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The term '''gamma diversity''' (γ-diversity) was introduced by R. H. Whittaker<ref name=Whittaker1960>Whittaker, R. H. (1960) Vegetation of the Siskiyou Mountains, Oregon and California. Ecological Monographs, 30, 279–338.</ref> together with the terms alpha diversity (α-diversity) and beta diversity (β-diversity). Whittaker's idea was that the total species diversity in a landscape (γ) is determined by two different things, the mean species diversity in sites or habitats at a more local scale (α) and the differentiation among those habitats (β). According to this reasoning, alpha diversity and beta diversity constitute independent components of gamma diversity:
:<math>\gamma = \alpha \times \beta</math>

==Scale considerations==

The area or landscape of interest may be of very different sizes in different situations, and no consensus has been reached on what spatial scales are appropriate to quantify gamma diversity.<ref>Whittaker, R. J. et al. (2001). Scale and species richness: towards a general, hierarchical theory of species diversity. Journal of Biogeography 28: 453-470. {{doi|10.1046/j.1365-2699.2001.00563.x}}</ref> It has therefore been proposed that the definition of gamma diversity does not need to be tied to a specific spatial scale, but gamma diversity can be measured for an existing dataset at any scale of interest.<ref name=Tuomisto2010a>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}}</ref> If results are extrapolated beyond the actual observations, it needs to be taken into account that the species diversity in the dataset generally gives an underestimation of the species diversity in a larger area. The smaller the available sample in relation to the area of interest, the more species that actually exist in the area are not found in the sample.<ref>Colwell, R. K. and Coddington, J. A. (1994) Estimating terrestrial biodiversity through extrapolation. Philosophical Transactions: Biological Sciences, 345, 101-118.</ref><ref>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}}</ref> The degree of underestimation can be estimated from a [[species-area curve]].

==Different gamma diversity concepts==

Researchers have used different ways to define [[species diversity | diversity]], which in practice has led to different definitions of gamma diversity as well. Often researchers use the values given by one or more [[Diversity index | diversity indices]], such as [[species richness]], the [[Shannon index]] or the [[Simpson index]].<ref name=Whittaker1960 /><ref>Lande, R. (1996) Statistics and partitioning of species diversity, and similarity among multiple communities. Oikos, 76, 5-13.</ref><ref>Veech, J. A. et al. (2002) The additive partitioning of species diversity: recent revival of an old idea. Oikos, 99, 3-9.</ref> However, it has been argued that it would be better to use the effective number of species as the universal measure of species diversity. This measure allows weighting rare and abundant species in different ways, just as the diversity indices collectively do, but its meaning is intuitively easier to understand. The effective number of species is the number of equally-abundant species needed to obtain the same mean proportional species abundance as that observed in the dataset of interest (where all species may not be equally abundant).<ref name=Tuomisto2010a /><ref>Hill, M. O. (1973) Diversity and evenness: a unifying notation and its consequences. Ecology, 54, 427–432</ref><ref name=Jost2006>Jost, L. (2006) Entropy and diversity. Oikos, 113, 363–375</ref><ref>Jost, L. (2007) Partitioning diversity into independent alpha and beta components. Ecology, 88, 2427–2439.</ref><ref name=Tuomisto2010c>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}}</ref><ref>Tuomisto, H. (2011) Commentary: do we have a consistent terminology for species diversity? Yes, if we choose to use it. Oecologia, 167, 903-911.</ref>

==Calculating gamma diversity==

Suppose species diversity is equated with the effective number of species in a dataset. Then gamma diversity can be calculated by first taking the weighted mean of species proportional abundances in the dataset, and then taking the inverse of this mean. The equation is:

:<math>{}^q\!D_{\gamma}={1 \over{\sqrt[q-1]{{\sum_{i=1}^S p_i p_i^{q-1}}}}}</math>

The denominator equals mean proportional species abundance in the dataset as calculated with the weighted generalized mean with exponent ''q'' - 1. In the equation, ''S'' is the total number of species (species richness) in the dataset, and the proportional abundance of the ''i''th species is <math>p_{i}</math>.

Large values of ''q'' lead to smaller gamma diversity than small values of ''q'', because increasing ''q'' increases the weight given to those species with the highest proportional abundance, and fewer equally-abundant species are hence needed to obtain this proportional abundance.<ref name=Tuomisto2010a /><ref name=Tuomisto2010c />

==See also==

*[[Alpha diversity]]
*[[Beta diversity]]
*[[Diversity index]]
*[[Global biodiversity]]

==References==
{{reflist}}

[[Category:Measurement of biodiversity]]
[[Category:Summary statistics for categorical data]]

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