Rapid Vegetation Survey

“Best bet” Land-use Systems

Thematic reports

Impact of different land uses on biodiversity

An Intensive Biodiversity Baseline Study in Jambi Province,Central Sumatra, Indonesia

 

Unique id: 2

Source file: D:\Projects\ASB\ASB Country and Thematic reports - xml\Above ground biodiversity assessmet WG\C-Sec1-3.xml

 

Authors: A.N. Gillison

 

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            Introduction:

 

Evidence for the need to conserve biodiversity is well established in the literature and is reflected in the international Convention on Biological Diversity that has addressed a series of issues for attention by its signatories (CBD 1994).  Despite the agreed urgency to develop a framework for biodiversity conservation, there is, as yet, no operational definition for biodiversity. According to Weitzman (1995), the implementation of any plan to preserve biodiversity is hampered by the lack of an operational framework or an objective function, and “We need a more-or-less consistent and useable measure of the value of biodiversity that can tell us how to trade off one form of diversity against another”.  Miller and Lanou, (1995) also maintain  “The value of biodiversity is determined largely by the interaction between human society and biodiversity”.  This implies that among other things, there should be a dynamic link between biodiversity and productivity for human needs. The World Bank (1995) asserts it is necessary to integrate biodiversity concerns into national decision making, but the mechanisms for this remain elusive. In Indonesia, the Government recognises a lack of scientific and management expertise in biodiversity conservation  (Government of Indonesia, 1993), that is further hampered by the current regime of property rights on public lands and waters, and the failure to use much of the financial returns from exploiting the country’s living resources to support biodiversity conservation (Barber et al. 1995). 

 

These pressures highlight both the need for a working definition of biodiversity and a cost-efficient, generic tool for its assessment that can be used in turn to inform policy planners and managers. While the species remains the sole currency unit for biodiversity assessment (Heywood and Baste 1995)  there will be little progress (cf. Wulff 1943).  Species richness and abundance used alone and without other attributes of behaviour and performance can seriously misinform and impede biodiversity assessment. Parity in richness does not guarantee equivalence in either genetic composition or response to environment. Partly for this reason, an emerging school of thought now considers assessment should include functional features or types as well as species. (Box 1981, Gillison 1981, 1988,  Nix and Gillison 1985, Cowling et al. 1994a,b, Huston, 1994, Collins, S.L. and Benning, T. 1996, Martinez 1996, Woodward  et al. 1996).  Varying definitions of functional types are so far most commonly associated with guilds (Bahr 1981, Gillison 1981, Huston 1994, Gitay and Noble 1996, Mooney 1996, Shugart 1996, Smith, 1996, Smith et al., 1996, Gillison and Carpenter 1997), but as Martinez (1996) asserts “..the functional aspects of biodiversity are a broad and vague concept that needs substantial added specification in order to become scientifically more useful.”  Cramer (1996) also feels the task of screening all the world’s species for functional types is impossible and that for a global model, a breakdown of the world’s vegetation can only be done based on major physiognomic or otherwise recogniseable features.  Recent global ecoregional studies (Gillison and Thomas, unpublished) suggest that, to the contrary, broad physiognomic and structural features can mask important functional and taxonomic differences in biodiversity.  Gillison and Carpenter (1997) and Gillison (1997) and Gillison and Alegre (1999, unpubl.)  have also shown it is possible to use generic functional or adaptive morphological attributes to characterise and quantify vegetation response to environmental change such as land use, climate and soil.

