCH, Weinheim: Cambridge. Kaye, B. H. (1989 b). Image analysis techniques for characterising fractal structures. In The Fractal Approach to Heterogeneous Chemistry (ed. D. Avnir), pp. 55-66. john Wiley &; Sons: Chichester. Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. Freeman: Oxford. Markx, G. H. & Davey, C. L. (1990). Applications of fractal geometry. Binary 2, 169-175.
Obert, M., Pfeifer, P. & Sernetz, M. (1990). Microbial growth patterns described by fractal geometry. Journal of Bacteriology 172, 1180--1185. Pfeifer, P. & Obert, M. (1989). Fractals: basic concepts and terminology. In The Fractal Approach to Heterogeneous Chemistry (ed. D. Avnir), pp. 11-43. john Wiley & Sons: Chichester. Rayner, A. D. M. (1991). Conflicting flows: the dynamics of mycelial territoriality. Mellvanea 10, 24-35. Ritz, K. & Crawford, j. (1990). Quantification of the fractal nature of colonies of Trichoderma viride. Mycological Research 94, 113&-1152. Sugihara, G. & May, R. M. (1990). Applications of fractals in ecology. Trends in Ecology and Evolution 5, 79-86.
762
Prinled in Greal Brilain
Characterization of the spatial aspects of foraging mycelial cord systems using fractal geometry
RORY G. BOL TON AND LYNNE BODDY School of Pure and Applied Biology, University of Wales, Cardiff CFl 3TL UK
The fractal geometry of foraging mycelial systems of Phanerochaete velutina and Hypholoma fasciculare, extending into soil from woody resource bases of varying nutrient status, was determined. The degree of structural heterogeneity and branching of systems, as described by the fractal dimension, was greater when the nutrient status of the resource base was high. H. fasciculare produced more-branched, slower-extending systems, with a greater commitment of mycelial biomass to exploration than P. velutina. The potential use of fractal geometry as a descriptor of foraging strategies of cord-forming, saprotrophic baSidiomycetes, and the possible mechanisms operating to generate fractal growth in these systems are discussed.
Fractal geometry has been applied to the description of many complex objects in natural systems (Gleick, 1987; Kaye, 1989 a; Markx & Davey, 1990; Sugihara & May, 1990), and its potential for describing the growth and branching patterns of fungal mycelia has been recognized (Obert, Pfeifer & Sernetz, 1990; Ritz & Crawford, 1990; Ainsworth & Rayner, 1991). Fractal geometry is applicable to structures that exhibit self-similarity (Mandelbrot, 1982; Kaye, 1989a; Pfeifer & Obert, 1989), that is, they have a geometry that is repeated over magnifications ad infinitum. In practice, such self-similarity only occurs in 'ideal fractal structures', such as Koch's triadic island (Kaye, 1989a). With natural, heterogeneous objects there are limits to the range over which self-similarity applies. Often the heterogeneity of a structure is not identical when viewed under different magnifications, so that any mathematical relation applied to the structure, concerning scale (see below), is sustained only approximately. Such structures are termed 'statistically self-similar' (Kaye, 1989 a), and although fractal geometry is still applicable, there are limitations. The theory, justification and implications of fractal geometry as applied to fungal mycelia have been discussed by Ritz & Crawford (1990). Briefly, the parameter of major interest is the fractal dimension (0). For whole structures embedded in two dimensions, 0 ranges between I and 2, with larger values representing objects of increasing structural irregularity and complexity. Thus, for fungal colonies 0 represents a measure of the heterogeneity and branching of the mycelium (Ritz & Crawford, 1990). When assigning a fractal dimension to complex objects it is assumed that a power law relationship exists for any parameter used to measure a structure (Mandelbrot, 1982; Kaye, 1989 a; Pfeifer & Obert, 1989). Thus in fractal structures the parameter measured is proportional to the units of its measurement, at a rate that is determined by O. To date, two different approaches have
been adopted for the calculation of 0 in fungal colonies grown across two-dimensional surfaces. Firstly, Ritz & Crawford (1990) calculated the mycelial mass contained within a given radius, originating at the centre of a colony, over a range of different radii. Secondly, Obert et al. (1990) employed the 'box-counting method', in which two different types of fractal structure were identified: (I) mass fractals, where the whole mass of the colony is fractal; and (2) surface fractals, where only the colony margin or border is fractal owing to the overlapping of hyphae in the colony centre. According to this terminology, the method of Ritz & Crawford (1990) measures the mass fractal dimension, assuming a colony has a constant dimension across the zone of the search surface investigated. This technique is useful when studying the spatial aspects of foraging systems, since the point of inoculation can be used as the centre of the search surface during calculation, thus defining the search surface as the potential area of exploration for the fungal mycelium. In the present study, fractal geometry was used to investigate spatial aspects of foraging systems of two contrasting mycelial cord-forming, saprotrophic basidiomycetes Phanerochaete velutina (L.: Hook.) Greville and Hypholoma fasciculare (Huds.: Fr.) Kummer as they extended out from a food base into non-sterile soil (d. Dowson et al., 1986, 1988, 1989). The commitment of mycelial biomass to exploration by these systems was also determined and related to their fractal geometry.
