Runs the Zalpha function — Zalpha • zalpha

Returns a $Z_{\alpha}$ value for each SNP location supplied to the function. For more information about the $Z_{\alpha}$ statistic, please see Jacobs (2016). The $Z_{\alpha}$ statistic is defined as: $$Z_{\alpha}=\frac{{|L| \choose 2}^{-1}\sum_{i,j \in L}r^2_{i,j} + {|R| \choose 2}^{-1}\sum_{i,j \in L}r^2_{i,j}}{2}$$ where |L| and |R| are the number of SNPs to the left and right of the current locus within the given window ws, and $r^2$ is equal to the squared correlation between a pair of SNPs

Zalpha(pos, ws, x, minRandL = 4, minRL = 25, X = NULL)

Arguments

pos	A numeric vector of SNP locations
ws	The window size which the $Z_{\alpha}$ statistic will be calculated over. This should be on the same scale as the `pos` vector.
x	A matrix of SNP values. Columns represent chromosomes; rows are SNP locations. Hence, the number of rows should equal the length of the `pos` vector. SNPs should all be biallelic.
minRandL	Minimum number of SNPs in each set R and L for the statistic to be calculated. Default is 4.
minRL	Minimum value for the product of the set sizes for R and L. Default is 25.
X	Optional. Specify a region of the chromosome to calculate $Z_{\alpha}$ for in the format `c(startposition, endposition)`. The start position and the end position should be within the extremes of the positions given in the `pos` vector. If not supplied, the function will calculate $Z_{\alpha}$ for every SNP in the `pos` vector.

Value

A list containing the SNP positions and the $Z_{\alpha}$ values for those SNPs

References

Jacobs, G.S., T.J. Sluckin, and T. Kivisild, Refining the Use of Linkage Disequilibrium as a Robust Signature of Selective Sweeps. Genetics, 2016. 203(4): p. 1807

Examples

## load the snps example dataset
data(snps)
## run Zalpha over all the SNPs with a window size of 3000 bp
Zalpha(snps$bp_positions,3000,as.matrix(snps[,3:12]))
#> $position
#>  [1]  100  200  300  400  500  600  700  800  900 1000 1100 1200 1300 1400 1500
#> [16] 1600 1700 1800 1900 2000
#> 
#> $Zalpha
#>  [1]         NA         NA         NA         NA 0.09893585 0.10944106
#>  [7] 0.11602964 0.11215782 0.12419556 0.12962040 0.12583275 0.11980489
#> [13] 0.10802033 0.12064462 0.10873917 0.10267168         NA         NA
#> [19]         NA         NA
#> 
## only return results for SNPs between locations 600 and 1500 bp
Zalpha(snps$bp_positions,3000,as.matrix(snps[,3:12]),X=c(600,1500))
#> $position
#>  [1]  600  700  800  900 1000 1100 1200 1300 1400 1500
#> 
#> $Zalpha
#>  [1] 0.1094411 0.1160296 0.1121578 0.1241956 0.1296204 0.1258327 0.1198049
#>  [8] 0.1080203 0.1206446 0.1087392
#>

pos	A numeric vector of SNP locations
ws	The window size which the \(Z_{\alpha}\) statistic will be calculated over. This should be on the same scale as the `pos` vector.
x	A matrix of SNP values. Columns represent chromosomes; rows are SNP locations. Hence, the number of rows should equal the length of the `pos` vector. SNPs should all be biallelic.
minRandL	Minimum number of SNPs in each set R and L for the statistic to be calculated. Default is 4.
minRL	Minimum value for the product of the set sizes for R and L. Default is 25.
X	Optional. Specify a region of the chromosome to calculate \(Z_{\alpha}\) for in the format `c(startposition, endposition)`. The start position and the end position should be within the extremes of the positions given in the `pos` vector. If not supplied, the function will calculate \(Z_{\alpha}\) for every SNP in the `pos` vector.