 

A new quantitative method has been developed for characterising vascular plants according to a set of 35 Plant Functional Attributes that describe a plant as a three component  ‘coherent’ (sensu Vogel 1991) or functional model. This consists of  the photosynthetic envelope, modified Raunkiaerean life form (Raunkiaer 1934) and above-ground root system. The method uses a semantic rule set and grammar (Gillison and Carpenter, 1997) to generate a theoretically finite set of unique PFA combinations for the world’s vascular plants. Any one combination is termed a functional modus. Using this rule set, about 7.2 million combinations or modi are possible, although it is thought that in reality the number is closer to 4,000. There is no a priori interdependence between modi and species; as the mapping is many-to-many, i.e. more than one modus can occur within a species and vice versa . The advantage of  functional over solely species-based methodsis that the former can be universally applied by observers with limited botanical and ecological experience. It can be used to compare functional characteristics of individuals and sets of individuals independently of species, e.g. where taxa may be geographically disjunct but may possess similar adaptations to environment.  In a comparative study of methods of characterising site productivity and growth patterns in North Queensland rain forests, Vanclay et al. 1996 showed the PFA method outperformed traditional methods of site characterisation. The method is now undergoing further tests by the Forestry Department, Qld DPI (Keenan, Woldring pers. com.). Gillison et al., (1996) has shown consistently high correlations between total numbers of species and total numbers of unique modi recorded from 40 x 5m plots across a wide range of environments (Annex II and cf. Baskin 1994). The implications from this are that in surveys where botanical expertise is lacking, modi can be used to predict species richness with a high degree of confidence. This may also benefit rapid assessment of plant biodiversity and improve correlations between plant and animal biodiversity (cf. Gillison et al. 1996). A field proforma specifically designed for rapid survey (see section 2.4) can now be used by observers with minimal training to characterise site physical features, vegetation structure, species composition and modi to rapidly describe a specific habitat for a taxon or set of taxa.

 

Richness in species and unique modi can be a useful complementary descriptor of habitat.  But while these contribute to characterising biodiversity, they do not by themselves reflect evenness or dominance of individuals per species such as the frequently used diversity indices of  Shannon-Wiener and Simpson (Magurran 1988). Many diversity indices have been developed, but the search goes on (Cousins 1991, Majer and Beeston 1996). The great majority are based on species abundance and at best are usually regarded simply as another species-based, stand attribute. A problem for survey in tropical forests is that to generate such indices requires time-consuming counts of individuals which is not cost-effective. To help circumvent this problem, Gillison et al. (Appendix 2.1) have developed a complementary measure of functional diversity based on the numbers of modi per species for each plot. This differs from approaches by others (e.g. Martinez 1996) and has the advantage that in rapid survey it is only species rather than numbers of individuals of species that are counted.  A  measure of functional complexity has also been developed by the same authors based on a computed functional ‘distance’ between  modal assemblages derived from a table of weighted ‘transformation’ values between specific PFAs (Gillison and Carpenter 1997).

 

It is one of the tenets of RBA that for practical purposes there should be indicators or surrogates of more complex plant and animal assemblages. Whether this is a realistic assertion is a continuing source of debate (Cranston and Hillman 1992, Reid et al. 1993, Pearson 1995, Howard et al. 1996), and there is often questionable theoretical support for targeting so-called keystone species (Tanner et al. 1994). There is nonetheless an increasing need for reduced attribute sets that can be used to carry other information such as the status of key pollinators and seed dispersers that may not be available at the time of survey (Miller et al. 1995)  To demonstrate indicator efficiency requires calibration from very intensive baseline studies of taxa and functional types at a comprehensive range of spatial, temporal and environmental scales. Such baseline studies are almost non-existent in complex tropical environments. Ongoing studies within the context of ASB show varying correlative trends. In a baseline study of  Sumatran rain forests, Gillison et al. (1996) showed that while plant biodiversity increased with elevation from 500 to 900m asl, the converse was true for insects and birds. While such confounding effects can be accommodated by appropriate regression models and multiple discriminant formulations, predictive models of biodiversity based on environmental correlates such as elevation clearly need to be carefully evaluated before being used by managers.  It follows that environmental context and scale are important in designing  field studies of biodiversity (see also He, et al., 1994,).

