Isonome Mapping: 
Graphic Analysis of Patterns of 
Species Distribution 
I. M. Brewer (nee Pidgeon) 
Brewer, I.M., Isonome mapping: graphic analysis of patterns of species distribution. Proc. 
Soc. Linn. N.S.W. 115: 259-279 (1995). 
Fine scale analysis of species distribution and abundance is important in under- 
standing processes of vegetation change. A novel mapping technique based on simple 
quadrat-sampling was devised in 1941 for this purpose and used to describe and analyse the 
structure and patterns of species distribution in two vegetation types on Hawkesbury sand- 
stone of the Hornsby Plateau. In moist shrubland and in the understorey of adjacent 
Eucalyptus woodland at two sites, relative densities of shrubby species were calculated from 
the total numbers of plants of individual species recorded in rectangular (9.1 x 0.9 m) 
quadrats arranged in a grid. For each species with a sufficiently high density, the variation 
in its relative density across the grid was mapped as contour lines of equal percentage value 
called 'isonomes' (from iso, equal, and nome, distribution) . In isonome maps for individual 
species, mostly complex systems of isonomes with one or more centres of high relative den- 
sity emerged. By superimposing isonome maps of individual species, the composite pattern 
of species distribution over the area revealed a complex social structure in which the cen- 
tres of high relative density formed a mosaic, around the margins of which there was over- 
lapping of the lower-value isonomes. Graphic analysis by isonome mapping has provided 
information on sandstone vegetation not previously reported: e.g. sociology of woodland 
and scrub communities, patterns of occurrence and density of species across sharp eco- 
tones, and specific patterns have generated an hypothesis of temporal change operating at 
a small scale. In the application of isonome mapping techniques to other vegetation types, 
the investigator has to choose the appropriate size and spacing of the rectangular quadrats, 
so that variation in relative density of species across the grid will generate discernible pat- 
terns. This paper is of historic interest, not only as the first quantitative method devised to 
show the pattern of species distribution and abundance in a community, but also as the first 
quantitative analysis of sandstone vegetation. It is also a record of species composition of 
pristine communities, devoid of introduced species, in urban fringe, pre-development veg- 
etation of Sydney. 
I.M. Brewer, 18 Eastbourne Road, Darling Point, NSW 2027, Australia; manuscript received 15 
November 1 994, accepted for publication 15 February 1995. 
KEYWORDS: isonome mapping, species distribution, Hawkesbury sandstone vegetation. 
Introduction 
The twentieth century has seen the evolution of new methods and techniques for 
the classification, description and quantitative analysis of vegetation. 
The basis of quantitative investigations in plant sociology is the quadrat method, 
originally proposed for pastures by Stapledon (1912) . Statistical methods of analysis gave 
information on the floristic composition of the community, or on density and type of 
distribution of species (random, over- and under-dispersion). With random dispersion, 
ecologists and agronomists had a valuable tool for studying changes in plant populations 
(Blackman, 1935; Ashby, 1935; Clapham, 1936). 
The arrival of Ashby in 1938, as Professor of Botany at Sydney University, and his 
fascination with the complexity of sandstone vegetation stimulated studies by Beadle in 
arid western NSW and that of Pidgeon on the sandstone vegetation. It also led to the 
collaboration with Pidgeon (now I.M. Brewer) in 1939 in a rigorous statistical analysis 
(using random-sampling techniques and rectangular strip-quadrats) of the effects of 
over-grazing on vegetation around Broken Hill (Pidgeon and Ashby, 1940) . 
Proc. Linn. Soc. N.s.w., 115, 1995 
260 ISONOME MAPPING OF SPECIES DISTRIBUTION 
Further investigations planned in applied ecology (see Pidgeon & Ashby, 1940) 
were relinquished when Ashby established and directed the Australian Liaison Bureau to 
maximize science in the war effort, and the Botany Department began its co-operation 
with the CSIR (later CSIRO) Food Preservation Research Laboratory which involved 
some of the teaching and research staff in solving problems related to fruit storage and 
marketing. 
The complex Hawkesbury sandstone vegetation had not been analysed by quantita- 
tive techniques prior to 1941, as until then there was no quantitative method whereby the 
structure or pattern of a community could be determined. In 1941, Ashby and Pidgeon 
devised a novel 'isonome' mapping technique, based on simple quadrat sampling in 
grids, to record patterns of distribution and abundance of species. It was used in 1941 by 
Pidgeon on Hawkesbury sandstone and sand dune vegetation. The technique was first 
oudined by Pidgeon and Ashby (1942) , but the data have been recorded only in the D.Sc. 
thesis (Pidgeon, 1942) , and have not been explored, expanded, or related to information 
since published on the flora of the central coast, NSW. 
From the 1950's, different approaches to describing and analysing vegetation were 
developed: objective methods (Goodall, 1961), and quantitative techniques (Grieg- 
Smith, 1983). Ordination (Bray & Curtis, 1957) was followed by computer-based methods 
of association analysis (Williams & Lambert, 1959, and others) and multivariate analysis 
(Gauch, 1982; James & McCulloch, 1990). These powerful and sophisticated techniques 
are now used almost exclusively in analysis of vegetation. 
The research described in this paper was done more than fifty years ago, during 
tenure (1937-41) of a Linnean Macleay Fellowship at the University of Sydney. The war 
and other priorities interrupted the publication of a number of quantitative studies in the 
thesis (Pidgeon, 1942). 
Data on isonome mapping of sandstone vegetation might well have been left buried 
in the thesis, but for a number of reasons it is offered for publication. It is a contribution of 
historical interest, not only as the original quantitative method devised to analyse the 
structure and pattern of species distribution and abundance in a plant community, but 
also as the first quantitative analysis of plant communities on Hawkesbury sandstone. 
