Ecological Modelling 179 (2004) 499–513

Formulating diversity vector for ecosystem comparison

A. Roya, S.K. Tripathib, S.K. Basua,∗a Computer Application Programme, Computer Centre, Banaras Hindu University, Varanasi 221005, India

b Department of Botany, Banaras Hindu University, Varanasi 221005, India

Received 13 February 2003; received in revised form 12 September 2003; accepted 23 November 2003

Abstract

Extensive variations in the taxonomic variety and morphology of living organisms and their spatial distribution have created amajor problem for precise assessment of biodiversity. Biodiversity is fundamentally a multidimensional concept and cannot bereduced sensibly to a single number [Purvis, A., Hector, A., 2000. Getting the measure of biodiversity. Nature 405, 212–219].A number of diversity indices are available but each has its own limitations, as they are not adequate for comprehensiverepresentation of biodiversity of an ecosystem. We propose a vector for making a comprehensive quantitative and qualitativedescription of ecosystem diversity. This vector gives a fair idea about the physical and biological aspects of the ecosystem andcan be used for modeling and comparison of intra- and inter-ecosystem diversity in the form of concise numerical information.The diversity vector has five components: environmental index, life-form index, Shannon–Weiner index, taxonomic index andfunctional index. The scheme takes care of species abundance, taxonomic variety and satisfies monotonicity. Moreover, thesecomponents can be easily calculated. Field data from two contrasting ecosystems are used to explain the scheme. Though wehave confined to the plant kingdom, the scheme can be logically extended to incorporate the animal kingdom.© 2004 Elsevier B.V. All rights reserved.

Keywords: Ecosystem diversity; Community; Life-forms; Shannon–Wiener index; Taxonomic distance

1. Introduction

The biodiversity losses have been noted through-out the world primarily due to the over-exploitationof natural resources, habitat degradation, and climaticchanges. The current species extinction rate has in-creased up to a few thousand times that of the back-ground rate as inferred from fossil records (Barbautand Sastrapadja, 1995) and is of the order of thou-sand species per decade per million species (Pimm andRaven, 2000). Major drivers of future changes in bio-diversity are land-use changes, climate change, nitro-

∗ Corresponding author. Tel.:+91-542-2307050(O)/91-542-2369480(R), fax:+91-542-2368174.

E-mail address: swapankb@bhu.ac.in (S.K. Basu).

gen deposition, increase in the atmospheric CO2 con-centration and biotic exchange (Sala et al., 2000). Pre-dicted increase in the human population may lead tochange in the land-use pattern. The result of greaterresource exploitation by the increased population willlead to further loss in biodiversity at an alarming rate.This has necessitated the importance of its conserva-tion at the national and the international levels (Noss,1991; Wilson, 1992). Biodiversity conservation re-quires critical monitoring and baseline information inquantitative terms at each level of organization (fromthe regional to the global level). However, the conser-vation of biodiversity and the projected biodiversitychanges based on modeling require a proper assess-ment in the form of concise numerical informationrepresenting inter- and intra-ecosystem diversity.

0304-3800/$ – see front matter © 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.ecolmodel.2003.11.018

500 A. Roy et al. / Ecological Modelling 179 (2004) 499–513

Although a few diversity indices are extensively inuse, each has its own limitation. These indices mainlyreflect the number of species and the proportion ofindividuals of the species in an ecosystem and do notgive any idea of the variety in the composition andthe extent of the variability. There seems to be a gapbetween the existing indices of diversity (Simpson,1949; Shannon and Weaver, 1963; Rao, 1982) and thenewer notions of biological diversity (Chapin et al.,2000; Tilman, 2001; Norberg et al., 2001). Izsak andPapp (2000)mentioned scarcity of ecological diver-sity indices in the literature and such an index shouldtake care of species abundance, taxonomic variety andshould have monotonicity property. Wide variationsin the taxonomic variety and morphology of livingorganisms and their spatial distribution have created amajor problem for precise assessment of biodiversity.Pielou (1975)has stressed the need of taking intoconsideration the taxonomic differences among thespecies and has proposed a way to represent themby integrating the species and the genus level di-versity in the Shannon–Wiener index. However, thisindex still does not represent the information em-bodied in the structure of the ecosystem such as thetaxonomic spectrum, the life form, their functionalattributes, etc. Index based on Shannon negantropycannot capture the information embodied in the struc-ture (Brooks, 2003). We do not have comprehensiveindices for measuring the biodiversity of a region andthe changes in its magnitude. In fact the currentlyused indices do not give any idea about the nature ofthe communities in which they are assessed, which isessential for cross biome or community comparisonand mathematical modeling of the diversity.