 

 Most practitioners now concede the landscape matrix is critical to supporting biodiversity (cf. Forman and Godron, 1986, Franklin 1993), and this has been central to survey design and data collection across all the ASB and CIFOR ercoregional benchmark sites. Because disturbance is a critical determinant of biodiversity (Petraitis et al.., 1989, van der Maarel 1993, Phillips et al.. 1994), factors such as agriculture, shifting cultivation and forest fragmentation (Grime 1979,  Bierregard et al., 1992, Sayer and Wegge 1992, Margules and Gaston 1994, Brooker and Margules 1996) should be considered when designing a survey. For this reason, the ASB sites have been located specifically to sample a range of dynamic conditions, along successional gradients of land use from pristine rain forest, logged-over forest,  plantations to degraded grasslands.  Although the issue of plot size is a continuing  source of debate in plant ecology,  recent  studies show that for plant diversity, useful information can be recorded from plots as small as 50 x 2m (Parker and Bailey 1992, Parker and Carr 1992, Parker et al. 1993) and 40 x 5m. (Gillison et al. 1996). The advantage of ‘small and many’ vs. ‘few and large’ is that the former is more cost-effective when sampling variation in biodiversity at landscape level (cf. Keel et al. 1992). Variation of this kind demands cost-effective survey techniques (cf.  Margules and Haila 1996). Because the distribution of plants and animals is determined mainly by environmental gradients, gradient-based techniques using the gradsect approach offer one means of sampling such variation (Gillison and Brewer 1985). With gradsects, sites are located according to a hierarchical nesting of assumed physical environmental determinants such as climate, elevation, parent rock type, soil, vegetation type and land use. This approach has been shown to be more cost-efficient than purely random or purely systematic (e.g. grid-based) survey design (Gillison and Brewer 1985, Austin and Heyigers 1989).  As gradients themselves are being sampled, this will enhance the efficiency of extrapolative spatial models.

 

Issues of biodiversity conservation inevitably raise important questions of site representativeness. For a programme involved in the selection of ‘best-bet’ options for biodiversity and productivity, a manager may need to choose between different locations to ensure optimal management.  For this a range of sophisticated computer-based solutions already exists. These are based mostly on species occurrence but may include environmental features such as land classes (Nicholls and Margules 1993, Pressey et al. 1996, Csuti et al.. 1997, Pressey et al. 1997). Other species-based approaches use additional levels of higher taxa (Prance 1995) or a measure of ‘phylogenetic distance’ to include taxic richness or  genealogical relationships as embodied in taxonomic classifications, typically by a weighting of the relative number of species per genus, genera per family etc.  (Vane-Wright et al. 1991, Williams et al.. 1992, Faith 1992, 1993, 1995). A problem with species-dependent approaches of this kind is that for many tropical lowland forests, species identification is difficult and time-consuming. In addition, the majority of these algorithms require expertise that is frequently lacking in developing countries.  For this reason, and because functional types can be more easily identified than species,  Gillison et al., (unpublished 1998) developed an analagous concept of ‘functional distance’ based on modi (outlined in Annex I). The algorithm is being incorporated in a new data-entry software package PFAPRO designed to run on a PC as a Windows application (Carpenter and Gillison, unpublished 1998). When data from a series of plots containing functional modi have been entered, PFAPRO has the facility to generate a distance matrix on demand.  By this method, managers can readily identify levels of similarity between plots or landscape units.  

