Package 'zalpha'

Title: Run a Suite of Selection Statistics
Description: A suite of statistics for identifying areas of the genome under selective pressure. See Jacobs, Sluckin and Kivisild (2016) <doi:10.1534/genetics.115.185900>.
Authors: Clare Horscroft
Maintainer: Clare Horscroft <[email protected]>
License: MIT + file LICENSE
Version: 0.3.0.9999
Built: 2024-11-10 03:59:36 UTC
Source: https://github.com/chorscroft/zalpha

Help Index

Creates an LD profile

Description

An LD (linkage disequilibrium) profile is a look-up table containing the expected correlation between SNPs given the genetic distance between them. The use of an LD profile can increase the accuracy of results by taking into account the expected correlation between SNPs. This function aids the user in creating their own LD profile.

Usage

create_LDprofile(dist, x, bin_size, max_dist = NULL, beta_params = FALSE)

Arguments

dist

A numeric vector, or a list of numeric vectors, containing the genetic distance for each SNP.
x

A matrix of SNP values, or a list of matrices. Columns represent chromosomes; rows are SNP locations. Hence, the number of rows should equal the length of the dist vector. SNPs should all be biallelic.
bin_size

The size of each bin, in the same units as dist.
max_dist

Optional. The maximum genetic distance to be considered. If this is not supplied, it will default to the maximum distance in the dist vector.
beta_params

Optional. Beta parameters are calculated if this is set to TRUE. Default is FALSE.

Details

The input for dist and x can be lists. This allows multiple datasets to be used in the creation of the LD profile. For example, using all 22 autosomes from the human genome would involve 22 different distance vectors and SNP matrices. Both lists should be the same length and should correspond exactly to each other (i.e. the distances in each element of dist should go with the SNPs in the same element of x)

In the output, bins represent lower bounds. The first bin contains pairs where the genetic distance is greater than or equal to 0 and less than bin_size. The final bin contains pairs where the genetic distance is greater than or equal to max_dist-bin_size and less than max_dist. If the max_dist is not an increment of bin_size, it will be adjusted to the next highest increment. The final bin will be the bin that max_dist falls into. For example, if the max_dist is given as 4.5 and the bin_size is 1, the final bin will be 4. max_dist should be big enough to cover the genetic distances between pairs of SNPs within the window size given when the ZαZ_{\alpha} statistics are run. Any pairs with genetic distances bigger than max_dist will be assigned the values in the maximum bin of the LD profile.

By default, Beta parameters are not calculated. To fit a Beta distribution to the expected correlations, needed for the Zalpha_BetaCDF and Zbeta_BetaCDF statistics, beta_params should be set to TRUE and the package 'fitdistrplus' must be installed.

Ideally, an LD profile would be generated using data from a null population with no selection, For example by using a simulation if the other population parameters are known. However, often these are unknown or complex, so generating an LD profile using the same data as is being analysed is acceptable, as long as the bins are large enough.

Value

A data frame containing an LD profile that can be used by other statistics in this package.

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

See Also

Zalpha_expected, Zalpha_rsq_over_expected, Zalpha_log_rsq_over_expected, Zalpha_Zscore, Zalpha_BetaCDF, Zbeta_expected, Zbeta_rsq_over_expected, Zbeta_log_rsq_over_expected, Zbeta_Zscore, Zbeta_BetaCDF, Zalpha_all.

Examples

## load the snps example dataset
data(snps)
## Create an LD profile using this data
create_LDprofile(snps$cM_distances,as.matrix(snps[,3:12]),0.001)
## To get the Beta distribution parameter estimates, the fitdistrplus package is required
if (requireNamespace("fitdistrplus", quietly = TRUE)==TRUE) {
  create_LDprofile(snps$cM_distances,as.matrix(snps[,3:12]),0.001,beta_params=TRUE)
}

Runs the L_plus_R function

Description

Returns the (∣L∣2)+(∣R∣2){|L| \choose 2} + {|R| \choose 2} value for each SNP location supplied to the function. |L| and |R| are the number of SNPs to the left and right of the current locus within the given window ws. For more information about the L_plus_R diversity statistic, please see Jacobs (2016).

Usage

L_plus_R(pos, ws, X = NULL)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the L_plus_R statistic will be calculated over. This should be on the same scale as the pos vector.
X

Optional. Specify a region of the chromosome to calculate L_plus_R 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 L_plus_R for every SNP in the pos vector.

Value

A list containing the SNP positions and the L_plus_R 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 L_plus_R over all the SNPs with a window size of 3000 bp
L_plus_R(snps$bp_positions,3000)
## only return results for SNPs between locations 600 and 1500 bp
L_plus_R(snps$bp_positions,3000,X=c(600,1500))

Dataset containing an example LD profile

Description

A simulated LD profile, containing example LD statistics for genetic distances of 0 to 0.0049, in bins of size 0.0001.

Usage

data(LDprofile)

Format

A data frame with 50 rows and 5 variables:

bin

the lower bound of each bin

rsq

the expected r2r^2 value for a pair of SNPs, where the genetic distance between them falls in the given bin

sd

the standard deviation of the expected r2r^2 value

Beta_a

the first shape parameter for the Beta distribution fitted for this bin

Beta_b

the second shape parameter for the Beta distribution fitted for this bin

Runs the LR function

Description

Returns the |L||R| value for each SNP location supplied to the function, where |L| and |R| are the number of SNPs to the left and right of the current locus within the given window ws. For more information about the |L||R| diversity statistic, please see Jacobs (2016).