There was a lapse of thirty years before other quantitative studies, using computer-analy- 
sis, of the vegetation of the central coast of NSW were published: Siddiqi et al. (1972), 
Burroughs al. (1977), Buchanan & Humphreys (1980). 
Another motive for offering this paper is the historic aspect of the data. Plant 
communities like species, can become endangered. With the spread of urbanisation, this 
has indeed happened to many communities on Hawkesbury sandstone, which, like the 
two sites investigated in 1941, are now lost to streets and housing. The complete floristic 
composition of these communities, given in the Appendix (a total of 1 10 species, includ- 
ing densities) provide a record of typical urban fringe sandstone communities in the 
1940s, prior to development. The species composition of these pristine communities, par- 
ticularly the absence of introduced species now common in urban fringe vegetation, is 
remarkable. 
This paper also re-evaluates the isonome mapping technique, which although 
superseded by other techniques using computer-analysis, nevertheless has some intrinsic 
merits. The technique may interest ecologists who wish to summarize, in a simple way, the 
sociology of plant communities. By examining the vividly descriptive isonome maps, ecol- 
ogists can readily obtain information on distribution and abundance of species, often 
more rapidly than from computer analysis. Isonome mapping may also reveal graphic 
evidence of temporal change, as in the analysis of sandstone vegetation, where some 
shrub species, abundant in scrub, were present in woodland as isolated, low-value 
isonomes, interpreted as 'relics'. 
Analysis of patterns of species distribution and abundance may point to important 
ecological processes operating at small scales, e.g. changes in local density and distribu- 
Proc. Linn. Soc. n.S.w., 115, 1995 
I. M. BREWER 
261 
tion of obligate-seeder woody shrubs in relation to fire history (R. Whelan pers. comm.) . 
As patterns are not always apparent by inspection, techniques for quantifying fine-scale 
patterns in vegetation are needed. Isonome mapping is one simple technique of those 
available to ecologists. 
Previous studies of the vegetation of the central coast of New South Wales have been 
largely in terms of its variation across a range of habitats (Pidgeon 1937, 1938, 1940, 1941, 
1942; Davis 1936, 1941; Siddiqi et al. 1972; Burrough el al. 1977; Buchanan 1980; 
Buchanan and Humphreys 1980; Outhred etal. 1985; Thomas and Benson 1985). 
Locality Description 
Terrain and Soils 
Two sites were selected on Hawkesbury Sandstone in the south-eastern portion of 
the uplands of the Hornsby Plateau (Fig. 1), the boundaries of which are described by 
Bembrick etal. 1980. 
Fig. 1. Location of Sites A and B in 
the south-eastern section of the 
Hornsbv Plateau. 
Proc Linn. Soc. n.s.w., us, 1995 
262 ISONOME MAPPING OF SPECIES DISTRIBUTION 
The plateau, of fairly uniform elevation (180-210m ASL), is composed mainly of 
Hawkesbury Sandstone, a highly cemented and indurated quartz sandstone with thin 
interbedded shales and pebble lenses (Standard, 1969) . The terrain of flat-topped divides 
and V-shaped valleys is typified by structural benches and a blocked and stepped appear- 
ance, resulting from the coarse jointing and horizontal bedding of the sandstone (Healy, 
1972). Some sandstone strata and their intercalated shales are relatively impervious 
(Corbett, 1972). Where these underlie slopes of low angle, drainage is poor or impeded, 
thus de terming the type of vegetation. 
Soils derived from Hawkesbutry Sandstone are low in nutrients, especially phospho- 
rus (Beadle, 1962) and nitrogen (Hannon, 1956) and range on the plateau from light-tex- 
tured sandy lithosols to yellow podzolics, with discontinuous patches of acid peats. 
Vegetation 
The structural and floristic range of the vegetation of the plateau has been 
described previously by Pidgeon, (1938, 1940); Buchanan, (1980); Buchanan and 
Humphreys, 1980; Outhred etal, (1985); Thomas and Benson, (1985). 
The vegetation of the plateau is predominantly dry sclerophyll woodland with an 
open canopy (Beadle and Costin, 1952; Specht, 1970), mainly of Eucalyptus spp. and 
shrublands dominated by sclerophyllous shrubs, many of which also occur in the under- 
storey of adjoining woodlands. 
Differences in lithology, micro-topography, drainage and soils determine the distri- 
bution of two main types of shrubland: dry and moist scrub (Pidgeon, 1938). Dry scrub is 
found mainly on well drained skeletal soils, resting on sandstone close to the surface. 
Moist scrub occurs in habitats with impeded drainage, caused by impervious beds of mas- 
sive sandstone or impervious sub-soils weathered from shale lenses. The soils are intermit- 
tently moist, occasionally water-logged but the surface is sandy without much organic 
matter (Pidgeon, 1938) . Sometimes perched on benches, the majority of moist scrubs are 
found in areas of low slope (Buchanan, 1980) . The dominance of indicator species, main- 
ly moisture-tolerant shrubs especially Hakea teretifolia, readily identify these communities. 
Many shrubs are common to both dry and moist scrub (Pidgeon, 1938) and the two 
communities may be in proximity (see Fig. 2) . 
Study Sites 
A characteristic feature of the sandstone uplands is the recurring pattern of 
Eucalyptus woodland on well-drained soils interspersed with areas of moist scrub. In these 
adjacent communities, two sites of apparently similar floristic composition were selected 
for quantitative analysis: Site A, at east Gordon, and Site B, about 10 km to the east in the 
vicinity of Elanora Heights (Fig. 1 ) . Selected close to roads for easy access; both sites have 
since been absorbed by suburban development. 