 

Data collected during this project will be used to generate and test spatial models of key sets of taxa and functional types and to couple these with productivity patterns based on land use. For this purpose a potential mapping software package DOMAIN (Carpenter et al. 1993) will be used. Unlike other packages such as BIOCLIM (Busby 1991) or CLIMEX  (Sutherst and Maywald 1985) that are either climate-dependent or require detailed, process-based knowledge about the species in question, DOMAIN uses any georeferenced data that are considered important in influencing performance of an individual. This may include environmental data used to construct a gradsect–based survey. DOMAIN then accepts known distribution points for specific taxa or functional types and constructs an environmental envelope for these using environmental correlates and a distance measure based on the Gower metric. It then computes a grid-based distribution map of  according to the similarity matching of each pixel or grid with the original environmental domain. DOMAIN has been used in previous baseline studies in Sumatra (Gillison et al. 1996) and has been modified by CIFOR to run as a user-friendly, Windows based package on a PC. The software is available gratis from the CIFOR home page on the internet. Since its installation in August 1997 CIFOR has recorded downloads from users in 35 countries.  Because DEMs were constructed for each of the ASB benchmark sites in Phase II, it is anticipated DOMAIN will be used for generating and testing spatial models of biodiversity and related productivity.  The effective extrapolation of data will depend to a large degree on the availability of georeferenced environmental data. These data have been compiled at CIFOR using mapping sources from within Indonesia (Laumonier et al. and other sources from within the GoI Ministry of Forestry). Remote sensing of tropical rain forest vegetation has been used elsewhere with some success (Tuomisto et al. 1994) and is expected to play a significant role in DOMAIN applications. Data for normalized difference vegetation index (NDVI) are available and can be used in DOMAIN.  NDVI is commonly used with AVHRR (advanced very high resolution radiometer) data for which appropriate calibrations are necessary (Roderick et al., 1996a,b).

 

Most vegetation classification and survey methods incorporate a combination of broad structural variables coupled with seasonality (deciduousness) and a list of dominant species, e.g.’Very tall  evergreen Dipterocarp forest’. While this is useful for many geographic purposes it is insufficiently diagnostic for management purposes. In addition, structurally similar vegetation types are usually annotated by regionally different plant species. Within a region, vegetation described according to vegetation structure may be adequate for describing animal habitat but similar structure in separate global ecoregions are not necessarily ecologically equivalent. For ecologically sensitive classifications additional, response-based attributes such as adaptive features or plant functional attributes (PFAs) provide added value. As PFAs are generic and largely independent of species, they can be used to make ecological comparisons between geographically remote areas where environments and adaptive features may be similar but where species differ.

2.2        Methods:

 

The Plant Functional Attribute proforma (modified from Gillison, 1988 and updated by Gillison and Carpenter, 1997) was used to record site physical features [georeference by GPS in degrees, minutes and seconds; slope percent (clinometer); elevation (m) (digital aneroid altimeter); aspect in degrees (compass); parent rock type; soil type; vegetation structure, (mean canopy height (m), crown cover percent, basal area (m2ha-1); litter depth (cm); Domin scale cover-abundance estimates of wood plants <2m tall and Domin estimates of bryophytes; all vascular plant species and plant functional types (PFTs]. As described by Gillison and Carpenter (1997), Plant Functional Types or PFTs or functional modi are combinations of essentially adaptive morphological or functional attributes  (e.g. leaf size class, leaf inclination class, leaf form and type (distribution of chlorophyll tissue), coupled with a modified Raunkiaerean life form and type of above-ground rooting system.  PFTs are derived according to a specific grammar or rule set from a minimum set of 35 functional attributes. An individual with microphyll-sized, vertically inclined, dorsiventral leaves supported by a phanerophyte life form would be a PFT expressed as MI-VE-DO-PH.  Although they tend to be indicative of a species, they are independent of species in that more than one species can occur in one PFT and more than one PFT in a species. PFTs allow the recording of genetically determined, adaptive responses of plant individuals that can reveal infraspecific as well as interspecific response to environment (e.g. LUTs) in a way that is not usually contained in a species name. They have a major advantage in that, because they are generic, they can be used to record and compare data sets derived from geographically remote regions where, for example, adaptive responses and environments may be similar but where species differ. The data are recorded along a 40x5m strip transect located along the contour.

