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# skbio.diversity.alpha.kempton_taylor_q

skbio.diversity.alpha.kempton_taylor_q(counts, lower_quantile=0.25, upper_quantile=0.75)

  Calculate Kempton-Taylor Q index of alpha diversity.

  Kempton-Taylor Q index measures diversity based on the middle-ranking taxa in the abundance distribution. Specifically, it estimates the slope of the cumulative abundance curve in the interquantile range. It is defined as:

  \[Q = \frac{S_{lower..upper}}{\ln n_{lower} - \ln n_{upper}}\]

  where “lower” and “upper” are the taxa at the lower and upper quantiles of the abundance distribution, \(S\) is the number of taxa, and \(n\) is the number of individuals.

  By default, the lower and upper quartiles are used. Therefore:

  \[Q = \frac{S}{2(\ln n_{0.25} - \ln n_{0.75})}\]

  The quantiles are rounded inwards in this implementation.

  Parameters:
    counts 1-D array_like, int

      Vector of counts.

    lower_quantile float, optional

      Lower bound of the interquantile range. Defaults to lower quartile.

    upper_quantile float, optional

      Upper bound of the interquantile range. Defaults to upper quartile.

  Returns:
    float

      Kempton-Taylor Q index of alpha diversity.

  Notes

  The index is defined in [1]. The implementation here is based on the description given in the SDR-IV online manual [2].

  The implementation provided here differs slightly from the results given in Magurran 1998. Specifically, we have 14 in the numerator rather than 15. Magurran recommends counting half of the taxa with the same # counts as the point where the UQ falls and the point where the LQ falls, but the justification for this is unclear (e.g. if there were a very large # taxa that just overlapped one of the quantiles, the results would be considerably off). Leaving the calculation as-is for now, but consider changing.

  References

  [1]

  Kempton, R. A. and Taylor, L. R. (1976) Models and statistics for species diversity. Nature, 262, 818-820.

  [2]

  http://www.pisces-conservation.com/sdrhelp/index.html