Figures 2 and 3 show moist scrub in areas of low slope. The boundary between scrub 
and woodland was quite sharp at Site B (Fig. 3) but less clearly defined at Site A. Grids at 
Site A were laid 40m apart in typical moist scrub and woodland, whereas the grid at Site B 
traversed the abrupt shrub-tree junction. 
Methods 
Sampling Technique 
To sample the vegetation at each site, a grid of rectangular quadrats was used. In 
dense vegetation, it is easier to count individual plants across the narrow width of a rectan- 
gle than in squares and, as Clapham (1932) showed, they may estimate density of plants 
with less variance than square quadrats of the same area (see Pidgeon and Ashby 1940) . 
Tapes were laid in parallel lines 15 feet (4.6m) apart across each site. Every 30 feet 
Proc. Linn. Soc. n.s.w., i 15, 1995 
I.M. BREWER 
263 
(9.1m) along the tapes, and for 3 feet (0.9m) to one side, the numbers of individual plants 
of each species were counted. In this way, data were collected at each site for rows of con- 
tiguous quadrats (8.3m 2 ) arranged in columns 12 feet (3.7m) apart (see Fig. 4A). 
Fig. 2. Moist scrub at Site A, East Gordon, with dry scrub on the ridge. (Photograph: I.M. Pidgeon, 1941). 
Fig. 3. Abruptjunction between moist scrub and woodland at Site B, Elanora Heights. (Photograph: I.M. Pidgeon, 
1941). 
Proc. Linn. Soc. n.s.w., 115, 1995 
264 
ISONOME MAPPING OF SPECIES DISTRIBUTION 
Isonome Mapping Technique 
In each quadrat, the number of individual plants of each species was totalled and 
the relative density (relative abundance or importance value) was calculated as a percent- 
age (e.g. 40 individuals of a species out of a total of 200 plants in the quadrat represent a 
frequency of 20%). The percentage frequencies for individual species in every quadrat 
can then be plotted on separate maps of the site, drawn to scale (Fig. 4A) . 
For each species, the variation in its relative density across the grid was mapped by 
lines drawn to connect areas with the same percentage values, in the same way as contour 
maps are constructed. These lines, termed 'isonomes' (from iso, equal, and nome, distribu- 
tion) show the pattern of distribution for that species over the site, with one or more cen- 
tres of high relative density emerging (Fig. 4B) . The method of construction for an 
isonome map is fully explained in Results: Site A, Moist Scrub. By superimposing isonome 
maps for all species in sufficient abundance to generate discernible patterns, a composite 
pattern of species distribution over the area may be obtained. 
The patterns in the isonome maps are obviously dependent on (a) quadrat size and 
spacing (how these are chosen for a particular type of vegetation is explored in the 
Discussion) and (b) variation in density of a given species over the grid. 
Results 
Isonome maps were prepared (in 1941) for twenty-three species selected to illus- 
trate various features of the floristic analysis of mainly shrubby species (Table 1 and Figs. 4- 
9). Overall, one hundred and ten species were recorded (see Appendix). Some species 
were restricted to moist scrub, others to woodland, while a third group was common to 
both (see Table 2) . 
Table 1 
Species represented in isonome maps and density per 85m^. 
* denotes the site and vegetation type of species represented in Figs. 4-9, 
x denotes less than 1 per 85m , (S) seedlings. 
SITE A 
SITEB 
Moist 
Woodland 
Moist 
Woodland 
Species 
Scrub 
Scrub 
Actinotus minor (Sm.) DC. 
21 
77* 
100 
20 
Angophora hispida (Sm.) Blaxell 
27 
16 
60* 
3 
Baeckea diosmifolia Rudge 
236* 
2 
22 
Banksia ericifoliah.f. var. ericifolia 
15 
9 
196* 
22* 
B. serralah.f. 
28* 
9* 
70* 
Dillwynia floribunda Sm. 
X 
75* 
D. retorta (Wendl) Druce 
49* 
3 
44 
Epacris microphyllaR.hr. 
49* 
1 
1 
E. pulchella Ca\ . 
29 
60* 
90* 
Eucalyptus gummifera (Sol. ex Gaertn.) Hochr. 
15* 
5(S) 
19 
Grevillea sericea (Sm.) R.Br. 
12 
3 
37* 
G. speciosa (Knight) McGillivray 
11 
62* 
1 
Hakea leretifolia (Salisb.) J. Britten 
160* 
12* 
238* 
39* 
Kunzea capitata Reichb. 
673* 
19* 
246* 
14* 
Isplospermum trinervium (Sm.) J. Thompson 
40* 
31 
9 
38 
L. squarrosum Gaertner 
566* 
15* 
86 
20 
Isucopogon mi crop hyllus R.Br. 
85* 
6* 
90 
13 
Mirrantheum ericoidei Desf. 
1 
218* 
29 
Petrcrphile, pulchella (Schrad.) R.Br. 
235* 
204* 
98 
74 
Pimelea lini/olia Sm . 
25(S) 
273* 
Pullenaea elliptica Sm . 
2 
8 
125* 
48* 
P. daphnoidesWendl. 
27* 
P. rflusa9>m. 
16* 
Proc. Linn. Soc. n.s.w., i 15, 1995 
I. M. BREWER 
265 
Table 2 
Species restricted to moist scrub, woodland, and common to both excluding densities of 5 or less per 85m . 
A & B denote the presence of species at either or both sites. 
For common species, (S) denotes higher densities in moist scrub, (W) in woodland. 
* denotes seedlings or young plants recorded in moist scrub. 
Authorities for binomials as in Harden (ed.) Flora of N.S.W. Vols. 1-4. 
