kempton_taylor_q {abdiv} | R Documentation |
The Kempton-Taylor Q index is designed to measure species in the middle of the abundance distribution.
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.