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| − | * '''Menhinick’s diversity index''':
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| − | DMn =
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| − | Where N = the total number of individuals in the sample and S = the number of species recorded.
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| − | Despite the attempt to correct for sample size, both measures remain strongly influenced by sampling effort. Nonetheless they are intuitively meaningful indices and can play a useful role in investigations of biological diversity.
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| − | ===2. Heterogeneity measures===
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| − | Heterogeneity measures are those that combine the richness and the evenness component of diversity. Heterogeneity measures fall into two categories: parametric indices, which are based on a parameter of a species abundance model, and nonparametric indices, that make no assumptions about the underlying distributions of species abundances.
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| − | ====Parametric indices====
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| − | * '''The log series index ''' (Fisher et al., 1943)(see also log-series distributions 1.2.4.3) is a parameter of the log series model. The parameter is independent of sample size. describes the way in which the individuals are divided among the species, which is a measure of diversity. The attractive properties of this diversity index are: it provides a good discrimination between sites, it is not very sensitive to density fluctuations and it is normally distributed, in this way confidence limits can be attached to .
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| − | The log series takes the form:
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| − | x is the number of species to have one individual, x²/2 those with two individuals, and so on. Since 0<x<1, and and x are presumed to be constant, the expected number of species will be the highest in the first abundance class. x is calculated interatively from:
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| − | And can be calculated from the equation:
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| − | ====Non-parametric indices====
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| − | The first two indices are based on information theory. These indices are based on the rationale that the diversity in a natural system can be measured in a similar way to the information contained in a code or message.
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| − | * The most widely used diversity index in the ecological literature is the '''Shannon-Wiener diversity index'''. It assumed that individuals are randomly sampled from an infinitely large community, and that all species are represented in the sample. The Shannon index is calculated from the equation:
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| − | H’ = -
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| − | pi is the proportion of individuals found in the ith species.
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| − | * Where the randomness cannot be guaranteed, for example when certain species are preferentially sampled, the '''Brillouin index''' is the appropriated form of the information index. It is calculated as follows:
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| − | H =
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| − | * In which = N1.N2…Ni and Ni = the number of individuals in species i and N is the total number of individuals in the community. One of the best known and earliest evenness measures is the '''Simpson ’s index''' which is given by:
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| − | pi is the proportion of individuals found in the ith species
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| − | This index is used for large, sampled communities. Simpson’s index expresses the probability that any two individuals drawn at random from an infinitely large community belong to the same species.
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| − | * '''The Hill numbers''' (Hill, 1973)show the relation between the species-richness indices and the evenness-indices. Hill defined a set of diversity number of different order. The diversity number of order a is defined as:
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| − | where pi = the proportional abundance of species i in the sample and a = the order in which the index is dependent of rare species.
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| − | The most known are
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| − | H0 = S
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| − | H1 = (exponential of Shannon-Wiener diversity index)
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| − | H2 = (the reciprocal of Simpson’s )
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| − | ===3. Taxonomic indices===
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| − | If two data-sets have identical numbers of species and equivalent patterns of species abundance, but differ in the diversity of taxa to which the species belong, it seems intuitively appropriate that the most taxonomically varied data-set is the more diverse. As long as the phylogeny of the data-set of interest is reasonably well resolved, measures of taxonomic diversity are possible.
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| − | * '''Clarke and Warwick’s taxonomic distinctness index''', which describes the average taxonomic distance – simply the “path length” between two randomly chosen organisms through the phylogeny of all the species in a data-set – has different forms: . taxonomic diversity and taxonomic distinctness
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| − | * '''Taxonomic distinctness indices'''
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| − | • Taxonomic diversity (Δ) reflects the average taxonomic distance between any two organisms, chosen at random from a sample. The distance can be seen as the length of the path connecting these two organisms through a phylogenetic tree or a Linnean classification. This index includes aspects of taxonomic relatedness and evenness.
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| − | • Taxonomic distinctness (Δ*) is the average path length between two randomly chosen but taxonomically different organisms. This measure is measure of pure taxonomic relatedness.
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| − | • When only presence/absence data is considered both Δ and Δ* converge to the same statistic Δ+, which can be seen as the average taxonomic path length between any two randomly chosen species. (Clarke & Warwick, 1998).
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| − | ===4. Functional diversity===
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| − | The positive relationship between ecosystem functioning and species richness is often attributed to the greater number of functional groups found in richer assemblages. Petchey and Gaston (2002) proposed a method for quantifying functional diversity. It is based on total branch length of a dendrogram, which is constructed from species trait values. One important consideration is that only those traits linked to the ecosystem process of interest are used. Thus a study focusing on bird-mediated seed dispersal would exclude traits such as plumage color that are not related to this function, but traits such as beak size and shape should be included With standard clustering algorithms a dendrogram is then constructed. The method makes sense. For example a community with five species with different traits will have a higher functional diversity than a community of equal richness but where the species are functional similar
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A variety of objective measures have been created in order to empirically measure biodiversity. The basic idea of a diversity index is to obtain a quantitative estimate of biological variability that can be used to compare biological entities, composed of direct components, in space or in time. It is important to distinguish ‘richness’ from ‘diversity’. Diversity usually implies a measure of both species number and ‘equitability’ (or ‘evenness’). Three types of indices can be distinguished:
1. Species richness indices: Species richness is a measure for the total number of the species in a community. However, complete inventories of all species present at a certain location, is an almost unattainable goal in practical applications.
A visualization of the species richness: with respectively 5 and 10 species.
2. Evenness indices: Evenness expresses how evenly the individuals in a community are distributed among the different species.
A visualization of the evenness of 5 species.
3. Taxonomic indices: These indices take into account the taxonomic relation between different organisms in a community. Taxonomic diversity, for example, reflects the average taxonomic distance between any two organisms, chosen at random from a sample. The distance can be seen as the length of the path connecting these two organisms along the branches of a phylogenetic tree.
These three types of indices can be used on different spatial scales:
- Alpha diversity refers to diversity within a particular area, community or ecosystem, and is usually measured by counting the number of taxa within the ecosystem (usually species level)
- Beta diversity is species diversity between ecosystems; this involves comparing the number of taxa that are unique to each of the ecosystems. For example, the diversity of mangroves versus the diversity of seagrass beds.
- Gamma diversity is a measure of the overall diversity for different ecosystems within a region. For example, the diversity of the coastal region of Gazi Bay in Kenia.
Diversity measurement is based on three assumptions
1. All species are equal: this means that richness measurement makes no distinctions amongst species and threat the species that are exceptionally abundant in the same way as those that are extremely rare species. The relative abundance of species in an assemblage is the only factor that determines its importance in a diversity measure.
2. All individuals are equal: this means that there is no distinction between the largest and the smallest individual, in practice however the smallest animals can often escape for example by sampling with nets.
Taxonomic and functional diversity measures, however, do not necessarily treat all species and individuals as equal.
3. Species abundance has been recorded in using appropriate and comparable units. It is clearly unwise to use different types of abundance measure, such as the number of individuals and the biomass, in the same investigation. Diversity estimates based on different units are not directly comparable.
Diversity measures
1. Species richness indices
- Species richness S is the simplest measure of biodiversity and is simply a count of the number of different species in a given area. This measure is strongly dependent on sampling size and effort. Two species richness indices try to account for this problem:Margalef’s diversity index:
DMg =
References