Usage

LR(pos, ws, X = NULL)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the LR statistic will be calculated over. This should be on the same scale as the pos vector.
X

Optional. Specify a region of the chromosome to calculate LR 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 LR for every SNP in the pos vector.

Value

A list containing the SNP positions and the LR 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 LR over all the SNPs with a window size of 3000 bp
LR(snps$bp_positions,3000)
## only return results for SNPs between locations 600 and 1500 bp
LR(snps$bp_positions,3000,X=c(600,1500))

Dataset containing details on simulated SNPs

Description

A dataset containing the positions, genetic distances and alleles for 20 SNPs, across 10 simulated chromosomes.

Usage

snps

Format

A data frame with 20 rows and 12 variables:

bp_positions

location of the SNP on the chromosome e.g. in base pairs

cM_distances

genetic distance of the SNP from the start of the chromosome e.g. in centimorgans

chrom_1

allele of the SNP on the first example chromosome

chrom_2

allele of the SNP on the second example chromosome

chrom_3

allele of the SNP on the third example chromosome

chrom_4

allele of the SNP on the fourth example chromosome

chrom_5

allele of the SNP on the fifth example chromosome

chrom_6

allele of the SNP on the sixth example chromosome

chrom_7

allele of the SNP on the seventh example chromosome

chrom_8

allele of the SNP on the eighth example chromosome

chrom_9

allele of the SNP on the ninth example chromosome

chrom_10

allele of the SNP on the tenth example chromosome

Examples

snps

Runs the Zalpha function

Description

Returns a ZαZ_{\alpha} value for each SNP location supplied to the function. For more information about the ZαZ_{\alpha} statistic, please see Jacobs (2016). The ZαZ_{\alpha} statistic is defined as:

Zα=(∣L∣2)−1∑i,j∈Lri,j2+(∣R∣2)−1∑i,j∈Lri,j22Z_{\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 r2r^2 is equal to the squared correlation between a pair of SNPs

Usage

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

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the ZαZ_{\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 ZαZ_{\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 ZαZ_{\alpha} for every SNP in the pos vector.

Value

A list containing the SNP positions and the ZαZ_{\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$bp_positions,3000,as.matrix(snps[,3:12]))
## only return results for SNPs between locations 600 and 1500 bp
Zalpha(snps$bp_positions,3000,as.matrix(snps[,3:12]),X=c(600,1500))

Runs all the statistics in the zalpha package

Description

Returns every statistic for each SNP location, given the appropriate parameters. See Details for more information.

Usage

Zalpha_all(
  pos,
  ws,
  x = NULL,
  dist = NULL,
  LDprofile_bins = NULL,
  LDprofile_rsq = NULL,
  LDprofile_sd = NULL,
  LDprofile_Beta_a = NULL,
  LDprofile_Beta_b = NULL,
  minRandL = 4,
  minRL = 25,
  X = NULL
)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the statistics will be calculated over. This should be on the same scale as the pos vector.
x

Optional. 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.
dist

Optional. A numeric vector of genetic distances (e.g. cM, LDU). This should be the same length as pos.
LDprofile_bins

Optional. A numeric vector containing the lower bound of the bins used in the LD profile. These should be of equal size.
LDprofile_rsq

Optional. A numeric vector containing the expected r2r^2 values for the corresponding bin in the LD profile. Must be between 0 and 1.
LDprofile_sd

Optional. A numeric vector containing the standard deviation of the r2r^2 values for the corresponding bin in the LD profile.
LDprofile_Beta_a

Optional. A numeric vector containing the first estimated Beta parameter for the corresponding bin in the LD profile.
LDprofile_Beta_b

Optional. A numeric vector containing the second estimated Beta parameter for the corresponding bin in the LD profile.
minRandL

Minimum number of SNPs in each set R and L for the statistics to be calculated. L is the set of SNPs to the left of the target SNP and R to the right, within the given window size ws. 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 the statistics 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 the statistics for every SNP in the pos vector.

Details

Not all statistics will be returned, depending on the parameters supplied to the function.
If x is not supplied, only Zalpha_expected, Zbeta_expected, LR and L_plus_R will be calculated.
For any of the statistics which use an expected r2r^2 value, the parameters dist, LDprofile_bins and LDprofile_rsq must be supplied. This includes the statistics: Zalpha_expected, Zalpha_rsq_over_expected, Zalpha_log_rsq_over_expected, Zalpha_Zscore, Zalpha_BetaCDF, Zbeta_expected, Zbeta_rsq_over_expected, Zbeta_log_rsq_over_expected, Zbeta_Zscore and Zbeta_BetaCDF.

The LD profile describes the expected correlation between SNPs at a given genetic distance, generated using simulations or real data. Care should be taken to utilise an LD profile that is representative of the population in question. The LD profile should consist of evenly sized bins of distances (for example 0.0001 cM per bin), where the value given is the (inclusive) lower bound of the bin. Ideally, an LD profile would be generated using data from a null population with no selection, however one can be generated using this data. See the create_LDprofile function for more information on how to create an LD profile. For more information about the statistics, please see Jacobs (2016).

Value

A list containing the SNP positions and the statistics 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

See Also

Zalpha, Zalpha_expected, Zalpha_rsq_over_expected, Zalpha_log_rsq_over_expected, Zalpha_Zscore, Zalpha_BetaCDF, Zbeta, Zbeta_expected, Zbeta_rsq_over_expected, Zbeta_log_rsq_over_expected, Zbeta_Zscore, Zbeta_BetaCDF, LR, L_plus_R, create_LDprofile.

