# Beta diversity

The term beta diversity (β-diversity) was introduced by R. H. Whittaker[1] together with the terms alpha diversity (α-diversity) and gamma diversity (γ-diversity). The idea was that the total species diversity in a landscape (γ) is determined by two different things, the mean species diversity at the habitat level (α) and the differentiation among habitats (β). Whittaker proposed several ways of quantifying differentiation, and subsequent generations of ecologists have invented more. As a result, the definition of beta diversity has become quite contentious.[2][3] Some use beta diversity as a broad umbrella term that can refer to any of several indices related to compositional heterogeneity.[4][5][6] Others argue that such broad usage should be avoided because it leads to confusion. Instead, they propose that the term beta diversity be used to refer to one phenomenon only (true beta diversity), and that other things be referred to by other names.[2][3][7][8][9][10]

## Beta diversity in the strict sense (True beta diversity)

Gamma diversity and alpha diversity can be calculated directly from species inventory data.[2][11] The simplest of Whittaker's original definitions of beta diversity is

β = γ/α

Here gamma diversity is the total species diversity of a landscape, and alpha diversity is the mean species diversity per habitat. Because the limits among habitats and landscapes are diffuse and to some degree subjective, it has been proposed that gamma diversity can be quantified for any inventory dataset, and that alpha and beta diversity can be quantified whenever the dataset is divided into subunits. Then gamma diversity is the total species diversity in the dataset and alpha diversity the mean species diversity per subunit. Beta diversity quantifies how many subunits there would be if the total species diversity of the dataset and the mean species diversity per subunit remained the same, but the subunits shared no species.[2][7]

## Other things the term 'beta diversity' can refer to

### Absolute species turnover

Some researchers have preferred to partition gamma diversity into additive rather than multiplicative components.[12][13] Then the beta component of diversity becomes

βA = γ - α

This quantifies how much more species diversity the entire dataset contains than an average subunit within the dataset. This can also be interpreted as the total amount of species turnover among the subunits in the dataset.[2]

When there are two subunits, and presence-absence data are used, this can be calculated with the following equation:

$\beta_A=(S_1-c)+(S_2-c)$[14]

where, S1= the total number of species recorded in the first community, S2= the total number of species recorded in the second community, and c= the number of species common to both communities.

### Whittaker's species turnover

If absolute species turnover is divided by alpha diversity, a measure is obtained that quantifies how many times the species composition changes completely among the subunits of the dataset. This measure was proposed by Whittaker,[15] so it has been called Whittaker's species turnover.[2] It is calculated as

βW = (γ - α)/α = γ/α - 1

When there are two subunits, and presence-absence data are used, this equals the one-complement of the Sørensen similarity index.[2][16]

### Proportional species turnover

If absolute species turnover is divided by gamma diversity, a measure is obtained that quantifies what proportion of the species diversity in the dataset is not contained in an average subunit.[2] It is calculated as

βP = (γ - α)/γ = 1 - α/γ

When there are two subunits, and presence-absence data are used, this measure as ranged to the interval [0, 1] equals the one-complement of the Jaccard similarity index.[2]

### Compositional dissimilarity

Traditionally beta diversity has been used as an umbrella term, and then any of the numerous available measures of compositional dissimilarity can be thought of as a measure of beta diversity.[4] Because the different indices quantify different aspects of the data, they can give very different values for the same data set, and can change in opposite ways when dataset properties are changed. The values of some indices may be comparable, whereas comparing the values of other indices can be misleading and lead to erroneous conclusions.[2]

## References

1. ^ Whittaker, R. H. (1960) Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs, 30, 279–338.
2. Tuomisto, H. (2010) A diversity of beta diversities: straightening up a concept gone awry. Part 1. Defining beta diversity as a function of alpha and gamma diversity. Ecography 33: 2–22. doi:10.1111/j.1600-0587.2009.05880.x
3. ^ a b Tuomisto, H. (2010) A diversity of beta diversities: straightening up a concept gone awry. Part 2. Quantifying beta diversity and related phenomena. Ecography, 33, 23-45. doi:10.1111/j.1600-0587.2009.06148.x
4. ^ a b Koleff, P., Gaston, K. J. and Lennon, J. J. (2003) Measuring beta diversity for presence–absence data. Journal of Animal Ecology 72, 367–382. doi: 10.1046/j.1365-2656.2003.00710.x
5. ^ Anderson, M. J. et al. (2011) Navigating the multiple meanings of β diversity: a roadmap for the practicing ecologist. Ecology Letters 14, 19–28. doi:10.1111/j.1461-0248.2010.01552.x
6. ^ Gorelick, R. (2011) Commentary: Do we have a consistent terminology for species diversity? The fallacy of true diversity. Oecologia 167, 885-888. doi:10.1007/s00442-011-2124-8
7. ^ a b Tuomisto, H. 2010. A consistent terminology for quantifying species diversity? Yes, it does exist. Oecologia 4: 853–860. doi:10.1007/s00442-010-1812-0
8. ^ Jurasinski, G. and Koch, M. (2011) Commentary: do we have a consistent terminology for species diversity? We are on the way. Oecologia, 167, 893-902. doi:10.1007/s00442-011-2126-6
9. ^ Moreno, C. E: and Rodríguez, P. (2011) Commentary: Do we have a consistent terminology for species diversity? Back to basics and toward a unifying framework. Oecologia, 167, 889-892. doi:10.1007/s00442-011-2125-7
10. ^ Tuomisto, H. (2011) Commentary: do we have a consistent terminology for species diversity? Yes, if we choose to use it. Oecologia, 167, 903-911. doi:10.1007/s00442-011-2128-4
11. ^ Jost L (2006) Entropy and diversity. Oikos 113, 363–375. doi: 10.1111/j.2006.0030-1299.14714.x
12. ^ Lande, R. (1996) Statistics and partitioning of species diversity, and similarity among multiple communities. Oikos, 76, 5-13.
13. ^ Veech, J. A. et al. (2002) The additive partitioning of species diversity: recent revival of an old idea. Oikos, 99, 3-9. doi: 10.1034/j.1600-0706.2002.990101.x
14. ^ James S. Albert; Roberto E. Reis (8 March 2011). Historical Biogeography of Neotropical Freshwater Fishes. University of California Press. p. 308. ISBN 978-0-520-26868-5. Retrieved 28 June 2011.
15. ^ Whittaker, R. H. (1972) Evolution and measurement of species diversity. Taxon, 21, 213-251.
16. ^ Sørensen, T.A. (1948) A method of establishing groups of equal amplitude in plant sociology based on similarity of species content, and its application to analyses of the vegetation on Danish commons. Kongelige Danske Videnskabernes Selskabs Biologiske Skrifter, 5, 1–34.