MATERIALS AND METHODS Strains and culture media Laboratory stocks of P. velutina and H. fasciculare were used. P. velutina was originally isolated from decaying beech (Fagus
763
R, G, Bolton and Lynne Boddy
sylvatica L.) wood, and H. fasciculare from tissue of a fruit body on a beech log, both collected from the Forest of Dean, Gloucester, U,K, (SO 611145), Cultures were maintained and routinely subcultured on 2 % (w Iv) malt extract agar (MEA; 20 g Munton & Fison spray malt, 15 g Lab M no, 2 agar [-1 distilled water), Growth and photography of mycelial cord systems Foraging mycelial cord systems were grown in 24 x 24 cm lidded bioassay dishes (Nunc: Gibco, Paisley, U.K,), according to the method of Dowson et al. (1986, 1988, 1989), across compressed, non-sterile soil from beech wood block inocula (pre-colonized in agar culture flasks) of different sizes and states of decay (as indicated below). The soil was frozen to - 20°C twice, prior to incorporation into systems, This inhibited the growth of invertebrates such as Collembola spp., which graze fungi and sometimes affect mycelial outgrowth patterns, All cord systems were photographed regularly (see below) using an Olympus OM-2 camera body fitted with a 50 rom OM-system macro lens and Ilford FP4 (125 ASA) 35 mm black and white film, as described in detail by Bolton, Morris & Boddy (1991),
Calculation of fradal dimension (D), rate of mycelial extension, and extra resource mycelial biomass
o was calculated using the method of Ritz & Crawford (1990), except that mycelial area rather than mycelial mass was the parameter measured. Mycelial area has been shown to be directly proportional to mycelial biomass in foraging cord systems of P, velutina, when developing in two dimensions and growing on compressed soil (Bolton et al., 1991), The power law relationship from Ritz & Crawford (1990) may therefore be represented as: A(r)
the image analysis method of Bolton et al. (1991). In addition, a biomass expenditure index of total extra-resource mycelial biomass per total area explored (mg mm- 2 ) was calculated for each P. velutina treatment.