Examples

## load the snps and LDprofile example datasets
data(snps)
data(LDprofile)
## run Zalpha_all over all the SNPs with a window size of 3000 bp
## will return all 15 statistics
Zalpha_all(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq,LDprofile$sd,LDprofile$Beta_a,LDprofile$Beta_b)
## only return results for SNPs between locations 600 and 1500 bp
Zalpha_all(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq,LDprofile$sd,LDprofile$Beta_a,LDprofile$Beta_b,X=c(600,1500))
## will only return statistics not requiring an LD profile
Zalpha_all(snps$bp_positions,3000,as.matrix(snps[,3:12]))

Runs the Zalpha function using a cumulative beta distribution function on the r-squared values for the region

Description

Returns a ZαBetaCDFZ_{\alpha}^{BetaCDF} value for each SNP location supplied to the function, based on the expected r2r^2 values given an LD profile and genetic distances. For more information about the ZαBetaCDFZ_{\alpha}^{BetaCDF} statistic, please see Jacobs (2016). The ZαBetaCDFZ_{\alpha}^{BetaCDF} statistic is defined as:

ZαBetaCDF=(∣L∣2)−1∑i,j∈LB(ri,j2;a,b)B(a,b)+(∣R∣2)−1∑i,j∈RB(ri,j2;a,b)B(a,b)2{Z_{\alpha}^{BetaCDF}}=\frac{{|L| \choose 2}^{-1}\sum_{i,j \in L}\frac{B(r^2_{i,j};a,b)}{B(a,b)} + {|R| \choose 2}^{-1}\sum_{i,j \in R}\frac{B(r^2_{i,j};a,b)}{B(a,b)}}{2}

where |L| and |R| are the number of SNPs to the left and right of the current locus within the given window ws, r2r^2 is equal to the squared correlation between a pair of SNPs, and B(ri,j2;a,b)B(a,b)\frac{B(r^2_{i,j};a,b)}{B(a,b)} is the cumulative distribution function for the Beta distribution given the estimated a and b parameters from the LD profile.

Usage

Zalpha_BetaCDF(
  pos,
  ws,
  x,
  dist,
  LDprofile_bins,
  LDprofile_Beta_a,
  LDprofile_Beta_b,
  minRandL = 4,
  minRL = 25,
  X = NULL
)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the ZαBetaCDFZ_{\alpha}^{BetaCDF} 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.
dist

A numeric vector of genetic distances (e.g. cM, LDU). This should be the same length as pos.
LDprofile_bins

A numeric vector containing the lower bound of the bins used in the LD profile. These should be of equal size.
LDprofile_Beta_a

A numeric vector containing the first estimated Beta parameter for the corresponding bin in the LD profile.
LDprofile_Beta_b

A numeric vector containing the second estimated Beta parameter for the corresponding bin in the LD profile.
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 ZαBetaCDFZ_{\alpha}^{BetaCDF} 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 ZαBetaCDFZ_{\alpha}^{BetaCDF} for every SNP in the pos vector.

Details

The LD profile describes the expected correlation between SNPs at a given genetic distance, generated using simulations or real data. Care should be taken to utilise an LD profile that is representative of the population in question. The LD profile should consist of evenly sized bins of distances (for example 0.0001 cM per bin), where the value given is the (inclusive) lower bound of the bin. Ideally, an LD profile would be generated using data from a null population with no selection, however one can be generated using this data. See the create_LDprofile function for more information on how to create an LD profile.

Value

A list containing the SNP positions and the ZαBetaCDFZ_{\alpha}^{BetaCDF} 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

See Also

create_LDprofile

Examples

## load the snps and LDprofile example datasets
data(snps)
data(LDprofile)
## run Zalpha_BetaCDF over all the SNPs with a window size of 3000 bp
Zalpha_BetaCDF(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$Beta_a,LDprofile$Beta_b)
## only return results for SNPs between locations 600 and 1500 bp
Zalpha_BetaCDF(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$Beta_a,LDprofile$Beta_b,X=c(600,1500))

Runs the Zalpha function on the expected r-squared values for the region

Description

Returns a ZαE[r2]Z_{\alpha}^{E[r^2]} value for each SNP location supplied to the function, based on the expected r2r^2 values given an LD profile and genetic distances. For more information about the ZαE[r2]Z_{\alpha}^{E[r^2]} statistic, please see Jacobs (2016). The ZαE[r2]Z_{\alpha}^{E[r^2]} statistic is defined as:

ZαE[r2]=(∣L∣2)−1∑i,j∈LE[ri,j2]+(∣R∣2)−1∑i,j∈RE[ri,j2]2{Z_{\alpha}^{E[r^2]}}=\frac{{|L| \choose 2}^{-1}\sum_{i,j \in L}E[r^2_{i,j}] + {|R| \choose 2}^{-1}\sum_{i,j \in R}E[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 E[r2]E[r^2] is equal to the expected squared correlation between a pair of SNPs, given an LD profile.