MOIST SCRUB 
SITES 
SITES 
Allocasuarina distyla 
A 
Gompholobium minus 
B 
Aotus ericoides 
A 
B 
Grevillea speciosa 
A 
B 
Baeckea densifolia 
A 
Hakea sericea 
B 
B. diosmifolia 
A 
B 
Isopogon anethifolius 
B 
B. imbricata 
A 
B 
Leucopogon esquamatus 
A 
B 
Bauera rubiodes 
B 
Persoonia lanceolata 
A 
B 
Conospermum ericifolium 
A 
Phyllota phylicoides 
B 
Drosera peltata 
A 
B 
Woollsia pungens 
A 
Epacris microphylia 
A 
WOODLAND 
Acacia longissima 
B 
Lomandra glauca 
A 
Adiantum sp. 
A 
B 
Lomatia silaifolia 
A 
B 
Billardieria scandens 
A 
Micrantheum ericoides 
A 
B 
Boronia ledifolia 
B 
Monotoca scoparia 
B 
Conospermum longifolium 
B 
Patersonia glabrata 
B 
Dillwyniafloribunda 
B 
Platysace linearifolia 
A 
B 
D. retorta 
A 
B 
Poranthera corymbosa 
B 
Eucalyptus gummifera 
A 
B* 
Pultenaea daphnoides 
A 
E. haemastoma 
A 
B* 
P. retusa 
B 
Gompholoblum virgatum 
B 
Pdcinocarpus pinifolius 
B 
Goodenia stelligera 
A 
Styphelia viridis 
B 
Grevellea sericea 
A 
B 
Tetratheca ericifolia 
B 
Hakea propinqua 
A 
B 
Xanthosia pilosa 
B 
Hibbertia aspera 
A 
B 
X. tridentata 
A 
B 
Lasiopetalum ferrugineum 
B 
COMMON 
Actinotus minor 
A 
B 
H. teretifolia 
A 
B(S) 
Angophora hispida 
A 
B(S) 
Hemigenia purpurea 
B 
Banksia ericifolia 
A 
B(S) 
Kunzea capitata 
A 
B(S) 
B. oblongifolia 
B(S) 
Lambertiaformosa 
B 
B. serrata 
A 
B(W) 
Leptospermum squarrosum 
A 
B(S) 
Boronia pinnata 
B 
L. trinervium 
A 
B 
Bossiaea heterophylia 
A 
B (W) 
Leucopogon microphyllus 
A 
B(S) 
B. scolopendria 
A 
Petrophile pulchella 
A 
B 
Comesperma ericinum 
B 
Pimelea linifolia 
B*(W) 
Epacris pulchella 
A 
B(W) 
Pultenaea elliptica 
A 
B(S) 
Hakea dactyloides 
A 
B(S) 
Xanthorrhoea resinifera 
A 
B(W) 
Site A: Moist Scrub 
Figures 4A and 4B illustrate the method of construction of the isonome map for 
Leptospermum trinervium, one of the eight most abundant shrubs in moist scrub (Table 1, 
Site A) . The grid map (to scale) in Fig. 4A shows relative densities of L. trinervium in each 
quadrat. Using the same principle as in contour mapping, 5% intervals were used to draw 
lines (isonomes) around these quadrats enclosing relative densities from 30% to 5% 
(interpolation of isonomes between two recorded frequencies is routine). In other parts 
of the grid, relative densities from 8% and 4% (column 1, rows 1 and 2) and 5% (column 
2, row 4) enabled additional 5% isonomes to be drawn. In column 7, row 2, the quadrat 
with 11% relative density was circumscribed by 10% and 5% isonomes, as the flanking 
quadrats were 1%. The 3% isonome circumscribes all quadrats with relative densities 
from 3% to 5%, and excludes quadrats with lesser values or no presence. Construction of 
isonomes is, of course, discretionary, but consistent when done by the same person. 
Isonome maps of the vegetation at this site show various levels of complexity. The 
Proc. Linn. Soc. n.s.w., i 15, 1995 
266 
ISONOME MAPPING OF SPECIES DISTRIBUTION 
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/7g. -M, A Method of construction of isonome map for Leptospermum trinervium, one of the eight co-dominant 
shrubs at Site A in moist scrub. A: Plan to scale of the grid; relative densities shown as percentages in each quadrat. 
B: Isonomeswith intervals 5%, and 3% (broken line) drawn as contours from data in A. (See text, Results) . 
Proc. Linn. Soc. n.s.w., 115, 1995 
I.M. BREWER 
267 
Baeckea diosmifolia 
30 ft 
9.14 m 
Leucopogon 
microphyllus 
Epacris 
microphylla 
Fig. 5. Site A, scrub: Isonome maps (intervals 5%) for the other seven co-dominant shrubs in moist scrub, Site A. 
Centres of high relative density are: Leptospermum 60%; Kunzea 55% 50%; Baeckea 45% 35% 20% 20%; Petrophite 
40% 25%; Hakea25% 20%; Leucopogon 20% 20%; Epacris20%. 
Proc. Linn. Soc. n.s.w., 115. 1995 
268 
ISONOME MAPPING OF SPECIES DISTRIBUTION 
Fig. 6A, B. Patterns of distribution for shrubs in moist scrub, Site A, obtained by superimposing high value 
isonomes from maps of species in Fig. 4B and Fig. 5. A: Integrity of all high centres exceeding 40%, with small 
amount of overlap for 30% isonomes in the four most abundant shrubs. B: Mosaic obtained by superimposing 
isonomes of 20% or more for the eight co-dominant shrubs. 