Global diversity includes diversity at all the organi-zational levels ranging from genetic diversity within apopulation to the diversity of ecosystems in landscape(Chapin et al., 2000). Thus, the biodiversity hierar-chy is composed of the genetic, species-population,community-ecosystem and landscape-regional levels(Grumbine, 1992; Harrod et al., 1996). Any changein the higher level of ecological organization such asthe landscape or the ecosystem will also include thelower levels such as the species or the genetic di-versity (Allen and Star, 1982; Noss, 1990). Wilsonet al. (1996)have identified attributes of biodiversitythat can be assessed at each level of ecological or-ganization. For instance, at the landscape level it is

the distribution and proportion of habitat type, at theecosystem level it is the richness, evenness, diversityof species, functional groups and communities, at thespecies level it is the abundance, density and biomassof each population, and at the genetic level it is thevariations in the individual organisms within a pop-ulation. Various approaches have been discussed byGaines et al. (1999)for quantification, interpretationand monitoring of biodiversity at all these levels oforganization.

To proceed with the study of biodiversity, we need toactually define the concept of biodiversity. We cannotassess how the biodiversity is distributed or how fastit is disappearing unless we assign units to it (Purvisand Hector, 2000). However, any attempt to measurebiodiversity runs into the problem that it is fundamen-tally a multidimensional concept and cannot be re-duced sensibly to a single unit. We believe that thebiodiversity of a region can be better expressed if theenvironmental factors (that is precipitation, tempera-ture, latitude, and altitude), taxonomic variability andlife-form variations of the community are included indescribing the diversity of an ecosystem. Such an in-ventory of the global diversity will make quantitativecross biome comparison of diversity much easier andfeasible. It is not possible to capture all the aspects ofan ecosystem in a single index, so a vector is the mosteffective way to describe different aspects of ecosys-tem diversity. We propose a vector that gives a set ofnumerical values depicting the diversity of an ecosys-tem in a concise manner. The vector includes numeri-cal representation of the compositional diversity (e.g.taxonomic variety of the species and the proportionof individuals belonging to different species), struc-tural diversity (e.g. stratification in an ecosystem) andthe functional diversity (e.g. productivity, decompo-sition and mineralization rates). The parameters usedin this scheme are easier to record and calculate andthus increases the suitability of the eco-diversity indexmanifold. Further, certain major environmental vari-ables such as the range of temperature, precipitationrate along with the latitude indicating the type and ge-ographical position of the ecosystems have also beenincluded in the vector. These are considered the ma-jor factors for representation of ecosystem diversity(Gaines et al., 1999).

The paper is divided into five sections.Section 1introduces the concept and discusses about the need

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for a new approach to define the diversity.Section 2describes the existing indices.Section 3describes theproposed eco-diversity vector.Section 4illustrates theuse of the proposed eco-diversity vector using fielddata andSection 5discusses the limitations of theeco-diversity vector and concludes the paper.

2. Existing indices

A number of diversity indices have been proposedby many workers from time to time. For instance,α-diversity was proposed to measure the diver-sity within a community (Simpson, 1949; Shannonand Weaver, 1963; McIntosh, 1967), β-diversityto determine inter-community diversity (Whittaker,1960; Cody, 1975; Wilson and Shmida, 1984)and γ-diversity to measure the landscape diver-sity (Schluter and Riocklefs, 1993; Halfter, 1998).Simpson’s index of diversity gives a numerical valueof the diversity based on the total number of species(species richness) and the proportion of individu-als (equitability or evenness) in the ecosystem. Al-though this index gives an idea of the number anddistribution of the individuals of the species in acommunity, it does not account for the extent ofvariability among the species (taxonomic varieties)and their spatial distribution (e.g. vertical zonationof plants). Shannon–Weiner index based on informa-tion theory improves upon the Simpson’s index bygiving more importance to the rarer species, whereasSimpson’s index mainly accounts for the abundantspecies.Pielou (1975)proposed a modified versionof the Shannon–Wiener index based on negantropy atthe different levels of the taxonomic hierarchy. Al-though this index is much more informative than theShannon–Wiener index, it cannot account for the in-formation embodied in the structure of an ecosystem.Further more, it cannot be calculated if unidentifiedspecies are present. Due to the integration of thetaxonomic hierarchy in the Pielou’s hierarchy index,there is a loss in the information from the originalShannon–Wiener index. The quadratic diversity index(Rao, 1982) expresses the expectancy of differencesamong the species. The Gini–Simpson index, whichis one minus the Simpson’s index, is a special caseof quadratic diversity index. However, all these in-dices are primarily based on the number of species

present within the community, between the commu-nity and a landscape, respectively, in theα-, β- andγ-diversities. In recent years a number of researchershave tried to represent biological diversity in a num-ber of ways (Ricotta, 2000; Yue et al., 2001). Ricotta(2000)has proposed the formulation of biological di-versity using the concept of geometrical complexity.Yue et al. (2001)has used the concept of Holdrigelife zone diversity. But almost all of them have usedthe Shannon’s negantropy for development of theirindices. Furthermore, all the proposed indices arescalars, wherein the compression of information leadsto loss in information. As we have already stated thatthe biological diversity is a multidimentional entityand so it cannot be adequately represented by a scalarquantity.