Usage

Zalpha_expected(
  pos,
  ws,
  dist,
  LDprofile_bins,
  LDprofile_rsq,
  minRandL = 4,
  minRL = 25,
  X = NULL
)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the ZαE[r2]Z_{\alpha}^{E[r^2]} statistic will be calculated over. This should be on the same scale as the pos vector.
dist

A numeric vector of genetic distances (e.g. cM, LDU). This should be the same length as pos.
LDprofile_bins

A numeric vector containing the lower bound of the bins used in the LD profile. These should be of equal size.
LDprofile_rsq

A numeric vector containing the expected r2r^2 values for the corresponding bin in the LD profile. Must be between 0 and 1.
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 ZαE[r2]Z_{\alpha}^{E[r^2]} 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 ZαE[r2]Z_{\alpha}^{E[r^2]} for every SNP in the pos vector.

Details

The LD profile describes the expected correlation between SNPs at a given genetic distance, generated using simulations or real data. Care should be taken to utilise an LD profile that is representative of the population in question. The LD profile should consist of evenly sized bins of distances (for example 0.0001 cM per bin), where the value given is the (inclusive) lower bound of the bin. Ideally, an LD profile would be generated using data from a null population with no selection, however one can be generated using this data. See the create_LDprofile function for more information on how to create an LD profile.

Value

A list containing the SNP positions and the ZαE[r2]Z_{\alpha}^{E[r^2]} 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

See Also

create_LDprofile

Examples

## load the snps and LDprofile example datasets
data(snps)
data(LDprofile)
## run Zalpha_expected over all the SNPs with a window size of 3000 bp
Zalpha_expected(snps$bp_positions,3000,snps$cM_distances,LDprofile$bin,LDprofile$rsq)
## only return results for SNPs between locations 600 and 1500 bp
Zalpha_expected(snps$bp_positions,3000,snps$cM_distances,LDprofile$bin,LDprofile$rsq,X=c(600,1500))

Runs the Zalpha function on the log of the r-squared values over the expected r-squared values for the region

Description

Returns a Zαlog10(r2/E[r2])Z_{\alpha}^{log_{10}(r^2/E[r^2])} value for each SNP location supplied to the function, based on the expected r2r^2 values given an LD profile and genetic distances. For more information about the Zαlog10(r2/E[r2])Z_{\alpha}^{log_{10}(r^2/E[r^2])} statistic, please see Jacobs (2016). The Zαlog10(r2/E[r2])Z_{\alpha}^{log_{10}(r^2/E[r^2])} statistic is defined as:

Zαlog10(r2/E[r2])=(∣L∣2)−1∑i,j∈Llog10(ri,j2/E[ri,j2])+(∣R∣2)−1∑i,j∈Rlog10(ri,j2/E[ri,j2])2{Z_{\alpha}^{log_{10}(r^2/E[r^2])}}=\frac{{|L| \choose 2}^{-1}\sum_{i,j \in L}log_{10}(r^2_{i,j}/E[r^2_{i,j}]) + {|R| \choose 2}^{-1}\sum_{i,j \in R}log_{10}(r^2_{i,j}/E[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, r2r^2 is equal to the squared correlation between a pair of SNPs, and E[r2]E[r^2] is equal to the expected squared correlation between a pair of SNPs, given an LD profile.

Usage

Zalpha_log_rsq_over_expected(
  pos,
  ws,
  x,
  dist,
  LDprofile_bins,
  LDprofile_rsq,
  minRandL = 4,
  minRL = 25,
  X = NULL
)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the Zαlog10(r2/E[r2])Z_{\alpha}^{log_{10}(r^2/E[r^2])} 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.
dist

A numeric vector of genetic distances (e.g. cM, LDU). This should be the same length as pos.
LDprofile_bins

A numeric vector containing the lower bound of the bins used in the LD profile. These should be of equal size.
LDprofile_rsq

A numeric vector containing the expected r2r^2 values for the corresponding bin in the LD profile. Must be between 0 and 1.
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 Zαlog10(r2/E[r2])Z_{\alpha}^{log_{10}(r^2/E[r^2])} 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 Zαlog10(r2/E[r2])Z_{\alpha}^{log_{10}(r^2/E[r^2])} for every SNP in the pos vector.

Details

The LD profile describes the expected correlation between SNPs at a given genetic distance, generated using simulations or real data. Care should be taken to utilise an LD profile that is representative of the population in question. The LD profile should consist of evenly sized bins of distances (for example 0.0001 cM per bin), where the value given is the (inclusive) lower bound of the bin. Ideally, an LD profile would be generated using data from a null population with no selection, however one can be generated using this data. See the create_LDprofile function for more information on how to create an LD profile.

Value

A list containing the SNP positions and the Zαlog10(r2/E[r2])Z_{\alpha}^{log_{10}(r^2/E[r^2])} 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

See Also

create_LDprofile

Examples

## load the snps and LDprofile example datasets
data(snps)
data(LDprofile)
## run Zalpha_log_rsq_over_expected over all the SNPs with a window size of 3000 bp
Zalpha_log_rsq_over_expected(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq)
## only return results for SNPs between locations 600 and 1500 bp
Zalpha_log_rsq_over_expected(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq,X=c(600,1500))

Runs the Zalpha function on the r-squared values over the expected r-squared values for the region

Description

Returns a Zαr2/E[r2]Z_{\alpha}^{r^2/E[r^2]} value for each SNP location supplied to the function, based on the expected r2r^2 values given an LD profile and genetic distances. For more information about the Zαr2/E[r2]Z_{\alpha}^{r^2/E[r^2]} statistic, please see Jacobs (2016). The Zαr2/E[r2]Z_{\alpha}^{r^2/E[r^2]} statistic is defined as:

Zαr2/E[r2]=(∣L∣2)−1∑i,j∈Lri,j2/E[ri,j2]+(∣R∣2)−1∑i,j∈Rri,j2/E[ri,j2]2{Z_{\alpha}^{r^2/E[r^2]}}=\frac{{|L| \choose 2}^{-1}\sum_{i,j \in L}r^2_{i,j}/E[r^2_{i,j}] + {|R| \choose 2}^{-1}\sum_{i,j \in R}r^2_{i,j}/E[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, r2r^2 is equal to the squared correlation between a pair of SNPs, and E[r2]E[r^2] is equal to the expected squared correlation between a pair of SNPs, given an LD profile.

