Clonal diversity is calculated using the generalized diversity index (Hill numbers)
proposed by Hill (Hill, 1973). See calcDiversity for further details.
To generate a smooth curve, \(D\) is calculated for each value of \(q\) from
min_q to max_q incremented by step_q. When uniform=TRUE
variability in total sequence counts across unique values in the group column
is corrected by repeated resampling from the estimated complete clonal distribution to a
common number of sequences. The complete clonal abundance distribution that is resampled
from is inferred by using the Chao1 estimator to infer the number of unseen clones,
followed by applying the relative abundance correction and unseen clone frequencies
described in Chao et al, 2015.
The diversity index (\(D\)) for each group is the mean value of over all resampling
realizations. Confidence intervals are derived using the standard deviation of the
resampling realizations, as described in Chao et al, 2015.
Significance of the difference in diversity index (D) between groups is tested by
constructing a bootstrap delta distribution for each pair of unique values in the
group column. The bootstrap delta distribution is built by subtracting the diversity
index Da in group a from the corresponding value \(Db\) in group b,
for all bootstrap realizations, yielding a distribution of nboot total deltas; where
group a is the group with the greater mean D. The p-value for hypothesis
Da != Db is the value of P(0) from the empirical cumulative distribution
function of the bootstrap delta distribution, multiplied by 2 for the two-tailed correction.
Note, this method may inflate statistical significance when clone sizes are uniformly small,
such as when most clones sizes are 1, sample size is small, and max_n is near
the total count of the smallest data group. Use caution when interpreting the results
in such cases.