Effed of inoculum resource size, extent of pre-colonization and time on D, rate of mycelial extension, and extra resource mycelial biomass In one experiment, 0 was calculated for mycelial cord systems of P, velutina extending from 0'2, 0'5 and 8 cm 3 wood blocks after 9, 18 and 25 d post-inoculation, and for cord systems of H. fasciculare extending from 0'5 and 8 cm 3 wood blocks after 11, 16 and 37 d post-inoculation, The incubation period for the different-sized inoculum blocks in culture flasks prior to inoculation was staggered, so that the degree of colonization by the test fungus was standardized for each block size, Thus the 0'2, 0-5 and 8 cm 3 wood blocks were incubated for 14, 21 and 35 d respectively, The .relative densities (g cm- 3 ) of the different block sizes were not significantly different (P > 0'05) for each species (Table 1). Table 1. Fractal dimension (0), rate of mycelial extension (rnrn d-'), and extra-resource mycelial biomass (mg) of mycelial cord systems of P, velutina and H. fasciculare extending from inoculum resources of different size with time P, velutina: inoculum volume (ern 3 ) and relative density (g cm- 3 ) in parentheses
Fractal dimension (0)
Biomass (mg)
where A(r) is the area of mycelium contained within radius r, was calculated from photographs of cord systems using the image analysis method of Bolton et al. (1991), Stencils of given radii were used during image capture to define the given area r under investigation. At least five different radii were investigated for each image. Analysis was not taken to the extending mycelial front of colonies owing to boundary effects (Ritz & Crawford, 1990), and differences in branching pattern exhibited by some systems in peripheral zones (see below), Double logarithmic (Robertson) plots of A against r were constructed with r on the x-axis, according to the methodology described by Markx & Davey (1990) and Kaye (1989a). Since A(r) was cumulative over the range of r investigated, the slope of the Robertson plots corresponds to (20 -1) (Kaye, 1989 b). Mycelial extension rate (mm d- 1 ) was estimated from the average of eight radial measurements of mycelial extent for each colony between time of inoculation of trays and sampling time. Extra-resource mycelial biomass (mg) was determined using
0'5 (0'51 a)
8 (0'55 a)
18
1'21 a 1'22 a
1'81 b 1'62 c
25
1'21 a
1'28 a 1'22 a 1'22 a
9
0'49 a 1'03 a 1'36 a
1'34 a 1'14 a 1'93 a
4'77 a 6'27 a 6'34 a
9
2'53 a
18 25
2'60 a
2'87 a 3'20 a 2'93 a
4'40 a 4'87 a 3'67 a
9
18 25
= K,v
K is a constant, and 0 is the fractal dimension, Mycelial area
0'2 (0'51 a)
Time (d)
Mycelial extension rate (mm d-')
2'00 a
1'62 c
H. fasciculare: inoculum volume (ern 3 ) and relative density (g ern- 3 ) in parentheses 0'5 (0'59 a)
Fractal dimension (0)
11 16
37
Biomass (mg)
11 16 37
Mycelial extension rate (rnrn d-')
11 16 37
8 (0'57 a)
1'68 a 1'70 a 1'59 a
1'93 b 1'92 b 1'84 ab
2'93 a 3'34 a 3'88 a
7'94 ab 13'1 b 25'3 c
1'43 a 1'77 ab 1'70 ab
2'43 ab 2'63 ab 2'67 b
Values for each parameter followed by the same letter are not significantly different (P> 0'05) using one-way ANOVA and S-tests, Comparisons are made within but not between species, for each parameter,
Fractal geometry of mycelial cord systems
764
Figs 1-4. Outgrowth patterns of mycelial cord systems of P. velutina extending from the following. Fig. 1. 0'2 cm 3 inoculum after 18 d. Fig. 2. 0'5 cm 3 inoculum after 25 d. Fig. 3. 8 cm 3 inoculum after 9 d. Fig. 4. 8 cm 3 inoculum after 18 d. The fractal dimensions of the system were 1'25, 1'33, 1'85 and 1'65 respectively. I, inoculum resource block; B, nutritionally inert plastic bait.
In a second experiment, D was calculated for mycelial cord systems of P. velutina extending from wood blocks colonized for different times prior to incorporation in experiments. Thus both 0-5 and 8 cm 3 wood blocks were pre-colonized in culture vessels for 14, 56 and 154 d. Relative density (g cm -3; Table 2) of ten blocks of each inoculum type was determined at the same time as inoculation of blocks into dishes. Four replicates of each treatment were set up.