Usage

Zalpha_rsq_over_expected(
  pos,
  ws,
  x,
  dist,
  LDprofile_bins,
  LDprofile_rsq,
  minRandL = 4,
  minRL = 25,
  X = NULL
)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the Zαr2/E[r2]Z_{\alpha}^{r^2/E[r^2]} 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.
dist

A numeric vector of genetic distances (e.g. cM, LDU). This should be the same length as pos.
LDprofile_bins

A numeric vector containing the lower bound of the bins used in the LD profile. These should be of equal size.
LDprofile_rsq

A numeric vector containing the expected r2r^2 values for the corresponding bin in the LD profile. Must be between 0 and 1.
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 Zαr2/E[r2]Z_{\alpha}^{r^2/E[r^2]} 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 Zαr2/E[r2]Z_{\alpha}^{r^2/E[r^2]} for every SNP in the pos vector.

Details

The LD profile describes the expected correlation between SNPs at a given genetic distance, generated using simulations or real data. Care should be taken to utilise an LD profile that is representative of the population in question. The LD profile should consist of evenly sized bins of distances (for example 0.0001 cM per bin), where the value given is the (inclusive) lower bound of the bin. Ideally, an LD profile would be generated using data from a null population with no selection, however one can be generated using this data. See the create_LDprofile function for more information on how to create an LD profile.

Value

A list containing the SNP positions and the Zαr2/E[r2]Z_{\alpha}^{r^2/E[r^2]} 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

See Also

create_LDprofile

Examples

## load the snps and LDprofile example datasets
data(snps)
data(LDprofile)
## run Zalpha_rsq_over_expected over all the SNPs with a window size of 3000 bp
Zalpha_rsq_over_expected(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq)
## only return results for SNPs between locations 600 and 1500 bp
Zalpha_rsq_over_expected(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq,X=c(600,1500))

Runs the Zalpha function using the Z score of the r-squared values for the region

Description

Returns a ZαZscoreZ_{\alpha}^{Zscore} value for each SNP location supplied to the function, based on the expected r2r^2 values given an LD profile and genetic distances. For more information about the ZαZscoreZ_{\alpha}^{Zscore} statistic, please see Jacobs (2016). The ZαZscoreZ_{\alpha}^{Zscore} statistic is defined as:

ZαZscore=(∣L∣2)−1∑i,j∈Lri,j2−E[ri,j2]σ[ri,j2]+(∣R∣2)−1∑i,j∈Rri,j2−E[ri,j2]σ[ri,j2]2{Z_{\alpha}^{Zscore}}=\frac{{|L| \choose 2}^{-1}\sum_{i,j \in L}\frac{r^2_{i,j}-E[r^2_{i,j}]}{\sigma[r^2_{i,j}]} + {|R| \choose 2}^{-1}\sum_{i,j \in R}\frac{r^2_{i,j}-E[r^2_{i,j}]}{\sigma[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, r2r^2 is equal to the squared correlation between a pair of SNPs, E[r2]E[r^2] is equal to the expected squared correlation between a pair of SNPs, given an LD profile, and σ[r2]\sigma[r^2] is the standard deviation.

Usage

Zalpha_Zscore(
  pos,
  ws,
  x,
  dist,
  LDprofile_bins,
  LDprofile_rsq,
  LDprofile_sd,
  minRandL = 4,
  minRL = 25,
  X = NULL
)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the ZαZscoreZ_{\alpha}^{Zscore} 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.
dist

A numeric vector of genetic distances (e.g. cM, LDU). This should be the same length as pos.
LDprofile_bins

A numeric vector containing the lower bound of the bins used in the LD profile. These should be of equal size.
LDprofile_rsq

A numeric vector containing the expected r2r^2 values for the corresponding bin in the LD profile. Must be between 0 and 1.
LDprofile_sd

A numeric vector containing the standard deviation of the r2r^2 values for the corresponding bin in the LD profile.
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 ZαZscoreZ_{\alpha}^{Zscore} 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 ZαZscoreZ_{\alpha}^{Zscore} for every SNP in the pos vector.

Details

The LD profile describes the expected correlation between SNPs at a given genetic distance, generated using simulations or real data. Care should be taken to utilise an LD profile that is representative of the population in question. The LD profile should consist of evenly sized bins of distances (for example 0.0001 cM per bin), where the value given is the (inclusive) lower bound of the bin. Ideally, an LD profile would be generated using data from a null population with no selection, however one can be generated using this data. See the create_LDprofile function for more information on how to create an LD profile.