 

The data were compiled in a laptop computer using a recently developed software package, PFAPro (Gillison and Carpenter, unpublished). PFAPro facilitates compilation according to the rule set developed by Gillison and Carpenter (1997).  It also facilitates the summary analysis of meta-data as well as producing graphs of relationships between different plant and vegetation variables. Using PFAPro, data logged for each 5x5m quadrat allow the generation of cumulative species and PFT totals per unit area and this allows the subjective inspection of asymptotic curves that can indicate whether or not a plot is an adequate sample of the vegetation or LUT (See Annex 1, Fig.1).

 

In addition to site physical data, simple totals of species, PFTs and vegetation structural variables, PFAPro can be used to generate a range of diversity indices for PFTs (Shannon-Weiner, Simpson and Fisher’s alpha). The calculations are not trivial as, unlike diversity indices for species that are based on abundances of individuals per species, the PFT indices are derived on the number of species per PFT. Since the species to PFT relationship is many-to-many, this must be taken into account when calculating diversity. The method is described more fully in Appendix 2.1.

 

Four observers (ecologist and assistant, botanist (x2) and two laborers) collected plant voucher material later identified and curated at the Herbarium Bogoriense. A complete set of identified species and associated PFTs is listed in Annex III, Table 3. This method facilitated sampling even the most complex rain forest plot of 177 species in less than three hours.  Photographic records were made of each plot. A sub-set of these has been scanned and will be cross-referenced with the data set.

 

            Results:

 

The data were analysed according to the methods described above and in Part B. The most useful interpretations came from multidimensional scaling in which a two vector solution was extracted from plot data (Part B, Annex I, Fig. 7). This graph shows a zone of maximum biodiversity richness that is associated with jungle rubber. The peak in richness can be explained in part by the greater variety of available ecological niches in this agroforestry system compared with pristine rainforest. The analyses are based on a minimum data set of mean canopy height, basal area, species richness, PFT richness and a ratio of species numbers to numbers of PFTs or modi. Cumulative species, modi and species/modi richness area curves per 40x5m plot are indicative of vegetation type per LUT (Part B, Annex I, Fig.1 (1-7)). More detailed results from analyses of combined sets of taxa and functional types are described in the synthesis (Section 11).  Other analyses dealing with variations on compositional structure of species, PFTs and vegetation structure and their relation to LUT will be dealt with in a later report. Plant taxa and functional types for each LUT are listed in Annex III Table 3. Summary data are listed in Table 2.1 and estimates of green biomass are given in Table 2.2 below. Relationships between vegetation and LUTs are described briefly in Section 3 below.

 

Table 2.1.

Summary of Taxa and Plant Functional Types (Modi) per LUT

 

No.

  Site

Family

Genus

Species

Uniq Sp/Plot

Modi

1

  BS1

44

82

103

102

37

2

  BS2

43

81

104

100

36

3

  BS3

32

48

  50

  50

20

4

  BS4

45

83

111

108

39

5

  BS5

43

82

117

112

38

6

  BS6

26

35

  42

  42

27

7

  BS7

25

43

  48

  46

33

8

  BS8

37

60

  68

  65

37

9

  BS9

31

52

  58

  54

30

10

BS10

53

97

115

111

47

11

BS11

49

89

100

  97

41

12

BS12

  6

10

  11

  11

10

13

BS13

  6

  7

    7

    7

5

14

BS14

  7

12

  15

  15

12

15

BS15

  8

19

  19

  19

13

16

BS16

22

40

  43

  42

34

 

Total

    477

    840

   1011

981

    459

 

 

 

 

 

 

 

 

Unique Total

91

    320

_

        557

    216

 

 

Table 2.2.