With regard to biological diversity in its currentsense, the abundance condition and evenness compo-nent as described by the above-mentioned indices areirrelevant (Izsak and Papp, 2000). Biological diversityof any ecosystem or landscape may be better repre-sented by including taxonomic variety (i.e. life formsand the taxonomic distance), the environmental indexalong with the ecosystem functional parameters in avector, rather than through an indication of the numberand proportion of individuals of species only. It seemslogical that the index of diversity should be such thatgreater the extent of the variation among the species,the greater should be the diversity. In the recent past,biodiversity measures have taken into account the dif-ference between the species, neglecting the abundanceconditions.Faith (1992)introduced phylogenetic di-versity based on feature mismatch between species andVane-Wright et al. (1991)introduced the taxonomicdistance based on taxonomic tree.

3. Eco-diversity vector

The level of diversity in the major terrestrial biomesof the world varies dramatically due to altered ecosys-tem characteristics such as latitude, altitude, temper-ature and precipitation (Holdridge, 1967; Kempton,2002). It has been generally observed that the increasein latitude and altitude causes a decrease in the levelof biodiversity. The mean annual temperature and pre-cipitation can also be correlated with the distributionof the world’s major terrestrial biomes. While the role

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of these factors in affecting the distribution of speciesis important, it should be noted that the distribution ofbiomes might also depend on seasonal factors such aslength of dry season or the lowest absolute tempera-ture, on soil properties, on land-use history and distur-bance pattern (Holdridge, 1967; Chapin et al., 2000).The proposed vector contains a complete set of infor-mation regarding biodiversity such as compositionaldiversity, structural diversity and functional diversityin an ecosystem. The vector will be useful for crossbiome comparisons.

A single index of species diversity as generallyreported in the literature (Simpson, 1949; Shannonand Weaver, 1963; McIntosh, 1967; Rao, 1982; Vane-Wright et al., 1991) is not enough to typically describethe diversity of the major aspects of an ecosystem.Ecosystem is structurally complex in the physicalsense. For example, a tree and a herb, both are separateindividuals but the impact of each on the ecosystemstructure and functioning is widely different than thatof the other. Since the currently used diversity indicesare not able to capture the structural information in anecosystem (Brooks, 2003), it is essential that the infor-mation embodied in the structure of the ecosystem berepresented by a diversity vector. Therefore, we pro-pose an eco-diversity vector represented by a 5-tuple(α, β, γ, δ, η) where each component in the 5-tuplerepresents a specific aspect of the eco-diversity. Thefirst component represents the environmental de-terminants (like latitude, altitude, temperature andprecipitation) which are responsible for major com-positional, structural and functional (described bylife forms) changes in the diversity. The componentstwo through five indicate major characteristics of anecosystem that represent a set of structural and func-tional aspects of the eco-diversity in the region. Theset of parameters considered for expressing the diver-sity vector are: (i) environmental index, (ii) life-formspectrum, (iii) Shannon–Wiener index (distributionof the species in the community), (iv) taxonomicvariation among the species and (v) functional index.

3.1. Environmental index (α)

Many ecological studies have demonstrated thatplant life is responsive to environmental parameterssuch as temperature, precipitation, etc. (Holdrigeet al., 1971; Yue et al., 2001). Yue et al. (2001)have

proposed the Holdrige life zone diversity but it doesnot give much information about the environmentalconditions of the region. Though it gives emphasison the distribution of species based on temperatureand precipitation, it does not consider the variationamong the species. The different ecosystems of theworld have different forms of diversity. The diversityin any ecosystem or community is based on the abi-otic variables of the ecosystem. Biodiversity changesalong the latitudinal gradient, tropical (0◦–20◦),sub-tropical (20◦–40◦), temperate (40◦–60◦) and arc-tic (60◦–80◦), and are generally characterized by adecrease in the biodiversity (Holdridge, 1967; Salaet al., 2000). Increase in altitude leads to a decreasein the biodiversity due to decrease in the temperature(decrease of 6.5◦C for every 1000 m increase in thealtitude). Likewise, precipitation alone and in combi-nation with temperature has a profound effect on thebiodiversity of a region. The environmental index ofthe eco-diversity vector is based on the following fourattributes: (a) latitude, (b) altitude, (c) temperature,(d) annual precipitation.

Based on the above-mentioned attributes, the majorbiomes of the earth have been broadly divided into sixcategories (Barbour et al., 1987). They are: (a) tropical,(b) subtropical, (c) temperate, (d) Mediterranean, (e)arctic/alpine, and (f) arid region.

The latitude has been graded into five categories as:latitude 0◦–25◦ as 1, latitude 25◦–45◦ as 2, latitude45◦–60◦ as 3, latitude 60◦–75◦ as 4, latitude 75◦–90◦as 5. This grading has been done based on the veg-etation zones that are found in these latitudinal belts(Holdridge, 1967). Similarly, altitude has been gradedinto four categories: 0–700 m as 1, 700–1500 m as 2,1500–2500 m as 3, above 2500 m as 4, and it is alsobased on the vegetation type which changes alongwith the altitude (Kempton, 2002). The temperature(expressed as the mean annual temperature) has beengraded into five categories:−20 to 0◦C as 1, 0–15◦Cas 2, 15–25◦C as 3, 25–35◦C as 4, 35◦C and aboveas 5. The total annual precipitation (expressed in mm)has been graded into seven categories: 100 and lessas 1, 100–400 as 2, 400–750 as 3, 750–1300 as 4,1300–2000 as 5, 2000–6000 as 6, 6000 and more as 7.The grading of temperature and the mean annual pre-cipitation has been done for the major biomes wherethese are found (Holdridge, 1967). For example, avalue ofα = 3122 for environmental index will rep-