Proc. Linn. Soc. n.s.w., i 15. 1995 
I. M. BREWER 
269 
1 1 /I 
' 1 v ' 
(j 
A Hakea teretifolia Kunzea capitata 
Leptospermum 
squarrosum 
Leucopogon 
microphyllus 
i 
J 
g Micrantheum ericoides Dillwynia retorta Pultenaea daphnoides 
i 
1 
7 
Petrophile pulchella 
Actinotus minor 
30 ft 
Banksia serrata 
Eucalyptus gummifera 
9.14 m 
Fig. 7. Site A, woodland: isonome maps for eleven species with different patterns of distribution (see text). 
7A: Four scrub species with restricted distribution of Hakea 5% 3%; Kunzeaznd Leptospermum 10% 5%; Leucopogon 
3%. 7B: Three woodland shrubs with decreasing centres of relative density: Micrantheum 35% 35%;Di//ur)infa20%; 
Pultenaea 15%. 7C: Two species occurring in scrub and woodland; centres of relative density are: Petrophile 60% 
35%, Actinotus30% 10%; and two species in the tree stratum: Banksia\5%; Eucalyptus 10%. 
Proc. Linn. Soc. n.S.w., i 15, 1995 
270 ISONOME MAPPING OF SPECIES DISTRIBUTION 
isonome map for L. trinervium is a simple pattern of distribution, with two centres of high 
frequency (30% and 10%) . Isonome maps (Fig. 5) for the other seven shrubs with the 
highest densities (Table 1 ) , show mostly complex patterns which have several centres of 
high relative density varying from 60% to 20% (see legend, Fig. 5) . 
Although Hakea teretifolia appeared to be the dominant shrub at both sites in moist 
scrub, at Site A its density was significantly less than that of Kunzea capitata and 
Leptospermum squamosum (see Table 1). However, as recorded in the thesis, only 10% 
(approx) of the population of//, teretifoliawas less than 30cm high, whereas 50% (approx) 
of the population of both K. capitataand L. squarrosumwdiS in this category. 
By superimposing isonome maps for the eight shrub species (Figs. 4B and 5), the 
composite pattern over the whole area (1112-m 2 ) may be examined. Figure 6B, showing 
relative densities of 20% and above, reveals a complex 'social' structure in which the 
centres of high relative density for the various species form a mosaic, around the margins 
of which there is overlapping of the lower-value isonomes. 
From the method of construction, it is clear that the collective number of relative 
densities cannot exceed 100% in any one place. The integrity of high centres greater than 
40% and the small amount of overlap for isonomes of 30% are illustrated by Fig. 6A. 
Site A: Woodland 
In 500-m 2 of the adjacent Eucalyptus gummifera — E. haemastomawoodland, isonome 
maps (Fig. 7) were selected for eleven species with varying density (Table 1 ) and different 
patterns of distribution. 
Four shrub species Hakea teretifolia, Kunzea capitata, Leptospermum squarrosum and 
Leucopogon microphyllus (Fig. 7A) that were abundant in moist scrub but had low densities 
in woodland (Table 1 ) , show restricted patterns of low-frequency isonomes (Fig. 7 A) . This 
contrasts with the complex isonome maps for these same species in moist scrub (Fig. 5). 
Three shrub species restricted to woodland (Table 2), Micrantheum ericoides, Dillwynia 
retorta and Pultenaea daphnoides (Fig. 7B) with less complex patterns had corresponding 
decreasing densities (Table 1 ) . 
Petrophile pulchella (Fig. 7C) with similar high densities in scrub and woodland 
(Table 1) reveals a pattern similar in complexity to its isonome map in scrub (Fig. 5). In 
contrast, Actinotus minor (Fig. 7C) , a herb also common to both habitats, but significantly 
less abundant than P. pulchella (Table 1 ) shows a simple pattern of distribution over part of 
the woodland. For two species in the tree canopy (Fig. 7C) the distribution of isonomes 
show no overlap. 
Site B 
At site B, the grid covered 933-m2 of moist scrub and 1510-m 2 of Eucalyptus gum- 
mifera — E. haemastoma woodland, with an abrupt tree boundary (Fig. 3). Isonome maps 
for twelve species of shrubs reveal various patterns of distribution (Figs. 8A, 8B, 9A, 9B) . 
Two species, Hakea teretifolia and Kunzea capitata, (Fig. 8A) with high densities 
(Table 1 ) and complex patterns in moist scrub, show restricted distribution in the adjoin- 
ing woodland, as at Site A (Fig. 7A) . Conversely, Pimelea linifolia (Fig. 8B) was restricted to 
woodland and occurred only at Site B where its isonome pattern is complex. Its occur- 
rence in moist scrub was solely as seedlings (Table 1). Epacris pulchella (Fig. 8B), though 
present only in the woodland at Site A (Table 1 ) occurred in both scrub and woodland at 
Site B, where the high centres of distribution on each side of the tree boundary are linked 
by lower-value isonomes. 
Pairs of species in three genera, Grevillea (Fig. 9A), Banksiaaxxd Pultenaea (Fig. 9B), 
have complementary patterns of distribution in scrub and woodland, with some overlap- 
ping: G. sericea'mto scrub, B. ericifolia and P. ellipitica into woodland. The isonomes for two 
species are abruptly terminated at the treeline, confining Dillwynia floribunda to wood- 
land, and Angophora hispida to scrub (Fig. 9A) . 
Proc. Linn. Soc. N.S.w., i 15, 1995 
I.M. BREWER 
271 
Discussion 
In these field trials of the isonome mapping technique, the priority was to deter- 
mine whether the selected size and spacing of the quadrats was appropriate for mapping 
isonomes in shrubland and woodland. Investigations at both sites were therefore limited 
to a floristic analysis. No soil samples (the obvious variable) were taken at this time. 
However, other field investigations by the author in similar areas indicated the impor- 
tance of soils and drainage patterns in determining the two vegetation types: woodland 
and moist scrub. 