RESULTS
Effect of inoculum resource size on V, rate of mycelial extension, and extra-resource mycelial biomass In the first experiment, H. fasciculare and P. velutina exhibited different patterns of outgrowth from inocula of different sizes (Figs 1-7). The D exhibited by H. fasciculare were consistently
larger than those of P. velutina for corresponding resources and times (Table 1). With both H. fasciculare and P. velutina, the D was significantly (P < 0'05) larger in systems extending from 8 cm 3 inocula than from smaller resources. D tended to decrease with time, significantly (P < 0'05) with systems of P. velutina extending from 8 cm 3 inocula. Mycelial extension of P. velutina was consistently more rapid than H. fasciculare, for corresponding resources and times (Table 1). D and rate of mycelial extension were significantly positively correlated (P < 0'001) for both P. velutina and H. fasciculare (Fig. 8). The increase in D with mycelial extension rate was more rapid with H. fasciculare compared with P. velutina. Extra-resource mycelial biomass was consistently larger in H. fasciculare compared with P. velutina, for corresponding resources and times (Table 1). Biomass was consistently greater in systems extending from relatively larger resources,
R. G. Bolton and Lynne Boddy
765
~
Figs 5-7. Outgrowth patterns of mycelial cord systems of H. fasciculare. Fig. 5.0'5 em 3 inoculum after 16 d. Fig. 6. 8 em 3 inoculum after 16 d. Fig. 7. 8 cm3 inoculum after 37 d. The fractal dimensions of the systems were 1'59. 1'89 and 1'8 respectively. I. inoculum resource block; B, nutritionally inert plastic bait.
2
0 08
00 0 0
1·8 0
§ c
0 '0;
.,c
•
0
•
0
1·6
•
• •
••
0
.6 'l:l ~ (j
•
0 0
0
1·4
'"...
••
~
1
•
•
1·2
, 0
1
•••
•
•
•
2
•
•
•• • • •
3
4
5
6
Mycelial extension rate (mmd- I ) Fig. 8. Relationship between fractal dimension (D) and rate of
mycelial extension (mm d- 1 ) for foraging mycelial cord systems of P. velufina (.) and H. fasciculare (0).
and consistently increased with time of outgrowth, significantly (P < 0'05) in the case of H. fasciculare.
Effect of extent of pre-colonization of inoculum resources on 0, rate of mycelial extension, and extra-resource mycelial biomass of P. velutina In the second experiment, different patterns of outgrowth occurred from resource bases pre-colonized for varied periods of time (Table 2). However, the relative densities of differentsized inocula pre-colonized for similar periods were only significantly different in 154 d treatments (P < 0'05). The D of systems extending from 8 ems inocula were generally larger than for 0'5 cm 3 inocula for comparable times of pre-colonization and outgrowth (Table 2). For systems developing from both sizes of inocula, precolonized for 14 d, D significantly decreased (P < 0'05) with
time. D also varied depending on the extent of precolonization. With 0'5 ems inocula, significantly (P < 0'05) larger D values were obtained with inocula pre-colonized for 56 d than for 14 or 154 d inocula. at the earlier stages of outgrowth. Significantly lower D values were observed from systems extending from inocula pre-colonized for 154 d. With 8 ems inocula there were no significant differences (P > 0'05) in D associated with the extent of pre-colonization. although the D of systems from 56 d inocula was significantly lower (P < 0'05) than other treatments, after 11 d outgrowth only. With 0'5 em3 inocula, the rate of mycelial extension was significantly different (P < 0'05) between all inoculum precolonization treatments, at the earlier stages of outgrowth, with the 56 and 154 d treatments exhibiting the highest and lowest values respectively. Extra-resource mycelial biomass was significantly larger (P < 0'05) in systems of P. veZutina extending from 8 cm 3 inocula than from 0'5 cm 3 inocula for corresponding times of pre-colonization and outgrowth (Table 2). Biomass was significantly (P < 0'05) greater from 0'5 cm 3 inocula precolonized for 56 d compared with 14 and 154 d inocula. at the earlier stages of outgrowth. With 8 cm 3 inocula, biomass increased with Hme of outgrowth, although not Significantly (P > 0'05) with the 154 d pre-colonized treatment.
Relutionship between D and biomuss expenditure
D was not proportional to the biomass expenditure (mg mm- 2 area explored) of mycelial cord systems of P. veZutina (Fig. 9).