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Table 1Life-form classification (modified afterRaunkiaer (1937))

Life form Description

Phanerophyte Perennating buds well above ground surfaceMegaphanerophyte A Perennating buds above 30 m highMesophanerophyte B Perennating buds between 8 and 30 m in heightMicophanerophyte C Perennating buds between 2 and 8 m in heightNanophanerophyte D Perennating buds under 2 m in height

Chamaephyte E Herbaceous or low woody plant whose buds are borne just above theground level up to 30 cm

Hemicryptophyte F Perennating buds close to the ground rather half hidden insideCryptophyte Perennating organs below soil or water surfaceGeophyte G Perennating buds situated undergroundHelophyte H Marsh plants with perennating buds or organs in the water logged mudHydrophyte I Perennating buds beneath the waterTherophyte J Survival in unfavourable season through seeds or spores

Table 2Life-form spectrum index for Sites A and B based onTable 1

Community Number of species % Distribution of the species among the life form Total

A B C D E F G H I J

Reference communitya 400 1 3 6 17 20 9 27 3 1 13 100Site A 20 0 25 10 65 0 0 0 0 0 0 100Site B 48 2.08 33.33 29.16 35.42 0 0 0 0 0 0 100

a Life-form spectrum described byRaunkiaer (1937).

resent a region located between 45◦ and 60◦ latitudewith an altitude of<700 m above the mean sea level,a temperature ranging from 0 to 15◦C and precipita-tion in the range 100–400 mm.

3.2. Life-form spectrum (β)

Plants are classified taxonomically into families,genera, species, etc. However, this is not the only wayto classify plants. In an ecosystem, the plant speciescan be grouped in life-form classes based on the sim-ilarities in their structure and functioning. When thelife-forms of all species are listed for a community, itcan be represented in the form of a spectrum. The sim-plest and the most effective form of biological spec-trum is the one proposed byRaunkiaer (1937). Theclassification is based on the relative position of thereproductive organ of the plant from the ground asshown inTable 1. As an example, the biological spec-trum of Site A (Appendix A) is represented inTable 2.The left side of the spectrum is of the higher plants

with greater size and biomass and the right side is ofthe plants with smaller size and less biomass. To reacha numerical figure about the life-forms, we proposethat the spectrum be divided recursively into two partsas shown inFig. 1 and then estimate the weightedcounts of life-forms on either side of the spectrum.

Fig. 1. Distribution of weights to the life forms in the biologicalspectrum.

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The weights are different depending on the levelof recursion. The species to the left of the spectrumwhich are larger in size and have a major impact on theecosystem processes have been given a higher weigh-tage, while the species which are to the right side ofthe spectrum have been given the lower weightage asthey are small and do not influence the ecosystem pro-cesses to a great extent. So if the proportion of thespecies in the population is crowded in the left sideof the spectrum, then the index will have higher valuewhile the index value will be lower if the proportion ofthe species is more towards the right side of the spec-trum, the value will be intermediate if the species arelocated at the middle of the spectrum. The weights ofspecies belonging to the groups A/B, B/C, C/D, D/E,F/G, G/H, I/J may be expressed as:

α1α2α4(AB) + α1α2(BC) + α1α5(CD) + α1(DE)

+ α3α6(FG) + α3(GH) + α7(HI) + (IJ)

where species belonging to the group ABCDE is givenα1 times weight compared to that belonging to FGHIJ.Similarly, species belonging to ABC and FGH aregiven weightsα2 andα3 times the weight of the speciesbelonging to CDE and HIJ, respectively. And AB, CD,FG and HI are givenα4, α5, α6 andα7 times weightcompared to BC, DE, GH and IJ, respectively.

The life-form spectrum index is expressed as:

β =α1α2α4(AB)+α1α2(BC)+α1α5(CD)+α1(DE)

+ α3α6(FG) + α3(GH) + α7(HI) + (IJ)

100

where (AB), (BC), etc. represent percentage of speciesbelonging to A and B, B and C,. . . , respectively.

The values obtained are in the range of 1–75 (evenif 100% of the species belong to group A, the indexwill be 75). The higher the value of the index, themore will be the height and biomass of the majorityof the species (as shown in theSection 4.2).

For example, the life-form index based on the valuesin Table 2is calculated as:

β = (25× 50) + (10× 15) + (65× 10)

100

= 2050

100= 20.5

For the sake of illustration we have assignedα1, α2,α3, α4, the values 10, 5, 5 and 1.5, respectively, as the

organisms to the left of the spectrum due to their largesize has a greater influence on the ecosystem. The val-ues ofα5, α6 andα7 are equal to that ofα4. Since, thespecies belonging to ABCDE are about 10–15 timesthe size of the species belonging to FGHIJ, so thevalue ofα1 is assumed to be 10. Similarly, the size ofthe species to the left of the spectrum in the next levelof recursion is 4–7 times the size of the species to theright and hence the values ofα2 andα3 have been as-sumed to be 5. In the next level, the value of the leftside of the spectrum is 1–2 times and so the values ofα4, α5, α6 andα7 are assumed to be 1.5. The valueof α1, α2, α3, α4, α5, α6 andα7 needs to be standard-ized for universal applicability. This index obviouslyhas the monotonicity property and reflects abundanceof species in terms of space occupied.

