Chapter 2: LITERATURE REVIEW
2.2 THE NATURE AND SIGNIFICANCE OF BIODIVERSITY
2.2.5 Indices of diversity
Information on diversity is often reduced by researchers into discrete, numerical measurements such as diversity indices (Kirk et al., 2004), in order to describe the diversity, irrespective of how it was determined (Pankhurst, 1997). Biodiversity is a function of two components, namely: (i) the total number of species present (i.e.
species richness or abundance); and (ii) the distribution of individuals among the species (i.e. species evenness or equitability) (Bohannan and Hughes, 2003; Kirk et al., 2004). In consequence, many attempts have been made to devise a single numerical index that measures both these properties (Gotelli and Graves, 1996), However, any given diversity index is a single value, which cannot indicate the total composition of a community (Bohannan and Hughes, 2003). A major problem is that since both richness and evenness play a role in determining the index value, different
communities can have the same index. Therefore, richness, evenness and diversity values should all be calculated when assessing community structure (Pankhurst, 1997;
Bohannan and Hughes, 2003). A further aspect of community diversity is the genetic relatedness of the operational taxonomic units (OTUs) present (Bohannan and Hughes, 2003). Accurate assessment of the level and patterns of genetic diversity is essential (Mohammadi and Prasanna, 2003). Several approaches to compare microbial diversity at the molecular level have been used, including parametric estimation, nonparametric estimation and community phylogenetics (Bohannan and Hughes, 2003).
2.2.5.1 Species richness
The easiest and simplest diversity index to interpret is species richness, as measured by a direct count of species. These counts are influenced by a combination of species richness, the total number of individuals counted and the size of the area sampled.
Therefore, unless communities are exhaustively and identically sampled, comparison of simple species counts is not appropriate. For comparing communities of different sizes, algorithmic rarefaction of large samples that subsequently can be compared with smaller samples, is one solution to the problem. However, rarefaction can only be used for interpolation to a smaller sample size and not for extrapolation to a larger sample size (Gotelli and Graves, 1996). As an alternative, numerous species- individuals relationships have provided bases for richness indices, such as the logarithmic relationship suggested by Margalef in 1958:
R 1 = (S – 1)/Log N ………..Equation 1
where S is the number of species and N is the total number of organisms (Pielou, 1977).
2.2.5.2 Species evenness
As diversity depends on both the number of species in a community and the evenness of their representation, it is sometimes necessary to treat the two components
separately (Pielou, 1977). To calculate evenness, the most frequent approach is to scale a heterogeneity measure relative to its maximum possible value when both sample size and species number are fixed. These two formulations for large samples are:
Evenness = (D – Dmin) / (D max – Dmin)………...Equation 2
Evenness = D/Dmax ……….Equation 3
where D is a heterogeneity value for the sampled population and Dmin and Dmax are the minimum and maximum values possible for the given species number and sample size (Peet, 1974).
2.2.5.3 Species diversity
Many indices have been developed, which are favoured by ecologists for measuring diversity (Pielou, 1977). To measure heterogeneity (dual concept diversity), two contributing components are required, the number of species, and the distribution of individuals among the species, or equitability (Peet, 1974). The first heterogeneity index used in ecology was that of Simpson (Pielou, 1977). This index measures the probability that two individuals, randomly selected from a sample, will belong to the same species. For an infinite sample the index is:
∑
== S
i
p i 1
λ 2 ……….Equation 4
For a finite sample the index is:
L = ∑ [ni (ni – 1)]/[N (N – 1)] ……….Equation 5 where pi is the proportion of individuals in species i, s is the number of species (species richness), ni the number of individuals in species i, and N the total sample size. As originally formulated, Simpson’s index varies inversely with heterogeneity (Peet, 1974). The Simpson index and the Shannon index are closely related but unlike
the Shannon index described below the former cannot be adapted for measuring hierarchical diversity (Pielou, 1977).
The Shannon diversity index is the most commonly used index for measuring species diversity or heterogeneity, with the most popular of the heterogeneity indices being those based on information theory, such as:
The Shannon-Wiener index:
H' = –∑pi ln (pi) ………Equation 6
where pi is the relative abundance of the ith species, (∑ pi = 1.0) (Gotelli and Graves, 1996).
The Shannon-Weaver index:
H' = -
∑
= S
i 1
i ilogp
p ………...Equation 7
where pi is the relative abundance of each species, calculated as the proportion of individuals of a given species, to the total number of individuals in the community, and s is the number of species (species richness) (Peet, 1974).
The Shannon-Weaver index (H') is often used, in the form:
H' = – ∑ (ni /N) log (ni /N)
= – ∑ pi (log pi) ………Equation 8 where ni is the importance value for each species, N is the total of importance values and pi is the importance probability for each species (ni/N). Thus H' takes into account both the ‘richness’ and ‘evenness’ component of diversity (Lynch et al., 2004).
However both these indices have their limitations, which include serious conceptual and statistical problems (Gotelli and Graves, 1996; Kennedy and Gewin, 1997;
Pankhurst, 1997).
The application of information theory to diversity measurement suggests that heterogeneity (or a combination of richness and equitability) can be equated with the amount of uncertainty regarding the species of an individual selected at random from a population. The more species there are and the more even their distribution, the greater the diversity (Peet, 1974; Pielou, 1977).
An alternative approach to conventional statistical methods for environmental studies is the use of artificial neural networks (ANNs) (Dollhopf et al., 2001; Kim et al., 2008). Two different ANN algorithms which are useful in ecological informatics are self-organizing maps (SOMs) and multilayer perceptrons (MLPs). These were used successfully to model convective flows and the associated oxygen transport in a wetland pond. These models were able to ‘learn’ the mechanism of convective transport, resulting in an ability to forecast oxygen saturation near the bottom of the wetland bed (Schramm et al., 2003). In a different study, SOMs and MLPs were efficient at revealing community associations and environmental effects in an inter- taxa study of microbes and benthic macroinvertebrates subjected to different pollution levels in a stream (Kim et al., 2008).