ldest_hap  R Documentation 
Given genotype (allele dosage) or genotype likelihood data for each individual at a pair of loci, this function will calculate the maximum likelihood estimates and their corresponding asymptotic standard errors of some measures of linkage disequilibrium (LD): D, D', the Pearson correlation, the squared Pearson correlation, and the Fisherz transformation of the Pearson correlation. This function can be used for both diploids and polyploids.
ldest_hap( ga, gb, K, reltol = 10^8, nboot = 100, useboot = FALSE, pen = 2, grid_init = FALSE, se = TRUE )
ga 
One of two possible inputs:

gb 
One of two possible inputs:

K 
The ploidy of the species. Assumed to be the same for all individuals. 
reltol 
The relative tolerance for the stopping criterion. 
nboot 
Sometimes, the MLE standard errors don't exist. So we use
the bootstrap as a backup. 
useboot 
A logical. Optionally, you may always use the bootstrap
to estimate the standard errors ( 
pen 
The penalty to be applied to the likelihood. You can think about
this as the prior sample size. Should be greater than 1. Does not
apply if 
grid_init 
A logical. Should we initialize the gradient ascent
at a grid of initial values ( 
se 
A logical. Should we calculate standard errors ( 
Let A and a be the reference and alternative alleles, respectively, at
locus 1. Let B and b be the reference and alternative alleles,
respectively, at locus 2. Let paa, pAb, paB, and pAB be the
frequencies of haplotypes ab, Ab, aB, and AB, respectively.
Let pA = pAb + pAB and let pB = paB + pAB
The ldest
returns estimates of the following measures
of LD.
D: pAB  pA pB
D': D / Dmax, where Dmax = min(pA pB, (1  pA) (1  pB)) if D < 0 and Dmax = min(pA (1  pB), pA (1  pB)) if D > 0
rsquared: The squared Pearson correlation, r^2 = D^2 / (pA (1  pA) pB (1  pB))
r: The Pearson correlation, r = D / sqrt(pA (1  pA) pB (1  pB))
Estimates are obtained via maximum likelihood under the assumption of HardyWeinberg equilibrium. The likelihood is calculated by integrating over the possible haplotypes for each pair of genotypes.
The resulting standard errors are based on the square roots of the inverse of the negative Fisherinformation. This is from standard maximum likelihood theory. The Fisherinformation is known to be biased low, so the actual standard errors are probably a little bigger for small n (n < 20). In some cases the Fisherinformation matrix is singular, and so we in these cases we return a bootstrap estimate of the standard error.
The standard error estimate of the squared Pearson correlation is not valid when r^2 = 0.
In cases where either SNP is estimated to be monoallelic
(pA %in% c(0, 1)
or pB %in% c(0, 1)
), this function
will return LD estimates of NA
.
A vector with some or all of the following elements:
D
The estimate of the LD coefficient.
D_se
The standard error of the estimate of the LD coefficient.
r2
The estimate of the squared Pearson correlation.
r2_se
The standard error of the estimate of the squared Pearson correlation.
r
The estimate of the Pearson correlation.
r_se
The standard error of the estimate of the Pearson correlation.
Dprime
The estimate of the standardized LD
coefficient. When type
= "comp", this corresponds
to the standardization where we fix allele frequencies.
Dprime_se
The standard error of Dprime
.
Dprimeg
The estimate of the standardized LD coefficient. This corresponds to the standardization where we fix genotype frequencies.
Dprimeg_se
The standard error of Dprimeg
.
z
The Fisherz transformation of r
.
z_se
The standard error of the Fisherz
transformation of r
.
p_ab
The estimated haplotype frequency of ab. Only returned if estimating the haplotypic LD.
p_Ab
The estimated haplotype frequency of Ab. Only returned if estimating the haplotypic LD.
p_aB
The estimated haplotype frequency of aB. Only returned if estimating the haplotypic LD.
p_AB
The estimated haplotype frequency of AB. Only returned if estimating the haplotypic LD.
q_ij
The estimated frequency of genotype i at locus 1 and genotype j at locus 2. Only returned if estimating the composite LD.
n
The number of individuals used to estimate pairwise LD.
David Gerard
set.seed(1) n < 100 # sample size K < 6 # ploidy ## generate some fake genotypes when LD = 0. ga < stats::rbinom(n = n, size = K, prob = 0.5) gb < stats::rbinom(n = n, size = K, prob = 0.5) head(ga) head(gb) ## generate some fake genotype likelihoods when LD = 0. gamat < t(sapply(ga, stats::dnorm, x = 0:K, sd = 1, log = TRUE)) gbmat < t(sapply(gb, stats::dnorm, x = 0:K, sd = 1, log = TRUE)) head(gamat) head(gbmat) ## Haplotypic LD with genotypes ldout1 < ldest_hap(ga = ga, gb = gb, K = K) head(ldout1) ## Haplotypic LD with genotype likelihoods ldout2 < ldest_hap(ga = gamat, gb = gbmat, K = K) head(ldout2)
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