The representation of diversity

Biological diversity is a multifaceted concept that cannot be expressed by a single number.

Considering solely the community level diversity (α-diversity) that exists within a particular locality, this represents a function of both the number of taxa (richness) and the comparative abundances of those taxa (evenness), and it can thus be characterised in many different ways.

Therefore the choice of diversity index is an important issue that can complicate comparisons between studies. To enable greater insight the use of multiple indices, each of which emphasise different aspects of diversity, may be beneficial.

Three of the most commonly used indices of diversity are the Shannon Index, the Simpson Index, and Fisher’s α. The Shannon Index is derived from information theory (Shannon, 1948).

Properly known as Shannon entropy (Jost, 2006), it quantifies the uncertainty in predicting the species identity of an individual picked at random from the sample:

∑

where pi is the proportion of stems belonging to species i. The simplest form of the Simpson Index (Simpson, 1949) is Simpson’s concentration. This measures the inverse of diversity and can be represented biologically as the probability that two individuals, randomly drawn with replacement from an infinitely large community, belong to the same species (Magurran, 2004):

∑

Both the Shannon and Simpson Indices make use of species abundance data. For the Simpson Index, the proportional species abundances are squared; this reflects species dominance. Thus the Simpson Index provides a representation of diversity that is more strongly influenced by evenness than by richness.

Fisher’s α is a parametric index derived from the log series distribution (Fisher et al., 1943), which is widely used to explore the diversity of tropical forests (Parmentier et al., 2007; Ter Steege et al., 2003). According to the log series distribution, species abundances are represented by:

where each term represents the number of species that are predicted to have 1,2,3,...n individuals within the sample. To calculate Fisher’s α, only the sample size and species richness are required, which means it can be used widely where abundance data is not available. When n > 1000, α is independent of sample size (Magurran, 2004).

3.2.2.1 Comparing richness and evenness using ‘effective number of species’ indices A frequently encountered problem with the representation of diversity is the difficulty in making comparisons between different indices. Indices follow many different forms, some taking values between 0 and 1, others values between 0 and infinity. The concept of ‘effective number of species’ (Macarthur, 1965) is recommended by Jost (2006) as a means to compare the values of multiple indices. If there are 20 species of equal abundance, any index of

‘effective number of species’ will give a value of 20. If species do not have equal abundance, the value given by different ‘effective number of species’ indices will diverge, but will all represent an equivalent diversity to a certain number of species of equal abundance. For example, a value of 20 obtained using a given diversity index could denote 20 species of equal

abundance, 25 species of marginally unequal abundance, or 50 species of highly unequal abundance. Modified forms of the well-known Shannon and Simpson indices can be used to represent effective number of species (Jost, 2006): these modified forms are exponential Shannon entropy (exp(H’)) and Simpson’s Reciprocal Index of diversity (1/λ), and will henceforth be referred to simply as Shannon diversity and Simpson diversity. Species richness is another example of an effective number of species index.

The key differentiator among the different indices of ‘effective number of species’ is the relative weight they give to rare versus dominant species, as formalised by Hill (1973). Indices corresponding to Hill numbers ⁰D (diversity of order 0), ¹D (diversity of order 1) and ²D (diversity of order 2) are the most widely used, and range from giving greater emphasis to rare species, to giving greater emphasis to dominant species. These Hill numbers refer, respectively, to species richness (⁰D), Shannon diversity (¹D), and Simpson diversity (²D).

With species richness (⁰D), each species contributes equally to the richness value, with no regard to the abundance of the species in question. Therefore, stems belonging to rare species are given relatively greater weighting than stems belonging to common species. With Shannon diversity (¹D), the contribution of each species to the diversity index value is directly proportionate to its abundance. With Simpson diversity (²D), dominant species provide a greater contribution than rare species, in proportion to their abundance, to the diversity index value. The use of this framework thus allows direct comparisons to be made of the effects of rare versus dominant taxa.

3.2.2.2 Comparing diversity across different levels of taxonomic classification

If phenotypic change takes place at a roughly constant rate, then there will likely be a correlation between evolutionary divergence times and the total functional differences between species (Cadotte et al., 2009). This represents an important argument for interest in phylogenetic relatedness and diversity. The most accurate representations of these aspects of diversity involve the construction of phylogenies and usage of explicit measures of phylogenetic diversity. However, higher taxon diversity can also be used to incorporate a degree of phylogenetic information in diversity metrics. The precise relatedness of higher taxa can be highly variable, in terms of time since lineage splitting (Harper and Hawksworth, 1995).

Nevertheless, the use of taxonomic classifications can provide results that are apparently robust (King, 2009; Petchey and Gaston, 2006). Identification of trees to genus and family level can also provide useful information in the case of individuals that cannot be identified to species level.