3.3. Distribution of the species (γ)

Distribution of species is also one of the impor-tant aspects of diversity. This aspect of diversity hasbeen represented for the first time by Simpson’s in-dex of diversity (Simpson, 1949) and improved byShannon–Wiener index based on information theory(Shannon and Weaver, 1963; Hamming, 1980). Weare using the Shannon–Wiener index to represent dis-tribution of species because it accounts for the oc-currence of rarer species, which is considered to beimportant in many ecosystems (Lyons and Schwartz,2001). The decrease in the evenness of the speciesabundance also results in a decrease in diversity (Lin,1996). The importance of rarer species is seen to bemuch more in the Shannon–Wiener index than in theSimpson’s index as illustrated inTable 3. The diver-sity of an ecosystem is calculated using the conceptof entropy in Shannon–Weiner index. Entropy denotesthe amount of uncertainty, surprise, or information thesystem contains. It says that higher the similarity ofthe components in an assemblage, the more the lossof information from the system.

The diversity of the species and their distribution(evenness) is taken into consideration in Shannon–Wiener index. This index is represented as:

H ′ = −s∑

i=1

(pi ln pi)

wherepi is the proportion of the total sample belong-ing to theith species, 1≤ i ≤ s.

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Table 3Comparison of Shannon–Wiener index of diversity and Simpson’s index of dominance showing the percentage contribution of the speciesto the indices

Species Density pi Shannon–Weiner (−pi ln pi) % Contribution Simpson (pi2) % Contribution

1 1690 0.383 0.36756 27.5 0.14200 49.002 1270 0.288 0.3585 26.9 0.08300 27.703 1150 0.261 0.35051 26.3 0.06800 22.704 130 0.029 0.10388 7.8 0.00086 0.295 70 0.016 0.06576 4.9 0.00025 0.086 100 0.023 0.08586 6.4 0.00051 0.17

Total 4410 H ′ = − ∑pi ln pi = 1.33208

∑ = 0.29

We have takenH′ as γ in our vector.

This index has the monotonicity property and ac-counts for abundance and rarity of species. For the ex-ample inTable 3, the Shannon–Wiener index is 1.332.

A much more realistic and informative index of dis-tribution of species in a community and the ecosystemis the hierarchical diversity proposed byPielou (1975).The index to some extent, reflect the taxonomic vari-ability among the species in the community. The hier-archical diversity of Pielou is a generalization basedon Shannon–Wiener index wherein he has basicallyadded up the negantropy of the different levels in thetaxonomic hierarchy. This index although much moreinformative than the Shannon–Wiener index, is sel-dom used because of the difficulty in its calculationand for the fact that it cannot account for the specieswhich has not been classified. If the taxonomic classi-fication of the species is not known, the calculation ofthe hierarchical diversity is not possible. Further, thehierarchical diversity accounts for the hierarchy justup to the family level, the other levels are not consid-ered and it is quite cumbersome to calculate the indexbeyond a few levels. In our paper, we have not consid-ered the hierarchical diversity as it is partly covered inthe taxonomic distance index of our scheme. Althoughthe hierarchical diversity does give some informationof the taxonomic variability, but it does not give anyinformation of the taxonomic spectrum of the speciesin the community.

3.4. Taxonomic distance (δ)

In nature any two species may be taxonomicallyclose to (related to) each other or far from eachother. In an ecosystem, the taxonomic variety of the

species present in the communities should also bereflected in the diversity. A community consisting ofthe species of the same or related family or order issupposed to have a lower diversity than a communityhaving the same number of species but of differentfamilies or orders. To reflect this variation in theecosystems, we are proposing the taxonomic distanceamong the species as a component of the eco-diversityvector.

Living organisms may be divided into kingdom,phylum, class, sub-class, order, family, genus andspecies mainly based on the natural system of classifi-cation (Bentham and Hooker, 1862–1883). However,certain other key characteristics of plants may be usedfor the classification. This classification is based onthe presence or absence of certain key characteristics,such as presence of seeds (Phanerogams) or absenceof seeds (Cryptogams), number of cotyledons (e.g.dicots and monocots), presence or absence of petalsin flowers (e.g. polypetalae and gamopetalae) and soon, and the evolutionary tendencies in species, thatis, how the species have evolved during the course oftime. Therefore, we have selected a system of classi-fication giving weightage to the individuals in such away that the presence of a genus of a plant with thatof a genus of an animal in an ecosystem will showmuch more diversity than two genera of the samefamily. The fourth component of the eco-diversityvector is the average taxonomic distance among thespecies. Taxonomic distance also reflects the phyloge-netic distance among the species as the classificationsystem of plants also includes certain evolutionarytendencies of the species. Although this distance isnot absolute and is constantly changing with the evo-

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Fig. 2. Taxonomic tree showing the taxonomic distances.

lution in the taxonomic advances, but till date this isthe most useful way to estimate the taxonomic dis-tance among the species. To estimate the taxonomicdistance, we have constructed a taxonomic tree asshown inFig. 2with each branch assigned a distance.The taxonomic distance between any two species isthe sum of vertical lines crossed in reaching a speciesfrom the other in the taxonomic tree, the numberof horizontal lines crossed are not counted (see alsoFig. 3).