Green biomass per Land Use Type*

 

Site.no

LUT

Av.kg/m2

stdev

coefvar

SEM

C-t/ha

BS01

NF

0.133

0.079

0.594

0.028

0.533

BS02

NF

0.000

0.000

*

0.000

0.000

BS03

LOF

0.000

0.000

*

0.000

0.000

BS04

LOF

0.045

0.083

1.854

0.029

0.179

BS05

LOF

0.007

0.020

2.828

0.007

0.028

BS06

HTI

0.247

0.159

0.642

0.056

0.987

BS07

HTI

0.092

0.131

1.424

0.046

0.368

BS08

RUB-P

0.107

0.126

1.178

0.044

0.426

BS09

RUB-P

0.083

0.093

1.121

0.032

0.331

BS10

J_RUB

0.033

0.400

1.194

0.014

0.133

BS11

J_RUB

0.018

0.035

1.913

0.012

0.073

BS12

IMP

0.227

0.057

0.252

0.033

0.908

BS13

IMP

0.180

0.008

0.045

0.004

0.719

BS14

CAS

0.207

0.028

0.136

0.016

0.829

BS15

CAS

0.288

0.089

0.308

0.051

1.150

BS16

CHROM

0.335

0.143

0.427

0.082

1.340

 

*Source  M.Van Noordwijk and K.Hairiah

 

NOTE: Additional results from the vegetation survey are described in Section 11

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Appendix 2.I

 

Unpublished measures of functional diversity and functional complexity

 used in this project

 

(extracted from Gillison, A.N. Carpenter, G. and Thomas, M., Plant functional diversity and complexity: two complementary measures of species diversity.)

 

 

 

Functional diversity 

 

 

Concepts of functional diversity vary; according to Martinez (1997) (see also Steele, 1991 quoted by Martinez), functional diversity is defined as “..the variety of interactions with ecological processes” and can be quantified by determining  the nature and extent to which functional groups are represented in an ecological system.  Functional diversity can also refer to the number of such groups in a community each of which contains one or more species (Smith and Huston, 1989; Scott and Benning 1996).  Whatever the nature of the functional groups it is generally accepted they will be fewer than the species under study, (Mooney 1997). In this sense  functional ‘diversity’ is simply a measure of group richness rather than an estimate of evenness or dominance based on the abundance of individuals per group.

 

As with species diversity, it would seem reasonable to derive a parallel measure of functional diversity based on the abundance of individuals per functional type or modus but without species-weighting. While logically viable, this is likely to be limiting in practice as to record all individuals, (e.g. in an epiphyte-rich, rain forest) can be excessively time-consuming and counterproductive if the aim is rapid assessment, and if the functional types or groups are likely to be significantly fewer than the species. Depending on the scale an purpose of the investigation, the additional effort may not be worth the gain. For these reasons, we explore the possibility of using species instead of individuals to serve as a ‘higher-order’ measure of abundance by deriving a species-weighted, rather than a spatial or density-driven, measure of Functional Diversity based on abundances of individuals. A species-weighted form of Functional Diversity (SFD) can therefore be defined as: The diversity of functional types expressed as a function of the number of species per type.  While the definition can be compared with that of Huston (1994) for species diversity where “The total species diversity of a community is described by the number of functional types multiplied by the average number of species per functional type”, this approach is more sensitive to evenness and dominance.  We achieve this in the same way that species abundance is used to calculate species diversity but with the important difference that counts of species per functional type are used instead of counts of individuals per species. For this we apply the Shannon-Wiener formula to estimate evenness and that of Simpson to estimate dominance. Another difference is that, unlike the ‘one-to-many’ species to individual relationship, the mapping between species and modi is’ many-to-many’ (i.e. more than one species can exist in one modus and vice versa) (Fig. 1). Both formulae have been modified to accommodate these multiple relationships. 

 

 

Fig. 1   An example of multiple linkages (many-to-many mapping) between Linnean species and functional types or modi.  Species A occurs in modi m1, m2; species B in modus m2, while m1 occurs in species A , and m2 in species A and B.  An individual is recorded once if it satisfies any one of these relationships – duplicates are omitted.