Isonome Mapping Techniques 
Based on relative abundances of the component species, the isonome method 
of analysis of vegetation uses density as the principal attribute with which to describe vege- 
tation. 
Isonome mapping seeks to display variation in patterns of distribution of individual 
species by mapping contours from the variation of their relative density in sampling units 
across the grid. The maps generated are dependent not only on the distribution and den- 
sity of the indivuals of species mapped, but also on the spacing and size of the quadrats 
Hakea teretifolia 
Kunzea capitata 
60 ft 
18.29 m 
Fig. 8A Site B: isonome maps for two shrubs dominant in moist scrub (see text) . Intervals 5%, with 2% boundaries 
(dotted lines). Centres of relative density are: Hakea 30% 20% 15% (scrub), 20% (woodland); Kunzea 40% 
(scrub), 10% (woodland). 
Proc Linn. Soc. N.S.W., 1 15, 1995 
272 
ISONOME MAPPING OF SPECIES DISTRIBUTION 
used. Clearly, if the size of these is so small that few individuals of few species are included 
in each sample, then relative densities will vary greatly over short distances, and it would 
be difficult to map isonome contours that are meaningful. Conversely, if the quadrats are 
very large, variation in relative density of species will be discerned only at large scales. 
The investigator has to choose the scales of variation that are of interest. In this case, 
interest was in variation of patterns of distribution in species, especially shrubs, between 
two structurally distinguishable types of vegetation: scrub and shrub-woodland. The area 
sampled in each had to be large enough to represent the range of variation in distribution 
of the common species in them, and the samples taken in them appropriately sized and 
spaced to explore that range of variation. The size of the samples, rectangular quadrats 
(9. 1 x 0.9m) , was large enough to contain individuals of a number of species and they were 
numerous enough and appropriately spaced to map isonome contours within the types of 
vegetation. The isonome maps produced thus reflected the variation in relative densities 
of species within the types of vegetation and allowed comparison of patterns of variation 
in relative abundances between them. 
The quadrat size and spacing may be varied to suit the type of vegetation: the 
method was worked out on dense scrub vegetation (see Figs 2, 3) . Other vegetation types 
Pimelea linifolia 
Epacris pulcliella 
60 ft 
18.29 m 
Fig. #.6 Site B: ecotone boundaries for two shrubs (see text). Isonome intervals 5% with 2% boundaries (dotted 
lines). Centres of relative density are: Pimelea 40% 35% 30% 25% (woodland) ; Epacris 30% 10% (woodland), 15% 
(scrub). 
Proc. Linn. Soc. n.s.w., i 15, 1995 
I.M. BREWER 
273 
may require quadrats of different dimensions. For sand dune vegetation (see Pidgeon, 
1942) it was more appropriate to use sampling units of half the length (compared with 
scrub and woodland) , to compensate for the spatial zonation of vegetation from fore- 
dune to hind-dune. In an investigation of grassland, it is very probable that the quadrats 
would need to be smaller and closer together than were used in this analysis. 
A similar system of isonomes is obtained if absolute densities (actual numbers) 
instead of percentages (relative densities) of each species is plotted. Isonomes not calcu- 
lated on a percentage basis have a limited application; they are not so useful when com- 
paring relative densities of species, and cannot be used as in Fig. 6 for a composite pattern 
of the area (Pidgeon & Ashby, 1942). 
It is generally more useful to eliminate variations in absolute density of the plant 
population over the area investigated by reducing figures to percentage cover of individu- 
al species. However, where there are considerable bare areas, e.g. on coastal dunes, or in 
arid regions, the vegetation cover may be expressed as percentage cover of total quadrat 
area; this also estimates at the same time the amount of the bare area. Percentage cover of 
each quadrat would also be estimated for stoloniferous grasses and for cloned species. 
With distinct two-layered communities, it may be advantageous to collect the data 
from the separate strata, and construct two sets of isonome maps; where the ground layer 
is insignificant, it may be ignored altogether. 
Grevillea sericea 
Dillwynia floribunda 
Grevillea speciosa o 
60 ft 
Angophora hlsplda 
18.29 m 
Fig. 9A Site B: ecotone boundaries for four shrubs (see text) . Intervals of 5% with 2% boundaries for Grevillea spp. 
Centres ofrelative density shown: G. sericea 20% (scrub) 10% 5% (woodland); G. speciosa 10% (exclusive to scrub); 
Dillwynia25% 15% 15% (exclusive to woodland) \Angophora 15% 10% (exclusive to scrub). 
Proc Linn. Soc. n.S.w., 115, 1995 
274 
ISONOME MAPPING OF SPECIES DISTRIBUTION 
The labour involved in counting individuals of several species in numerous samples 
limits isonome mapping to small areas of less than a hectare, more than sufficient to map 
patterns of distribution. With the assistance of about 20 second-year ecology students in 
1941, the field recordings in this study were completed in one day at each site. The work 
involved in constructing isonome maps would be reduced by computer graphics. 
Although random-sampling techniques are most frequently used in quantitative 
analysis, Buchanan and Humphreys (1980) also used a grid (of circular quadrats in 
columns and rows) traversing the sharp boundary between podzol and non-podzol soils at 
two sites on Hawkesbury sandstone, to analyse by modern techniques, the sudden floristic 
change which accompanies the change in soil type. 
Patterns of variation in distribution and abundance of species 
Tree seedlings which become established in moist scrub (see Appendix) during dry 
summer periods do not survive when the water table rises after prolonged wet periods. 
The lack of aeration affects their root systems, which penetrate deeper than the shrubby 
species. During a series of dry years, Buchanan (1980) also recorded, in dried swamps, the 
growth of Eucalypts to several metres, before the water table rose and killed them. 