We make a matrix of the distances among thespecies using this distance. For illustrative purpose,Fig. 2shows a taxonomic tree containing five species,

Fig. 3. The steps in the taxonomic tree.

x1, x2, x3, x4, x5. The taxonomic distance matrix forthis example is:

0

4 0

10 10 0

10 4 4 0

14 14 14 14 0

Using the distance matrix, we calculate the averagetaxonomic distance as following. LetP denote the setof species present in the ecosystem. For eachi ∈ P,

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Table 4Calculation of average taxonomic distance (δ)

Species Si

1 6.42 6.43 7.64 7.65 11.2

Average taxonomic distance (δ) 7.84

we define:

Si =∑j∈P

|xi − xj|,

where |xi − xj| represents the distance of speciesifrom that ofj in the taxonomic tree.

Average taxonomic distance(δ) =∑

i∈P Si

|P | ,

where |P| represents the number of species.For the above example, the average taxonomic dis-

tance is 7.84 (Table 4).The taxonomic index (δ) takes account of the

species difference, satisfies the monotonicity property,that is,δ (x1, x2, . . . , xi) ≤ δ (x1, x2, . . . , xi + 1) forall values ofi. We demonstrate this throughTable 5andFig. 4 based on field data for Site A.

3.5. Functional index (η)

The ecosystem functioning is one of the importantdeterminants of the biodiversity in a region. There-fore, the fifth component of the vector is used as theecosystem functional index. We have taken the pro-

Table 5Average taxonomic distance (δ) with increase in the number ofspecies in the ecosystem showing monotonicity (the species in thesmaller set are included in the larger set)

Species included δ

1–2 2.01–3 7.111–4 9.01–5 9.281–10 10.21–15 10.391–20 10.415

Fig. 4. Relation between the taxonomic distance and the numberof species showing monotonicity.

ductivity, decomposition and N-mineralization as thethree functional parameters to calculate the functionalindex. Productivity is the rate of synthesis of organicmatter in a given area per unit time (generally ex-pressed as Mg ha−1 year−1) which reflects the poten-tial of species or a community to capture the resources.The resource capture efficiency of a species dependson the intrinsic characteristics of the species and theenvironmental factors such as temperature, precipita-tion, etc. Decomposition (the percent weight loss oflitter per unit time) gives an idea about the rate of or-ganic matter and nutrients incorporated into the soilby the action of microorganisms. This is a reflectionof the nutrient turnover capacity of the ecosystem.N-mineralization is the process by which the nitrogenpresent in the organic matter gets converted to avail-able form by microbial action which can be taken upby the plants. These ecosystem processes provide afair idea about the fertility of the ecosystem.

We have graded the productivity, decompositionand N-mineralization. The productivity (expressed asMg ha−1 year−1) are graded into six categories: lessthan 5 as 1, 5–10 as 2, 10–15 as 3, 15–20 as 4,20–25 as 5 and 25 and above as 6. The decomposi-tion (expressed as percentage weight loss) is gradedinto five categories: 10 and less as 1, 10–40 as 2,40–80 as 3, 80–150 as 4 and 150 and above as 5. TheN-mineralization (expressed as mg kg−1 month−1) is

508 A. Roy et al. / Ecological Modelling 179 (2004) 499–513

graded into five categories: 10 and less as 1, 10–20as 2, 20–30 as 3, 30–40 as 4 and 40 and above as 5.For example, a value of 322 implies that the ecosys-tem has a productivity of 10–15 as Mg ha−1 year−1, adecomposition rate of 10–40%, and N-mineralizationrate of 10–20 mg kg−1 month−1. An ecosystem withthis value can be assumed to be a grassland ecosystem.

4. Ecosystem diversity vector examples

For illustrating formulation of the diversity vector,we have taken field data from the ecological studiesof the Ecological Research Group at the Departmentof Botany, Banaras Hindu University, India. The field

Table 6Environmental component of the vector showing the range of latitude, altitude, temperature and precipitation for Sites A and B

Site Latitude Altitude Temperature Precipitation

1 2 3 4 5 1 2 3 4 1 2 3 4 5 1 2 3 4 5 6 7

A 1 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1 0 0 0B 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 1 0