Value

A list containing the SNP positions and the ZαZscoreZ_{\alpha}^{Zscore} 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

See Also

create_LDprofile

Examples

## load the snps and LDprofile example datasets
data(snps)
data(LDprofile)
## run Zalpha_Zscore over all the SNPs with a window size of 3000 bp
Zalpha_Zscore(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq,LDprofile$sd)
## only return results for SNPs between locations 600 and 1500 bp
Zalpha_Zscore(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq,LDprofile$sd,X=c(600,1500))

Runs the Zbeta function

Description

Returns a ZβZ_{\beta} value for each SNP location supplied to the function. For more information about the ZβZ_{\beta} statistic, please see Jacobs (2016). The ZβZ_{\beta} statistic is defined as:

Zβ=∑i∈L,j∈Rri,j2∣L∣∣R∣Z_{\beta}=\frac{\sum_{i \in L,j \in R}r^2_{i,j}}{|L||R|}

where |L| and |R| are the number of SNPs to the left and right of the current locus within the given window ws, and r2r^2 is equal to the squared correlation between a pair of SNPs

Usage

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

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the ZβZ_{\beta} 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 ZβZ_{\beta} 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 ZβZ_{\beta} for every SNP in the pos vector.

Value

A list containing the SNP positions and the ZβZ_{\beta} 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 Zbeta over all the SNPs with a window size of 3000 bp
Zbeta(snps$bp_positions,3000,as.matrix(snps[,3:12]))
## only return results for SNPs between locations 600 and 1500 bp
Zbeta(snps$bp_positions,3000,as.matrix(snps[,3:12]),X=c(600,1500))

Runs the Zbeta function using a cumulative beta distribution function on the r-squared values for the region

Description

Returns a ZβBetaCDFZ_{\beta}^{BetaCDF} value for each SNP location supplied to the function, based on the expected r2r^2 values given an LD profile and genetic distances. For more information about the ZβBetaCDFZ_{\beta}^{BetaCDF} statistic, please see Jacobs (2016). The ZβBetaCDFZ_{\beta}^{BetaCDF} statistic is defined as:

ZβBetaCDF=∑i∈L,j∈RB(ri,j2;a,b)B(a,b)∣L∣∣R∣Z_{\beta}^{BetaCDF}=\frac{\sum_{i \in L,j \in R}\frac{B(r^2_{i,j};a,b)}{B(a,b)}}{|L||R|}

where |L| and |R| are the number of SNPs to the left and right of the current locus within the given window ws, r2r^2 is equal to the squared correlation between a pair of SNPs, and B(ri,j2;a,b)B(a,b)\frac{B(r^2_{i,j};a,b)}{B(a,b)} is the cumulative distribution function for the Beta distribution given the estimated a and b parameters from the LD profile.

Usage

Zbeta_BetaCDF(
  pos,
  ws,
  x,
  dist,
  LDprofile_bins,
  LDprofile_Beta_a,
  LDprofile_Beta_b,
  minRandL = 4,
  minRL = 25,
  X = NULL
)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the ZβBetaCDFZ_{\beta}^{BetaCDF} 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.
dist

A numeric vector of genetic distances (e.g. cM, LDU). This should be the same length as pos.
LDprofile_bins

A numeric vector containing the lower bound of the bins used in the LD profile. These should be of equal size.
LDprofile_Beta_a

A numeric vector containing the first estimated Beta parameter for the corresponding bin in the LD profile.
LDprofile_Beta_b

A numeric vector containing the second estimated Beta parameter for the corresponding bin in the LD profile.
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 ZβBetaCDFZ_{\beta}^{BetaCDF} 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 ZβBetaCDFZ_{\beta}^{BetaCDF} for every SNP in the pos vector.

Details

The LD profile describes the expected correlation between SNPs at a given genetic distance, generated using simulations or real data. Care should be taken to utilise an LD profile that is representative of the population in question. The LD profile should consist of evenly sized bins of distances (for example 0.0001 cM per bin), where the value given is the (inclusive) lower bound of the bin. Ideally, an LD profile would be generated using data from a null population with no selection, however one can be generated using this data. See the create_LDprofile function for more information on how to create an LD profile.

Value

A list containing the SNP positions and the ZβBetaCDFZ_{\beta}^{BetaCDF} 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

See Also

create_LDprofile

Examples

## load the snps and LDprofile example datasets
data(snps)
data(LDprofile)
## run Zbeta_BetaCDF over all the SNPs with a window size of 3000 bp
Zbeta_BetaCDF(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$Beta_a,LDprofile$Beta_b)
## only return results for SNPs between locations 600 and 1500 bp
Zbeta_BetaCDF(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$Beta_a,LDprofile$Beta_b,X=c(600,1500))

Runs the Zbeta function on the expected r-squared values for the region

Description

Returns a ZβE[r2]Z_{\beta}^{E[r^2]} value for each SNP location supplied to the function, based on the expected r2r^2 values given an LD profile and genetic distances. For more information about the ZβE[r2]Z_{\beta}^{E[r^2]} statistic, please see Jacobs (2016). The ZβE[r2]Z_{\beta}^{E[r^2]} statistic is defined as:

ZβE[r2]=∑i∈L,j∈RE[ri,j2]∣L∣∣R∣Z_{\beta}^{E[r^2]}=\frac{\sum_{i \in L,j \in R}E[r^2_{i,j}]}{|L||R|}

where |L| and |R| are the number of SNPs to the left and right of the current locus within the given window ws, and E[r2]E[r^2] is equal to the expected squared correlation between a pair of SNPs, given an LD profile.