Banksia serrata 
Pultenaea retusa 
Banksia erldfolla o 
60 (t 
Pultenaoa elllptlca 
18.29 m 
Fig. 9B. Site B: Distribution of four shrubs in relation to the ecotone; isonome intervals 5%. Centres of relative 
density are: Banksia serrata 10% 10% 5% 5% (exclusive to woodland) ; B. ericifolia20% 20% 20%; Pultenaea elliptica 
25% 20% 15%; P. retusab% 5%, 5% (exclusive to woodland). 
Proc. Linn. Soc. n.s.w., 115, 1995 
I. M. BREWER 275 
In the distribution of species between scrub and woodland, there were consistent 
results across both sites; some species were restricted to woodland, some to moist scrub; 
others were in common to both vegetation types; in this third group, most had substan- 
tially higher densities in scrub or woodland (Table 2) . With the more abundant species of 
shrub, isonome mapping illustrated variation in relative densities between woodland and 
moist scrub, again with a high degree of consistency between the two sites. Overall, the 
density of shrubs in scrub and woodland is in the approximate ratio of 2: 1 at both sites (see 
Appendix). 
Isonome mapping in this study revealed patterns of variation in abundance and 
distribution of species across the ecotones between woodland and moist scrub (Site B) 
that were not apparent even to the keen observer: 
( 1 ) The exact extent of the overlap for shrub species which intrude into woodland, 
or understorey shrubs which intrude into scrub 
(2) Complementary patterns of distribution between pairs of species of the same 
genera that were precisely defined in scrub and woodland 
(3) The abrupt termination, at the sharp shrub/tree ecotone of some species of 
shrub, exclusive to woodland or moist scrub 
Differentiation in distribution and density of species may be related to spatial varia- 
tion in soil or in the behaviour of fires. 
Buchanan (1980) observed that, at abrupt ecotones of moist shrubland and wood- 
land, an obvious change in understorey shrubs (not specified) coincided with an abrupt 
junction of the impervious sub-soil (less than lm below the surface) with the well drained 
sandstone soil of the woodland; a more gradual change in the understorey shrubs takes 
place when the impervious layer thins or deepens beneath the trees. As the abundance of 
some species of understorey shrubs at Site B is closely associated with the abrupt ecotone 
(Figs. 8B, 9A) it may be inferred from Buchanan's observations that the junction between 
the impervious sub-soil of the scrub with woodland soil at Site B was also abrupt, as was 
assumed, but not verified in 1941. 
Variations in vegetation on sandstone, related to variations in soil characteristics, 
have been observed by Pidgeon (1937, 1941),Siddiqi etal. (1972),Burrough etal. ( 1979) 
, Buchanan and Humphreys (1980) and noted by others, Thomas and Benson (1985), 
Outhred et al. (1985) . Though no observations were made on the soils at Sites A and B, the 
differences between woodland and moist shrubland soils are generally well known, partic- 
ularly the well-drained woodland soils in contrast to the temporary waterlogging charac- 
teristic of the moist scrub soils (Pidgeon 1938, Beadle 1962, Buchanan, 1980) . The overall 
distribution and abundance of species between woodland and moist scrub and the ex- 
clusive presence (or preference) for a particular habitat (Table 2) is more likely to be 
related to spatial variation in soils, than to spatial variation in the behaviour of fires. 
There was no evidence of recent fires at either site, confirmed by the dominance in 
moist scrub of shrubs killed by fire (Table 1 ) . Fire is probably the main factor in determin- 
ing composition and abundance of obligate-seeder species, largely controlled by fire 
frequency and inter-fire periods (see Thomas & Benson, 1985;Benson, 1985; and Keith in 
Press) . Recent research into population dynamics, starting with such observations, has 
been developed in studies of individual species (Bradstock & Myerscough, 1981; Auld, 
1 986) . Isonome mapping provides an avenue for relating these population-level studies to 
the sociology of communities which an experienced ecologist can interpret, often more 
rapidly than from computer-analysis. 
The restricted, low-value isonomes of obligate-seeder shrubs in woodland, abun- 
dant in scrub (Figs. 7A, 8A), could be considered as 'relics' of a pyric succession. 
Alternatively, they may be due to shading out by taller growing species in the absence of 
fire. 
In summary, isonome maps presented in this floristic analysis of moist scrub and 
woodland have revealed, for the first time in graphic detail, the structure, sociology, distri- 
Proc Linn. Soc. n.s.w., 115, 1995 
276 ISONOME MAPPING OF SPECIES DISTRIBUTION 
bution and abundance of species in these sandstone communities, and supported some 
observations by other researchers: 
(i) The association between high density of occurrence and vegetation type has 
been confirmed. 
(ii) Patterns of occurrence and density across ecotones have been revealed. 
(iii) Patterns of positive association, not previously apparent, have been 
discovered. 
(iv) Specific patterns i.e. relics in woodland of some obligate - seeder woody shrubs, 
abundant in adjacent scrub, have generated an hypothesis of temporal change 
operating at a small scale. 
In an age when sophisticated computer-based statistical techniques are used to anal- 
yse the structure of plant communities, the simplicity of isonome mapping, in association 
with investigation of micro-environmental factors, offers some advantages which are 
worth further exploration. 
Acknowledgments 
The constructive criticism and valuable advice by Professor R. J. Whelan, 
Department of Biological Sciences, University of Wollongong, and Dr P.J. Myerscough, 
School of Biological Sciences, University of Sydney, on the presentation of this paper, is 
gratefully acknowledged. I also acknowledge my indebtedness to the late Lord Ashby for 
his comments on an earlier draft and his endoresement to expand the 1941 data on the 
isonome mapping technique. I thank Dr W. T. Williams for reading an early draft, for his 
encouragement to publish, and his assurance that a program could be written for com- 
puting the data for graphic display. I thank Msjan Fragiacomo for her generous assistance 
in word processing. The field work and figures were completed when the author was a 
Linnean Macleay Fellow in Botany (1937-1941), at the University of Sydney. 