DISCUSSION This study suggests that the D values exhibited by foraging mycelial cord systems of P. velutina and H. fasciculare depend upon the potential of the nutrient base, from which the mycelium is extending. as a carbon/energy source, in that systems emanating from small-sized inocula had the lowest D values. A possible reason may be that whereas a low nutrient base is unable to sustain a complex mycelium with a high
766
Fractal geometry of mycelial cord systems Table 2. Fractal dimension (0), rate of mycelial extension (rom d-'), and extra-resource mycelial biomass (mg) of mycelial cord systems of P. ve/ulina extending from 0'5 and 8 em' inoculum resources of varying states of pre-colonization with time 0'5 em' inoculum size: inoculum pre-colonization time (d) and relative density (g em') in parentheses 14 (0'53 a)
56 (0'52 a)
154 (0'40 b)
IS 27
1'44 (a.l) 1'44 (a,I) 1'24 (a,2)
1'64 (b,l) 1'63 (b,I) 1'22 (ab,2)
1"24 (c,l) 1'21 (c,I) 1'11 (b,I)
11 IS 27
2'02 (a,l) 3'55 (ab,2) 1'15 (a,l)
4'57 (b,I) 6'17 (b,I) 3'18 (a,l)
0'75 (a,I) 1'32 (a,I) 0'53 (a,I)
Mycelial 11 extension IS rate (mm do') 27
3'75 (b,12) 4'00 (b,2) 2'81 (a,l)
6'62 (c,2) 6'62 (c,2) 3'33 (a,l)
1'70 (a,I) 2'05 (a,I) 1'30 (a,l)
Time (d) Fractal dimension (0)
Biomass (mg)
II
8 em3 inoculum size: inoculum pre-colonization time (d) and relative density (g em-') in parentheses 14 (0'57 a)
154 (0'49 a)
l'S8 (b,l) 1'65 (a,I) l'SI (a,l)
1'83 (a,l) 1'77 (a,l) 1'65 (a,I)
5'99 (a,1) 10'53 (a,12) 14'87 (a,2)
6'04 (a,l) 16'18 (a,12) 21'36 (a,2)
20'28 (b,I) 27'68 (a,I) 27'11 (a,l)
4'96 (a,I) 5'71 (a,l) 6'86 (a,l)
4'20 (a,l) 5'02 (a,l) 6'12 (a,l)
6'50 (a,I) 7'52 (a,I) 7'56 (a,I)
Fractal dimension (0)
II
IS 27
1'90 (a,l) 1'79 (a,12) 1'48 (a,2)
Biomass (mg)
11 15 27
Mycelial 11 extension IS rate (mm d-') 27
56 (0'54 a)
Data in the same column followed by the same number, and data in the same row followed by the same letter, for each different inoculum size and parameter, are not significantly different (P > 0'05) using one-way ANOYA and S-tests,
degree of branching, an increase in nutrient status affords a more space-filling, branched mycelium, This possibility is supported by the consistently increased extra-resource mycelial biomass observed in systems extending from resources of higher nutrient status. Furthermore, as exploratory growth proceeds, Le. where the nutrient base has not become exhausted, mycelial outgrowth becomes less complex, as represented by lower D. This reduction in D may be symptomatic of a biomass-conserving strategy, through reabsorption of nutrients from autolysed cord branches, such as is implied by the regression of remote cord branches observed during resource capture by these fungi (Dowson et al., 1986, 1988, 1989). The results also suggest that P. velutina may exhibit a base-line D of about 1'2, that represents the most affordable fractal-producing biomass expenditure when nutrients are limited. The effect of relative density/time of pre-colonization is less clear. With the 0'5 cm 3 resource, the peak D found in
systems growing from 56 d pre-colonized blocks may be attributable to: (1) greater fungal establishment than in the blocks pre-colonized for 14 d; (2) less depletion of nutrients than in the 154 d (0'40 g cm- 3 ) pre-colonized blocks. The generally higher D values for systems growing from 8 cm 3 compared with 0'5 cm 3 resources probably result from greater nutrient sources in the former, which in tum is a result of less decay (higher densities) and/or large size of resource. It is of interest that although prolonged pre-colonization of 8 cm 3 resources did not result in significant changes in D, there were consistent increases in extra-resource mycelial biomass and rate of mycelial extension. Again, this may be attributable to greater fungal establishment within the more pre-colonised resources. The observed increase in biomass expenditure without a consequent benefit from increased D indicates a relatively less efficient utilization of exploratory effort. This point demonstrates that D provides information concerning the spatial distribution of foraging biomass in mycelial cord systems that cannot be given by biomass expenditure measurements alone. The scatter of values on the plot of D against a biomass expenditure index (mg cm- 2 area explored) (Fig. 9) indicates the variability in the efficiency of spatial distribution of mycelial biomass, and demonstrates that foraging cord systems of P. velutina are not optimal in this respect. Systems that exhibited relatively higher D and lower biomass expenditure were more efficient in occupying the area that had been explored. Care must, however, be taken in interpreting the fractal data in terms of foraging efficiency. Clearly D, as calculated here, describes the spatial characteristics of colonies occupying an area already explored, In the context of foraging efficiency, the zone of mycelium at the periphery of the foraging mycelial front may be of greater importance with regard to resource capture, although it is important to note that resources may be distributed heterogeneously in time as well as space. Differences in branching pattern between the extending mycelial front and regions closer to the centre of foraging cord systems were clearly exhibited by H. fasciculare (Fig. 7). The method of Obert et al. (1990) is more suitable for investigating the fractal nature of this zone, since the current method of analysis breaks down in the peripheral regions of structures (Ritz & Crawford, 1990).