Usage

Zbeta_expected(
  pos,
  ws,
  dist,
  LDprofile_bins,
  LDprofile_rsq,
  minRandL = 4,
  minRL = 25,
  X = NULL
)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the ZβE[r2]Z_{\beta}^{E[r^2]} statistic will be calculated over. This should be on the same scale as the pos vector.
dist

A numeric vector of genetic distances (e.g. cM, LDU). This should be the same length as pos.
LDprofile_bins

A numeric vector containing the lower bound of the bins used in the LD profile. These should be of equal size.
LDprofile_rsq

A numeric vector containing the expected r2r^2 values for the corresponding bin in the LD profile. Must be between 0 and 1.
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 ZβE[r2]Z_{\beta}^{E[r^2]} 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 ZβE[r2]Z_{\beta}^{E[r^2]} for every SNP in the pos vector.

Details

The LD profile describes the expected correlation between SNPs at a given genetic distance, generated using simulations or real data. Care should be taken to utilise an LD profile that is representative of the population in question. The LD profile should consist of evenly sized bins of distances (for example 0.0001 cM per bin), where the value given is the (inclusive) lower bound of the bin. Ideally, an LD profile would be generated using data from a null population with no selection, however one can be generated using this data. See the create_LDprofile function for more information on how to create an LD profile.

Value

A list containing the SNP positions and the ZβE[r2]Z_{\beta}^{E[r^2]} 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

See Also

create_LDprofile

Examples

## load the snps and LDprofile example datasets
data(snps)
data(LDprofile)
## run Zbeta_expected over all the SNPs with a window size of 3000 bp
Zbeta_expected(snps$bp_positions,3000,snps$cM_distances,LDprofile$bin,LDprofile$rsq)
## only return results for SNPs between locations 600 and 1500 bp
Zbeta_expected(snps$bp_positions,3000,snps$cM_distances,LDprofile$bin,LDprofile$rsq,X=c(600,1500))

Runs the Zbeta function on the log of the r-squared values over the expected r-squared values for the region

Description

Returns a Zβlog10(r2/E[r2])Z_{\beta}^{log_{10}(r^2/E[r^2])} value for each SNP location supplied to the function, based on the expected r2r^2 values given an LD profile and genetic distances. For more information about the Zβlog10(r2/E[r2])Z_{\beta}^{log_{10}(r^2/E[r^2])} statistic, please see Jacobs (2016). The Zβlog10(r2/E[r2])Z_{\beta}^{log_{10}(r^2/E[r^2])} statistic is defined as:

Zβlog10(r2/E[r2])=∑i∈L,j∈Rlog10(ri,j2/E[ri,j2])∣L∣∣R∣Z_{\beta}^{log_{10}(r^2/E[r^2])}=\frac{\sum_{i \in L,j \in R}log_{10}(r^2_{i,j}/E[r^2_{i,j}])}{|L||R|}

where |L| and |R| are the number of SNPs to the left and right of the current locus within the given window ws, r2r^2 is equal to the squared correlation between a pair of SNPs, and E[r2]E[r^2] is equal to the expected squared correlation between a pair of SNPs, given an LD profile.

Usage

Zbeta_log_rsq_over_expected(
  pos,
  ws,
  x,
  dist,
  LDprofile_bins,
  LDprofile_rsq,
  minRandL = 4,
  minRL = 25,
  X = NULL
)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the Zβlog10(r2/E[r2])Z_{\beta}^{log_{10}(r^2/E[r^2])} 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.
dist

A numeric vector of genetic distances (e.g. cM, LDU). This should be the same length as pos.
LDprofile_bins

A numeric vector containing the lower bound of the bins used in the LD profile. These should be of equal size.
LDprofile_rsq

A numeric vector containing the expected r2r^2 values for the corresponding bin in the LD profile. Must be between 0 and 1.
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 Zβlog10(r2/E[r2])Z_{\beta}^{log_{10}(r^2/E[r^2])} 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 Zβlog10(r2/E[r2])Z_{\beta}^{log_{10}(r^2/E[r^2])} for every SNP in the pos vector.

Details

The LD profile describes the expected correlation between SNPs at a given genetic distance, generated using simulations or real data. Care should be taken to utilise an LD profile that is representative of the population in question. The LD profile should consist of evenly sized bins of distances (for example 0.0001 cM per bin), where the value given is the (inclusive) lower bound of the bin. Ideally, an LD profile would be generated using data from a null population with no selection, however one can be generated using this data. See the create_LDprofile function for more information on how to create an LD profile.

Value

A list containing the SNP positions and the Zβlog10(r2/E[r2])Z_{\beta}^{log_{10}(r^2/E[r^2])} 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

See Also

create_LDprofile

Examples

## load the snps and LDprofile example datasets
data(snps)
data(LDprofile)
## run Zbeta_log_rsq_over_expected over all the SNPs with a window size of 3000 bp
Zbeta_log_rsq_over_expected(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq)
## only return results for SNPs between locations 600 and 1500 bp
Zbeta_log_rsq_over_expected(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq,X=c(600,1500))

Runs the Zbeta function on the r-squared values over the expected r-squared values for the region

Description

Returns a Zβr2/E[r2]Z_{\beta}^{r^2/E[r^2]} value for each SNP location supplied to the function, based on the expected r2r^2 values given an LD profile and genetic distances. For more information about the Zβr2/E[r2]Z_{\beta}^{r^2/E[r^2]} statistic, please see Jacobs (2016). The Zβr2/E[r2]Z_{\beta}^{r^2/E[r^2]} statistic is defined as:

Zβr2/E[r2]=∑i∈L,j∈Rri,j2/E[ri,j2]∣L∣∣R∣Z_{\beta}^{r^2/E[r^2]}=\frac{\sum_{i \in L,j \in R}r^2_{i,j}/E[r^2_{i,j}]}{|L||R|}

where |L| and |R| are the number of SNPs to the left and right of the current locus within the given window ws, r2r^2 is equal to the squared correlation between a pair of SNPs, and E[r2]E[r^2] is equal to the expected squared correlation between a pair of SNPs, given an LD profile.