References 
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Proc. Linn. Soc. n.s.w., 115, 1995 

15 
4 
5 
2 
1 
X 
21 
77 
100 
20 
3 
31 
1 
7 
27 
16 
60 
3 
16 
78 
X 
2 
8 
236 
2 
22 
36 
1 
7 
15 
9 
196 
22 
3 
2 
5 
39 
9 
28 
9s 
70 
3 
5 
5 
75 
5 
1 
11 
X 
5 
30 
2 
19 
12 
1 
42 
7 
27 
278 isonome mapping of species distribution 
Appendix 
Species and densities per 85m. sq. recorded in quantitative analysis of adjacent areas 
f moist scrub and woodland, Sites A and B. 
x = recorded but less than 1 per 85 m. sq., + = cloned species not estimated, s = seedlings only 
Authorities for the binomials: Harden, Ed. (1990-93) , Vols. 1-4, Flora of New South Wales 
SITE A SITEB 
Species Moist Woodland Moist Woodland 
Scrub Scrub 
Allocasuarina distyla 19 1 
Acacia brownii 2 
A. longissima 
A. myrtifolia 
A. suaveolens 
Actinotus minor 
Adiantum sp. 
Angophora hispida 
Aotus ericoides 
Baeckea brevifolia 
B. densifolia 
B. diosmifolia 
B. imbricata 
Banksia ericifolia var. ericifolia 
B. oblongifolia 
B. marginata 
B. serrata 
B. spinulosa 
Bauera rubioides 
Billardieria scandens 
Boronia ledifolia 
B. pinnata 
Bossiaea heterophylla 
B. scolopendria 6 17 3 1 
Cassytha glabella x 
Caustis flexuosa x 
Ceratopetalum gummiferum x 
Choretrum candollei x 
Comesperma ericinum 23 18 
Conospermum ericifolium 8 
C. longifolium 
Dampiera stricta 
Darwiniafasicularis 
Dianella caerulea 
D. laevis 
Dillwynia retorta 
D.floribunda 
Drosera peltata 
Epacris microphylla 
E. pulchella 
Eucalyptus eugenioides 
E. gummifera 
E. haemastoma 
E. racemosa 
E. sieberi 
Gompholobium virgatum 
G. minus 
Goodenia stelligera 
Gcmocarpus teucrioides 
Grevillea buxifolia 
G. speciosa 
G. sericea 
Hake a dactyloides 
H. prrjpinqua 
H. sericea 
H. teretifolia 
Hemigenia purpurea 
Hibbertia aspera 
Proc. Linn. Soc.N.S.w., ii5, 1995 
14 
1 
4 
1 
3 
2 
1 
3 
49 
3 
44 
X 
75 
25 
3 
7 
X 
49 
1 
1 
29 
60 
90 
1 
15 
5s 
19 
Is 
5 
6s 
6 
X 
X 
1 
16 
8 
3 
25 
3 
1 
2 
1 
3 
4 
2 
11 
62 
1 
12 
3 
37 
11 
2 
53 
8 
5 
13 
8 
60 
12 
238 
39 
1 
10 
6 
8 
24 
I.M. BREWER 279 
SITE A 
Species Moist Woodland 
Scrub 
H. riparia 1 
Isopogon anethifolius 4 
Kunzea capitata 673 19 
Lambertiaformosa 1 
Lasiopetalumferrugineum 
Lepidosperma sp. 1 1 
L. laterals 1 
Leptospermum arachnoides x 1 
L. squamosum 566 15 
L. trinervium 40 31 
Leucopogon appressus 3 
L. esquamatus 15 5 
L. microphyllus 85 6 
Lindsaea microphylla 3 
Lomandra sp. 
Lomandra sp. 
L. glauca + + 
Lomatia silaifolia 1 2 
Micrantheum ericoides 1 218 
Mirbelia rubiifolia 1 
Monotoca scoparia 
Olax stricta 
Patersonia glabrata 
Persoonia hirsuta 2 
P. lanceolata 9 2 
P. mollis 
P. levis 
Petrophilepulchella 235 204 
Philotheca salsolifolia 
Phyllota phylicoides 
Pimelea linifolia 
Platylobiumformosum 
Platysace linearifolia 1 25 
Poranthera corymbosa 
Pteridium esculentum 
Pultenaea elliptica 2 8 
P. daphnoides 27 
P. retusa 1 6 
P. stipularis 2 
Restiofastigiatus + 
Pacinocarpus pinifolius 1 6 
Stylidium graminifolium 5 1 
Styphelia tubiflora 2 
5. viridis 4 9 
Telopea speciosissima 2 
Tetratheca ericifolia 1 2 8 
Woollsia pungens 13 1 
Xanthorrhoea resinosa 7 12 8 41 
Xanthosia pilosa 20 
X. tridentata 7 3 12 
Xylomelum pyriforme 4 
Zieria laevigata 5 1 
SITEB 
Moist 
Woodland 
Scrub 
2 
1 
24 
3 
246 
14 
17 
18 
X 
16 
8 
2 
86 
20 
9 
38 
98 
2 
90 
13 
X 
X 
+ 
+ 
+ 
6 
29 
5 
1 
11 
2 
1 
35 
16 
3 
1 
4 
4 
98 
74 
1 
59 
25s 
273 
2 
1 
13 
10 
1 
125 
48 
Proc. Linn. Soc. n.s.w., 115, 1995