In contrast to the study of Ritz & Crawford (1990), where an unlimited supply of nutrient was distributed homogeneously throughout the substratum, differences in mycelial cord outgrowth patterns do not directly reflect the balance between exploratory and exploitative growth. In cord-forming fungi, these two conflicting modes of growth can be said to be spatially separated, with exploitative growth limited to discontinuous resource packages. Therefore the space-filling efficiency of exploratory mycelial cord systems, as described here by D, affects the probability with which spatially discontinuous resource packages may be encountered. Exploratory fronts with high D would be more effective in locating resource units of small size, essentially blanketing the foraging area. Thus the strategy employed by a fungus may be indicative of its resource specificity, its tolerance to stressful microenvironmental conditions, and its combative ability (Cooke & Rayner, 1984; Dowson et aI., 1988). These
R. G. Bolton and Lynne Boddy
767
2
• • 1·8 -
S t::
.2
•
1·6
l-
.5 "0 ]
<>
....o:l
1-4
1·2
I
••
l-
• •• • ••• • -:.
••
r-.P: •• •
0
• •
•
"
•
• •
.\
• • •
•
•
••
•
-
•
•
• •
• •
• • • ••
•
•
•
• • • • • • • • •• • • •• •• •
I.l.
•
•••
•
~ ll)
•
• I
20
I
I
40 60 80 Biomass expenditure (mg mm-2 area explored x 10-5)
100
120
Fig. 9. Relationship between fractal dimension (D) and extra-resource mycelial biomass expenditure (mg mm- 2 area explored) for foraging mycelial cord systems of P. velutina.
factors, as well as the status of the resource base from which the mycelium is extending, will detennine D. Thus H. fasciculare, associated with unspecialized resource and microenvironmental requirements, and high attacking combative ability (Dowson ef al., 1988), exhibited relatively high D, indicative of a short-range foraging strategy. In contrast, the greater resource specificity exhibited by P. velufina, and consequent longer-range foraging strategy, was illustrated by its relatively low D, faster rate of mycelial extension, and smaller commitment to extra-resource mycelial biomass. Although D provides a valuable description of the branching patterns of mycelial cord systems, it does not elucidate the underlying processes generating the differences in structural complexity observed. Rayner (1991) has proposed a theory of hydraulic pressure distribution and differential insulation, whereby the pressure generated through uptake of solutes and subsequent osmosis of water is distributed through mycelial systems according to the degree of hyphal insulation. An increase in ratio between pressure and insulation would result in an increased tendency to branch. Such hydraulic pressure has been proposed to drive the translocation of nutrients in mycelium of Serpuia Iacrimans Gennings, 1991). The results presented here are congruent with hydraulic pressure-generated branching patterns. Clearly, resource bases of relatively higher nutrient status can generate a greater potential. Since mycelial cords extending through soil are located in a relatively hostile environment, the foraging mycelium is largely non-assimilative, and so the degree of insulation might be expected to be constitutively high. Thus, the increased D observed in systems extending from resources of high nutrient status may have more to do with increased hydraulic pressure than reduced insulation. The differences
observed in outgrowth pattern between systems of H. fasciculare and P. velufina extending from resources of comparable nutrient status, however, may be attributable to differences in how these fungi insulate their hyphae. The more-branched systems of H. fasciculare may be constitutively less insulated to internal pressure. The faster extension rates exhibited by P. velufina could be generated in a more insulated system, with pressure being directed to hyphal apices rather than being dispersed through branching. Note, however, that within-species comparisons indicate faster extension rates associated with higher D (Fig. 8). If the degree of insulation remains constitutively constant for each species, the increased internal pressure generated in systems extending from high nutrient bases may be sufficient to increase both branching and mycelial extension. Thus it is possible that the different correlations between D and the extension rate exhibited by the different species may provide a profile of insulation for different species. In conclusion, fractal geometry offers a valuable instrument for describing the space-filling characteristics and foraging idiosyncrasies of cord-fonning fungi. The structural complexity exhibited by these fungi allows for a high degree of functional co-ordination that is necessary for adaptation within an uncertain environment. This complexity may be generated through simple mechanisms that could be driven by the physical constraints of nutrient availability and source-sink relationships.