Shannon Wiener Index

 

The Shannon-Wiener index is calculated from the equation (ref.):

 

 

where quantity piis the proportion of individuals found in the ith species, and is estimated using the maximum likelihood estimator:

 

 

Where ni is the number of individuals in the ith species.  For species/population data, each individual in the sample belongs to exactly one species. And N is the total number of species recorded.  However with modus/species data, a species may be attributed to more than one modus if that species is present in multiple functional forms.  To accommodate this difference, the maximum likelihood estimator is modified to divide the proportional count for a species evenly between the  modal types in which that species is present.  The equation for pi, the proportion of species in the ith modus becomes:

 

 

Where Nspp  is the number of species,

nji is the number of records for species j, modusi (either 0 or 1)

nj is the number of records for species j,

and N is the total number of records.

 

Because the species to modus mapping is a many to many relationship N may be greater than both the number of species Nspp and the number of modi in the sample.

 

Simpson’s Index

 

The same modified form of the maximum likelihood estimator is used in the calculation of the Simpson index which is usually formulated as:

 

 

The Simpson index produces higher values for lower diversity, and is often expressed as

.

 

Limits

 

Diversity values for the Shannon-Wiener index become progressively smaller with increasingly uneven distribution of species between modi where, for example, a small number of  modal forms dominate the sample.  Given the number of species and the number of modi in the sample, the absolute minimum index value possible can be found by computing the largest possible value for maximum likelihood estimator (P0) for one modus, while minimizing the remaining Nm-1 estimators (Pi>0). The minimum estimator value occurs when only one species occurs in a modus, and that same species occurs in all other modi.  The minimum is formulated as:

 

 

The maximum value of the Shannon-Wiener index is generated when the species are evenly distributed between all modi, such that Pi =1/Nm, yielding as a final form:

 

 

The same proportion values determine the limits of the Simpson Index.  This index returns smaller values for increasing diversity.

 

Interpretation and Examples

 

When interpreting species-weighted functional diversity measures it is important recall that the measure describes the distribution of species between functional modi, not the distribution of individuals between functional types.

 

The values generated by of these species-weighted functional diversity measures, when applied over a broad range of sites, are typically higher than the equivalent measures from species/population data.  This reflects the reduced likelihood of dominance of any particular functional type, and a similar degree of discriminatory resolution (or granularity) between functional types and species.  The consistently high correlation between species counts and  modal counts at the global level is explored elsewhere (Gillison, submitted for publication – see Annex II)

 

 

 

Functional complexity          

 

 

Two approaches were adopted for the analysis of  modal composition. The first was an exact mirror of the analysis of species composition.  Instead of an analysis of species incidence, the incidence of each modus was used to generate a between-site Jaccard distance. This distance matrix was then input to the same multidimensional scaling procedure.

The second approach attempted to take account of the inherent similarity or dissimilarity between different modi. It was based on the syntactic distance between modi of Gillison and Carpenter (1997).

We consider sites X and Y, such that site X contains the set of modi  and site Y contains the set of modi . Now let be the distance between modia and b. We define the dissimilarity between sites X and Y to be:

 

.                 

 

This index will be zero only if sites X and Y contain the same set of modi. In particular, it will be non-zero if modi at one site are a proper subset of modi at the other. It should also be noted that the dissimilarity index is not a metric.

The expected value of the dissimilarity index depends on the number of modi at each site.  If the modi present at each site are generated by random sampling from a set of available modi, then the distance between two sites will decrease as the number of modi at each site increases.  In the absence of any other aspect of pattern, we would expect sites with many modi to be very similar, whilst sites with few modi would be dissimilar - both to other sites with few modi and to sites with many modi. Ordination of such a dissimilarity matrix would result in a hyper-sphere - with modi rich sites at the centre, and modi poor sites at the periphery.  Analyses of  data from a range of global environments tend to confirm the utility of this procedure (Gillison and Thomas, unpublished).