skbio.diversity.alpha.hill#
- skbio.diversity.alpha.hill(counts, order=2)[source]#
Calculate Hill number.
Hill number (\(^qD\)) is a generalized measure of the effective number of species. It is defined as:
\[^qD = (\sum_{i=1}^S p_i^q)^{\frac{1}{1-q}}\]where \(S\) is the number of taxa and \(p_i\) is the proportion of the sample represented by taxon \(i\).
- Parameters:
- counts1-D array_like, int
Vector of counts.
- orderint or float, optional
Order (\(q\)). Ranges between 0 and infinity. Default is 2.
- Returns:
- float
Hill number.
See also
Notes
Hill number was originally defined in [1]. It is a measurement of “true diversity”, or the effective number of species (ENS) ([2]), which is defined as the number of equally abundant taxa that would make the same diversity measurement given the observed total abundance of the community.
Hill number is a generalization of multiple diversity metrics. Depending on the order \(q\), it is equivalent to:
\(q=0\): Observed species richness (\(S_{obs}\)).
\(q \to 1\): The exponential of Shannon index (\(\exp{H'}\)), i.e., perplexity.
\(q=2\): Inverse Simpson index (\(1 / D\)).
\(q \to \infty\): \(1/\max{p}\), i.e., the inverse of Berger-Parker dominance index.
The order \(q\) determines the influence of taxon abundance on the metric. A larger (or smaller) \(q\) puts more weight on the abundant (or rare) taxa.
Hill number is equivalent to the exponential of Renyi entropy.
References