We acknowledge the Natural Environment Research Council for financial support during this study. We would also like to thank Steven Hendry and Dr A. D. M. Rayner for
Fractal geometry of mycelial cord systems useful discussion, the referees for their comments on the original manuscript, and Dr Julian Wimpenny for the use of his image analysis system.
768 Dowson, C. G., Springham, P., Rayner, A. D. M. &; Boddy, L. (1989). Resource relationships of foraging mycelial systems of Phanerochaete velutina and Hypholoma fascicular< in soil. New Phytologist 111, 501-509. Gleick, j. (1987). Chaos. Heinemann: London. jennings, D. H. (1991). The spatial aspects of fungal growth. Science Progress 75, 141-156.
REFERENCES Ainsworth, A. M. & Rayner, A. D. M. (1991). Ontogenetic stages from coenocyte to basidiome and their relation to phenoloxidase activity and colonization processes in Phanerochaele magnoliae. Mycological Research 95, 1414-1422.
Bolton, R. G., Morris, C. W. & Boddy, L. (1991). Non-destructive quantification of growth and regression of mycelial cords using image analysis. Binary 3, 127-132. Cooke, R. C. & Rayner, A. D. M. (1984). Ecology of Saprotrophic Fungi. Longman: London. Dowson, C. G., Rayner, A. D. M. & Boddy, L. (1986). Outgrowth patterns of mycelial cord-forming basidiomycetes from and between woody resource units in soil. Journal of General Microbiology 132, 203-211. Dowson, C. G., Rayner, A. D. M. & Boddy, L. (1988). Foraging patterns of Phallus impudicus, Phanerochaete laevis and Steccherinum fimbria tum between discontinuous resource units in soil. FEMS Microbiology Ecology 53, 291-298.
(Accepted 3 November 1992)
Kaye, B. H. (1989a). A Random Walk Through Fractal Dimensions. VCH, Weinheim: Cambridge. Kaye, B. H. (1989 b). Image analysis techniques for characterising fractal structures. In The Fractal Approach to Heterogeneous Chemistry (ed. D. Avnir), pp. 55-66. john Wiley &; Sons: Chichester. Mandelbrot, B. B. (1982). The Fractal Geometry of Nature. Freeman: Oxford. Markx, G. H. & Davey, C. L. (1990). Applications of fractal geometry. Binary 2, 169-175.
Obert, M., Pfeifer, P. & Sernetz, M. (1990). Microbial growth patterns described by fractal geometry. Journal of Bacteriology 172, 1180--1185. Pfeifer, P. & Obert, M. (1989). Fractals: basic concepts and terminology. In The Fractal Approach to Heterogeneous Chemistry (ed. D. Avnir), pp. 11-43. john Wiley & Sons: Chichester. Rayner, A. D. M. (1991). Conflicting flows: the dynamics of mycelial territoriality. Mellvanea 10, 24-35. Ritz, K. & Crawford, j. (1990). Quantification of the fractal nature of colonies of Trichoderma viride. Mycological Research 94, 113&-1152. Sugihara, G. & May, R. M. (1990). Applications of fractals in ecology. Trends in Ecology and Evolution 5, 79-86.