The Shannon index and the natural logarithm of the Simpson and Berger-Parker indices belong to the Renyi series for ranking a-diversity of a system. The a-diversity of system refers to the diversity within a particular area or ecosystem. If a community has higher values throughout the Renyi series, then it is considered more diverse in terms of species richness and evenness of distribution when compared to other systems with lower values throughout the series. It is useful to assess the value across the series because a single diversity index rarely provides sufficient information to rank systems in diversity.
The Shannon index has been described as an equit-ability index that takes into account both the species richness and evenness dimensions of diversity. It is the most widely used and most criticized biodiversity index. It is expressed numerically as s
beetles along an urban-rural gradient in which the Simpson index was used as the diversity index and Berger-Parker as the dominance index.
where pi is the proportion or number of individuals of species i in the total sample and s is the total number of species in the sample. High values of H indicate high species diversity. The Berger-Parker or the Simpson index are commonly used alongside the Shannon index. This index is affected by both the number of species and their equitability and should theoretically reach a maximum value when there is a high number of species that are equally abundant.
The Simpson index of dominance is also commonly used as a diversity index. It is also referred to as a dominance index and provides a very similar measure of diversity as the Berger-Parker index, and is written as
where N is the proportion or total number of individuals in a sample and n is the proportion or total number of individuals of species i in the sample. Although similar to the Berger-Parker index in what it aims to measure, this index has a more sophisticated calculation and has been more widely used than the Berger-Parker index. The larger the value of D, the greater the equitability of species throughout the sample and as D decreases the dominance of one species would be expected to increase.
The Margalef index is a species richness index that is often used to measure species richness, and is written as
where S is the total number of species and N is the total number ofindividuals in a sample. However, this does not provide information on the number of individuals per species.
The Simpson index has been shown to be more sensitive for detecting small differences between samples than the Berger-Parker index or other indices. For example, in a study comparing aquatic diversity across a polluted and nonpolluted sites, the Simpson index was the most sensitive index for discriminating small differences among sites than the Berger-Parker, the Margalef, or the Shannon indices. In some studies, Simpson index may be used as the predominant diversity index and Berger-Parker index as the dominance index. An example of this application of the two indices was an investigation of the environmental variation and associated assemblage changes of carabid
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