Measurements of biodiversity

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:

[math]D_{Mg} = {(S-1)\over ln N}[/math]

• Menhinick’s diversity index:

[math]D_{Mn} = {S\over\sqrt{N}}[/math]

Where N = the total number of individuals in the sample and S = the number of species recorded.

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.

2. Heterogeneity measures

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.

Parametric indices

• The log series index [math]\alpha\,[/math] (see also log-series distributions) 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 [math]\alpha\,[/math].

The log series takes the form:

[math]\alpha\,x[/math], [math]{\alpha\, x^2}\over 2[/math], [math]{\alpha\, x^3}\over 3[/math],..., [math]{\alpha\, x^n}\over n[/math]

[math]\alpha\,x[/math] is the number of species to have one individual, [math]\alpha\, x^2[/math] those with two individuals, and so on. Since 0<[math]\,x[/math]<1 and [math]\alpha\,[/math] and [math]\,x[/math] are presumed to be constant, the expected number of species will be the highest in the first abundance class. [math]\,x[/math] is calculated interatively from:

[math]{S\over N} = {(1-x)\over x}.ln{1\over (1-x)}[/math]

And [math]\alpha\,[/math] can be calculated from the equation:

[math]\alpha\, = {N(1-x)\over x}[/math]

Non-parametric indices

[math]\sqrt{2}[/math]

\sum_{k=1}^N k^2

[math]C=F\times\lambda[/math]

[math]F_D = 2F{C \over V}[/math]