Usage

Zbeta_rsq_over_expected(
  pos,
  ws,
  x,
  dist,
  LDprofile_bins,
  LDprofile_rsq,
  minRandL = 4,
  minRL = 25,
  X = NULL
)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the Zβr2/E[r2]Z_{\beta}^{r^2/E[r^2]} 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.
dist

A numeric vector of genetic distances (e.g. cM, LDU). This should be the same length as pos.
LDprofile_bins

A numeric vector containing the lower bound of the bins used in the LD profile. These should be of equal size.
LDprofile_rsq

A numeric vector containing the expected r2r^2 values for the corresponding bin in the LD profile. Must be between 0 and 1.
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 Zβr2/E[r2]Z_{\beta}^{r^2/E[r^2]} 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 Zβr2/E[r2]Z_{\beta}^{r^2/E[r^2]} for every SNP in the pos vector.

Details

The LD profile describes the expected correlation between SNPs at a given genetic distance, generated using simulations or real data. Care should be taken to utilise an LD profile that is representative of the population in question. The LD profile should consist of evenly sized bins of distances (for example 0.0001 cM per bin), where the value given is the (inclusive) lower bound of the bin. Ideally, an LD profile would be generated using data from a null population with no selection, however one can be generated using this data. See the create_LDprofile function for more information on how to create an LD profile.

Value

A list containing the SNP positions and the Zβr2/E[r2]Z_{\beta}^{r^2/E[r^2]} 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

See Also

create_LDprofile

Examples

## load the snps and LDprofile example datasets
data(snps)
data(LDprofile)
## run Zbeta_rsq_over_expected over all the SNPs with a window size of 3000 bp
Zbeta_rsq_over_expected(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq)
## only return results for SNPs between locations 600 and 1500 bp
Zbeta_rsq_over_expected(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq,X=c(600,1500))

Runs the Zbeta function using the Z score of the r-squared values for the region

Description

Returns a ZβZscoreZ_{\beta}^{Zscore} value for each SNP location supplied to the function, based on the expected r2r^2 values given an LD profile and genetic distances. For more information about the ZβZscoreZ_{\beta}^{Zscore} statistic, please see Jacobs (2016). The ZβZscoreZ_{\beta}^{Zscore} statistic is defined as:

ZβZscore=∑i∈L,j∈Rri,j2−E[ri,j2]σ[ri,j2]∣L∣∣R∣Z_{\beta}^{Zscore}=\frac{\sum_{i \in L,j \in R}\frac{r^2_{i,j}-E[r^2_{i,j}]}{\sigma[r^2_{i,j}]}}{|L||R|}

where |L| and |R| are the number of SNPs to the left and right of the current locus within the given window ws, r2r^2 is equal to the squared correlation between a pair of SNPs, E[r2]E[r^2] is equal to the expected squared correlation between a pair of SNPs, given an LD profile, and σ[r2]\sigma[r^2] is the standard deviation.

Usage

Zbeta_Zscore(
  pos,
  ws,
  x,
  dist,
  LDprofile_bins,
  LDprofile_rsq,
  LDprofile_sd,
  minRandL = 4,
  minRL = 25,
  X = NULL
)

Arguments

pos

A numeric vector of SNP locations
ws

The window size which the ZβZscoreZ_{\beta}^{Zscore} 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.
dist

A numeric vector of genetic distances (e.g. cM, LDU). This should be the same length as pos.
LDprofile_bins

A numeric vector containing the lower bound of the bins used in the LD profile. These should be of equal size.
LDprofile_rsq

A numeric vector containing the expected r2r^2 values for the corresponding bin in the LD profile. Must be between 0 and 1.
LDprofile_sd

A numeric vector containing the standard deviation of the r2r^2 values for the corresponding bin in the LD profile.
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 ZβZscoreZ_{\beta}^{Zscore} 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 ZβZscoreZ_{\beta}^{Zscore} for every SNP in the pos vector.

Details

The LD profile describes the expected correlation between SNPs at a given genetic distance, generated using simulations or real data. Care should be taken to utilise an LD profile that is representative of the population in question. The LD profile should consist of evenly sized bins of distances (for example 0.0001 cM per bin), where the value given is the (inclusive) lower bound of the bin. Ideally, an LD profile would be generated using data from a null population with no selection, however one can be generated using this data. See the create_LDprofile function for more information on how to create an LD profile.

Value

A list containing the SNP positions and the ZβZscoreZ_{\beta}^{Zscore} 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

See Also

create_LDprofile

Examples

## load the snps and LDprofile example datasets
data(snps)
data(LDprofile)
## run Zbeta_Zscore over all the SNPs with a window size of 3000 bp
Zbeta_Zscore(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq,LDprofile$sd)
## only return results for SNPs between locations 600 and 1500 bp
Zbeta_Zscore(snps$bp_positions,3000,as.matrix(snps[,3:12]),snps$cM_distances,
 LDprofile$bin,LDprofile$rsq,LDprofile$sd,X=c(600,1500))