Table 7Taxonomic distance matrix for Site A

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Totaldistance

1 0 4 14 14 14 14 4 14 14 14 4 4 14 4 14 14 14 14 14 142 4 0 14 14 14 14 4 14 14 14 4 4 14 4 14 14 14 14 14 143 14 14 0 12 12 12 14 12 10 12 14 14 12 14 12 12 12 12 12 124 14 14 12 0 4 4 14 10 12 10 14 14 10 14 10 10 4 10 4 85 14 14 12 4 0 2 14 10 12 10 14 14 10 14 10 10 4 10 4 86 14 14 12 4 2 0 14 10 12 10 14 14 10 14 10 10 4 10 4 87 4 4 14 14 14 14 0 14 14 14 4 4 14 4 14 14 14 14 14 148 14 14 12 10 10 10 14 0 12 4 14 14 6 14 10 10 10 10 10 109 14 14 12 10 12 12 14 12 0 12 14 14 12 14 12 12 12 12 12 12

10 14 14 12 10 10 10 14 4 12 0 14 14 6 14 10 10 10 10 10 1011 4 4 14 14 14 14 4 14 14 14 0 4 14 4 14 14 14 14 14 1412 4 4 14 14 14 14 4 14 14 14 4 0 14 4 14 14 14 14 14 1413 14 14 12 10 10 10 14 6 10 6 14 14 0 14 12 12 10 10 10 1014 4 4 14 14 14 14 4 14 14 14 4 4 14 0 14 14 14 14 14 1415 14 14 12 10 10 10 14 10 10 10 14 14 10 14 0 2 10 4 10 1016 14 14 12 10 10 10 14 10 10 10 14 14 10 14 2 0 10 4 10 1017 14 14 12 4 4 4 14 10 10 10 14 14 10 14 10 10 0 10 4 818 14 14 12 10 10 10 14 10 10 10 14 14 10 14 4 4 10 0 10 1019 14 14 12 4 4 4 14 10 10 10 14 14 10 14 10 10 4 10 0 820 14 14 12 8 8 8 14 10 10 10 14 14 10 14 10 10 8 10 8 0

I.D. 10.8 10.8 12 9.5 9.5 9.5 10.8 10.4 11.2 10.4 10.8 10.8 10.5 10.8 10.3 10.3 9.6 10.3 9.6 10.4 10.415

The numbers 1–20 are the individual species mentioned inAppendix A. I.D. represents the average individual distance.

data are from two places in the Indian subcontinent,which are relatively diverse. One set of field data isfrom the Bamboo-savanna ecosystem in central India(Site A) (Tripathi, 1991; Tripathi and Singh, 1996).The second data set is from the Sal forest ecosystemin the Nepal Himalayas (Site B) (Mandal, 1999; Singhet al., 2001).

4.1. Environmental index (α)

The environmental index for the two sites (Table 6)are:

• α for Site A – (1, 1, 4, 4)• α for Site B – (2, 2, 3, 6)

A. Roy et al. / Ecological Modelling 179 (2004) 499–513 509

4.2. Life-form index (β)

Life-form index (β) calculated as described inSection 3.2for the two sites (Table 2):

Table 8Taxonomic distance matrix for Site B

The numbers 1–48 are the individual species mentioned inAppendix A (Site B). I.D. is the average individual distance.

β for Site A = (25× 50) + (10× 15) + (65× 10)

100

=2050

100= 20.5

510 A. Roy et al. / Ecological Modelling 179 (2004) 499–513

Table 9Functional component of the vector showing the range of productivity, decomposition and N-mineralization for Sites A and B

Site Productivity Decomposition N-mineralization

1 2 3 4 5 6 1 2 3 4 5 1 2 3 4 5

A 0 0 0 1 0 0 ∗ ∗ ∗ ∗ ∗ 0 0 1 0 0B 0 0 0 0 1 0 ∗ ∗ ∗ ∗ ∗ 0 1 0 0 0

∗ Indicates data not available.

β forSite B=(75× 2.08) + (33.33× 50)

+ (29.16× 15) + (35.42× 10)

100

= 2614.1

100= 26.14

4.3. Distribution of species (γ)

• γ for Site A= 1.5• γ for Site B= 2.08

4.4. Taxonomic index (δ)

Individual distances among the species for the twosites are calculated (Tables 7 and 8) using distance treeand we make the distance matrix based on the tree asdescribed inSection 3.4. The average distance is takenas the taxonomic index. Taxonomic index (δ) of SiteA is 10.415 and Site B is 11.14.

4.5. Functional index (η)

The functional component is found from the avail-able field data of the two sites (Singh et al., 2001;Tripathi, 1991) (Table 9):

• η for Site A – [4,∗, 3]• η for Site B – [5,∗, 2]

The value ‘∗’ indicates that the particular value ofthe parameter is not available.

Hence, the diversity vector of the two ecosystemsare as follows:

• Site A [[1144], [4∗3], 20.5, 1.5, 10.41]• Site B [[2236], [5∗2], 26.1, 2.1, 11.14]

According to the proposed scheme, the vector rep-resenting [[1144], [4∗3], 20.5, 1.5, 10.41] for SiteA describes that the region is situated at a latitude

between 0◦ and 25◦, at an altitude of<700 m abovethe mean sea level, having a mean annual temper-ature between 25 and 35◦C, and precipitation be-tween 750 and 1300 mm, productivity between 15and 20 t ha−1 year−1, N-mineralization between 20and 30 mg kg−1 month−1, life-form spectrum index20.5, distribution of species index 1.5 and averagephylogenetic distance of the species present 10.41.

