Description Usage Arguments Details Value References

The Kempton-Taylor Q index is designed to measure species in the middle of the abundance distribution.

1 | ```
kempton_taylor_q(x, lower_quantile = 0.25, upper_quantile = 0.75)
``` |

`x` |
A numeric vector of species counts or proportions. |

`lower_quantile, upper_quantile` |
Lower and upper quantiles of the abundance distribution. Default values are the ones suggested by Kempton and Taylor. |

For a vector of species counts `x`

, the Kempton-Taylor Q statistic is
equal to the slope of the cumulative abundance curve across a specified
quantile range. The cumulative abundance curve is the plot of the number of
species against the log-abundance.

Kempton and Taylor originally defined the index as

*Q = \frac{\frac{1}{2}S}{\log{R_2} - \log{R_1}},*

where *S* is the
total number of species observed, *R_1* is the abundance at the lower
quantile, and *R_2* is the abundance at the upper quantile. However,
this definition only holds if one uses the interquartile range. Because we
allow the user to adjust the upper and lower quantiles, we have to find the
number of species at these abundance values. Here, we follow the
implementation in `scikit-bio`

and round inwards to find the quantile
values, taking the number of species and log-abundance values at these data
points exactly.

Equivalent to

`kempton_taylor_q()`

in`skbio.diversity.alpha`

.Similar to the

`qstat`

calculator in Mothur. Our implementation differs slightly, and this difference affects the result.

The Kempton-Taylor Q index, *Q < 0*. If the vector sums to zero,
we cannot compute the quantiles, and this index is undefined. In that
case, we return `NaN`

.

Kempton RA, Taylor LR. Models and statistics for species diversity. Nature. 1976;262:818-820.

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