Note that Tajima's D estimates from data that have been filtered or ascertained can be difficult to interpret. This function should ideally be used on sequence data prior to filtering.
Usage
pop_tajimas_d(.x, ...)
# S3 method for class 'tbl_df'
pop_tajimas_d(
.x,
n_cores = bigstatsr::nb_cores(),
block_size = bigstatsr::block_size(nrow(.x), 1),
...
)
# S3 method for class 'vctrs_bigSNP'
pop_tajimas_d(
.x,
n_cores = bigstatsr::nb_cores(),
block_size = bigstatsr::block_size(length(.x), 1),
...
)
# S3 method for class 'grouped_gen_tbl'
pop_tajimas_d(
.x,
n_cores = bigstatsr::nb_cores(),
block_size = bigstatsr::block_size(nrow(.x), 1),
...
)Arguments
- .x
a vector of class
vctrs_bigSNP(usually thegenotypescolumn of agen_tibbleobject), or agen_tibble.- ...
other arguments passed to specific methods, currently unused.
- n_cores
number of cores to be used, it defaults to
bigstatsr::nb_cores()- block_size
maximum number of loci read at once.
Value
A single numeric value (Tajima's D D) for the whole data set, NA
when the statistic is not defined. For grouped data a list of Tajima's D D
values (one per group) is returned.
Details
Nucleotide diversity is estimated at each locus with loci_pi(), so this
function works with diploid, polyploid, mixed-ploidy and pseudohaploid data.
Missing genotypes are accounted for following Bailey et al. (2025), as
implemented in pixy: the sample size \(n_x\) at each locus \(x\) is
the number of non-missing allele copies at that locus (i.e. the sum of the
ploidy of the genotyped individuals, with pseudohaploids contributing one
copy each). The two estimators of \(\theta\) are then:
\(\hat{\theta}_\pi = \sum_x \pi_x\), where \(\pi_x\) is the nucleotide diversity at locus \(x\), estimated from its \(n_x\) allele copies (loci with fewer than 2 allele copies contribute 0);
\(\hat{\theta}_W = \sum_x 1 / a_{n_x}\), summed over the segregating sites, where \(a_{n_x} = \sum_{i=1}^{n_x - 1} 1/i\) (i.e. each segregating site is weighted by its own sample size).
The standard deviation of \(\hat{\theta}_\pi - \hat{\theta}_W\) is
computed with the formula of Tajima (1989), using the number of
segregating sites \(S\) and the mean sample size across loci with at
least one non-missing allele copy (rounded to the nearest integer, as the
formula is only defined for integer sample sizes). When there are no
missing data, all loci have the same sample size and the statistic is
identical to the classic Tajima's D. Loci with no genotyped individuals
are ignored. Tajima's D is NA when there are no segregating sites, or
when the mean sample size is smaller than 2.
References
Tajima F (1989) Statistical method for testing the neutral mutation hypothesis by DNA polymorphism. Genetics 123:585-595.
Bailey N, Stevison L, Samuk K (2025) Correcting for bias in estimates of \(\theta_W\) and Tajima's D from missing data in next-generation sequencing. Molecular Ecology Resources, e14104. doi:10.1111/1755-0998.14104
Examples
example_gt <- load_example_gt("grouped_gen_tbl")
# Compute Tajima's D
example_gt %>% pop_tajimas_d()
#> [[1]]
#> [1] 0.944084
#>
#> [[2]]
#> [1] -0.780123
#>
#> [[3]]
#> [1] -Inf
#>