5. Conclusion and discussion

Ecosystem diversity vector is proposed taking intoconsideration the major ecological aspects to formu-late concise numerical indices for describing the inter-and intra-ecosystem variability. This vector capturesquantitatively the structural, functional and compo-sitional attributes of an ecosystem and provides ascheme for quantitative and qualitative comparisonof ecosystems’ diversity. It has been shown that thebiological components of the proposed vector cap-ture monotonicity property, difference and speciesabundance. This scheme can be helpful in creatingunifying eco-diversity information and to create auniform database of the global diversity irrespectiveof the ecosystem or the type of vegetation present.

The eco-diversity vector has been developed to fa-cilitate the mathematical modeling of the diversitychanges due to anthropogenic activities and globalchange. Mathematical modeling requires a numeri-cal value of the diversity, which should also possessmonotonicity so that any changes in the diversity maybe accessed by the model. The presently used in-dices of the diversity are not adequate in capturingthe structural information in a system. The proposedeco-diversity vector is a more extensive indicator ofthe ecological diversity. It is not possible to model bio-diversity in a succession (Roy et al., 2002) with thecurrently used indices. For example, when the type

A. Roy et al. / Ecological Modelling 179 (2004) 499–513 511

Table 10Changes in the various components of eco-diversity vector due to various types of environmental changes

Vector components Ecological succession(grassland to forest)

Land-use change(forest to savanna)

Global change(nitrogen loading)

Environmental index (α)Latitude (A) Constant Constant ConstantAltitude (B) Constant Constant ConstantTemperature (C) Constant Increase ConstantPrecipitation (D) Constant Decrease (?) Constant

Life-form index (β) Increase Decrease Decrease (?)Distribution of species (γ) Increase Decrease Decrease (?)Taxonomic index (δ) Increase Decrease Decrease

Functional index (η)Productivity (X) Increase Decrease IncreaseDecomposition (Y) Increase Decrease IncreaseN-mineralization (Z) Increase Decrease Decrease

? – needs further investigation.

of community changes, for example, from grasslandto forest, or vice versa due to land-use change (Salaet al., 2000), all aspects of the ecological diversitycannot be captured by the existing indices.Table 10illustrates the changes in the eco-diversity vector inan ecosystem undergoing progressive or retrogressivesuccessional changes. We further believe that the tem-poral variation in the biodiversity especially with re-spect to mass extinction can also be captured by theproposed eco-diversity vector. The change will be re-flected through a sudden drop in taxonomic distanceassociated with abrupt changes in the environmentalindex in the vector.

The limitations of our proposed eco-diversity vectorare

(i) The environmental and functional vector compo-nents describe a range.

(ii) From the life-form index, we cannot reconstructan approximate distribution of the life-formmembers.

(iii) Animal kingdom has been ignored. However, thelife-form and taxonomic indices can be extendedto include the diversity of the animals.

Acknowledgements

The first and the second authors acknowledge thefinancial help received from the Council of Scientificand Industrial Research, New Delhi, India.

Appendix A. List of species present on twocontrasting ecosystems

Site A (numbers 1–20 represent the species againstwhich they are mentioned)

Eragrostriella bifaria 1Heteropogon contortus 2Borreria hispida 3Zornia gibbosa 4Cassia pumila 5Cassia tora 6Anthroxon hispidus 7Corchorus aestuans 8Rungia repens 9Triumfetta neglecta 10Bracharia deflexa 11Setaria glauca 12Melachia sp. 13Dendrocalamus strictus 14Zyziphus glaberrima 15Zyziphus cenopilia 16Acacia catechu 17Ventilago calyculata 18Mimosa himalayana 19Lagerstroma parviflora 20

Site B (numbers 1–48 represent the species againstwhich they are mentioned)

512 A. Roy et al. / Ecological Modelling 179 (2004) 499–513

Eupatorium adenophorum 1Blumea lacera 2Hyptis suaveolens 3Scutelearia scandens 4Onychium siliculosum 5Cymbopogon microtheca 6nephrolepis cordifolia 7Borrheria latifolia 8Pogonatherum crinitum 9Sida veronicifolia 10Pteris biaurita 11Oplismenus compositus 12Pilea scripta 13Pilea umbrosa 14Adiantum caudatum 15Diciliptera cochleata 16Eragrostris tennela 17Maesa macrophylla 18Colebrookea oppsilifolia 19Clerodendrun infortunatum 20Woodfordia fruticosa 21Desmodium confortum 22Maesa chisia 23Leea edgworthii 24Boehmera platyphylla 25Myrsine semiserrata 26Murraya koenigii 27Inula cappa 28Cipadessa bassifera 29Murraya paniculate 30Xeromphis spinosa 31Shorea robusta 32Mallotus philippinensis 33Croton oblongifolius 34Careya aborea 35Schima wallichii 36Lagrustroemia parviflora 37Adina cordifolia 38Cassia fistula 39Castanopsis indica 40Callicarpa arbora 41Dulbargia latifolia 42Emblica officinalis 43Litsea monoptales 44Syzygium cumini 45Terminilia alata 46Ficus hispida 47Ficus semicarpae 48

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