kempton_taylor_q {abdiv}

Kempton-Taylor Q index

Description

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

Usage

kempton_taylor_q(x, lower_quantile = 0.25, upper_quantile = 0.75)

Arguments

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.

Details

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.

Value

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.

References

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