# Alpha diversity

Alpha diversity

Alpha diversity (α-diversity) is the biodiversity within a particular area, community or ecosystem, and is usually expressed as the species richness of the area.[1] This can be measured by counting the number of taxa (distinct groups of organisms) within the ecosystem (eg. families, genera, species). However, such estimates of species richness are strongly influenced by sample size, so a number of statistical techniques can be used to correct for sample size to get comparable values.

## Simpson's Diversity Index

$D=1-\frac{\sum_{i=1}^S n_i(n_i-1)}{N(N-1)}$

Where:

• S is the number of species
• N is the total number of organisms
• ni is the number of organisms of species i

## Shannon index

$H^\prime = -\sum_{i=1}^S p_i \ln p_i$

Where

• S is the number of species. Also called species richness
• 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: $n_i\over N$
• ni is the number of individuals in each species; the abundance of each species
• N is the total number of all individuals

## Fisher's Alpha

This is a parametric index of diversity that assumes that the abundance of species follows the log series distribution.

$(\alpha x),\frac{(\alpha x)^2}{2},\frac{(\alpha x)^3}{3},.....\frac{(\alpha x)^n}{n},... ,$

where each item gives the number of species predicted to have 1,2,3,....n individuals in the sample. The index is the α parameter. This is a useful index which has been widely used.

## Rarefaction

Rarefaction takes hypothetical subsamples of n organisms from the more-sampled region, and calculates the average number of species in such subsamples. This average can be compared to the number of species actually found in the less-sampled region

## Examples

Alpha diversity has been measured both in extant ecosystems and in extinct communities. It is an especially useful measure to track Earth's past biodiversity because if it is used correctly, diversity can be measured independently of the fossil record which is not complete and therefore subject to errors. Examples include:

• A study of the alpha diversity of Triassic tetrapod families found that recovery after the Permo-Triassic extinction event took 30 million years[2]
• A study on trilobites revealed that following the end-Ordovician extinction, trilobite alpha diversity was comparable to those of the Late Cambrian communities (Adrain et al. 2000)

## Other measures of diversity

Alternative ways to measure biodiversity include:[1]

• Beta diversity – species diversity between ecosystems; this involves comparing the number of taxa that are unique to each of the ecosystems
• Gamma diversity – taxonomic diversity of a region with several ecosystems
• Phylogenetic diversity – or 'Omega diversity'. The differences or diversity between taxa
• Global diversity – overall biodiversity of Earth

Diversity may not be congruent at all taxonomic levels and diversity patterns may vary depending on the type of diversity measured, as seen in the example to the left.

## References

1. ^ a b Whittaker, R.H. (1972). "Evolution and measurement of species diversity". Taxon (International Association for Plant Taxonomy (IAPT)) 21 (2/3): 213–251. doi:10.2307/1218190. JSTOR 1218190.
2. ^ Sahney, S. and Benton, M.J. (2008). "Recovery from the most profound mass extinction of all time" (PDF). Proceedings of the Royal Society: Biological 275 (1636): 759–65. doi:10.1098/rspb.2007.1370. PMC 2596898. PMID 18198148.

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