Turing machine equivalents

The term beta diversity (β-diversity) was introduced by R. H. Whittaker 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. Some use beta diversity as a broad umbrella term that can refer to any of several indices related to compositional heterogeneity. 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.

Beta diversity in the strict sense (True beta diversity)

Gamma diversity and alpha diversity can be calculated directly from species inventory data. 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.

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. Then the beta component of diversity becomes

β_A = 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.

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

${\beta }_A=(S_1-c)+(S_2-c)$

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, so it has been called Whittaker's species turnover. It is calculated as

β_W = (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.

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. It is calculated as

β_P = (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.

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. 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.

See also

• Alpha diversity
• Gamma diversity
• Global biodiversity
• Diversity index

References

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