gpi {GeneticsPed} | R Documentation |
gpi
calculates Genotype Probability Index (GPI), which indicates
the information content of genotype probabilities derived from
segregation analysis.
gpi(gp, hwp)
gp |
numeric vector or matrix, individual genotype probabilities |
hwp |
numeric vector or matrix, Hard-Weinberg genotype probabilities |
Genotype Probability Index (GPI; Kinghorn, 1997; Percy and Kinghorn, 2005) indicates information that is contained in multi-allele genotype probabilities for diploids derived from segregation analysis, say Thallman et. al (2001a, 2001b). GPI can be used as one of the criteria to help identify which ungenotyped individuals or loci should be genotyped in order to maximise the benefit of genotyping in the population (e.g. Kinghorn, 1999).
gp
and hwp
arguments accept genotype probabilities for
multi-allele loci. If there are two alleles (1 and 2), you should pass
vector of probabilities for genotypes (11 and 12) i.e. one value for
heterozygotes (12 and 21) and always skipping last homozygote. With
three alleles this vector should hold probabilities for genotypes (11,
12, 13, 22, 23) as also shown bellow and in examples.
2 alleles: 1 and 2 11 12 --> no. dimensions = 2 3 alleles: 1, 2, and 3 11 12 13 22 23 --> no. dimensions = 5 ... 5 alleles: 1, 2, 3, 4, and 5 11 12 13 14 15 22 23 24 25 33 34 35 44 45 --> no. dimensions = 14
In general, number of dimensions (k) for n alleles is equal to:
k = (n * (n + 1) / 2) - 1.
If you have genotype probabilities for more than one individual, you can
pass them to gp
in a matrix form, where each row represents
genotype probabilities of an individual. In case of passing matrix to
gp
, hwp
can still accept a vector of Hardy-Weinberg
genotype probabilities, which will be used for all individuals due to
recycling. If hwp
also gets a matrix, then it must be of the same
dimension as that one passed to gp
.
Vector of N genotype probability indices, where N is number of individuals
Gregor Gorjanc R code, documentation, wrapping into a package; Andrew Percy and Brian P. Kinghorn Fortran code
Kinghorn, B. P. (1997) An index of information content for genotype probabilities derived from segregation analysis. Genetics 145(2):479-483 http://www.genetics.org/cgi/content/abstract/145/2/479
Kinghorn, B. P. (1999) Use of segregation analysis to reduce genotyping costs. Journal of Animal Breeding and Genetics 116(3):175-180 http://dx.doi.org/10.1046/j.1439-0388.1999.00192.x
Percy, A. and Kinghorn, B. P. (2005) A genotype probability index for multiple alleles and haplotypes. Journal of Animal Breeding and Genetics 122(6):387-392 http://dx.doi.org/10.1111/j.1439-0388.2005.00553.x
Thallman, R. M. and Bennet, G. L. and Keele, J. W. and Kappes, S. M. (2001a) Efficient computation of genotype probabilities for loci with many alleles: I. Allelic peeling. Journal of Animal Science 79(1):26-33 http://jas.fass.org/cgi/reprint/79/1/34
Thallman, R. M. and Bennet, G. L. and Keele, J. W. and Kappes, S. M. (2001b) Efficient computation of genotype probabilities for loci with many alleles: II. Iterative method for large, complex pedigrees. Journal of Animal Science 79(1):34-44 http://jas.fass.org/cgi/reprint/79/1/34
## --- Example 1 from Percy and Kinghorn (2005) --- ## No. alleles: 2 ## No. individuals: 1 ## Individual genotype probabilities: ## * p(11, 12, 22) = (.1, .5, .4) ## Hardy-Weinberg probabilities: ## * p(1, 2) = (.75, .25) ## * p(11, 12, (.75^2, 2*.75*.25, ## 22) = .25^2) ## = (.5625, .3750, ## .0625) gp <- c(.1, .5) hwp <- c(.5625, .3750) gpi(gp=gp, hwp=hwp) ## --- Example 1 from Percy and Kinghorn (2005) extended --- ## No. alleles: 2 ## No. individuals: 2 ## Individual genotype probabilities: ## * p_1(11, 12, 22) = (.1, .5, .4) ## * p_2(11, 12, 22) = (.2, .5, .3) (gp <- matrix(c(.1, .5, .2, .5), nrow=2, ncol=2, byrow=TRUE)) gpi(gp=gp, hwp=hwp) ## --- Example 2 from Percy and Kinghorn (2005) --- ## No. alleles: 3 ## No. individuals: 1 ## Individual genotype probabilities: ## * p(11, 12, 13, (.1, .5, .0, ## 22, 23 = .4, .0, ## 33) .0) ## Hardy-Weinberg probabilities: ## * p(1, 2, 3) = (.75, .25, .0) ## * p(11, 12, 13, (.75^2, 2*.75*.25, .0, ## 22, 23, = 0.25^2, .0, ## 33) .0) ## = (.5625, .3750, .0 ## .0625, .0, ## .0) gp <- c(.1, .5, .0, .4, .0) hwp <- c(.5625, .3750, .0, .0625, .0) gpi(gp=gp, hwp=hwp) ## --- Example 3 from Percy and Kinghorn (2005) --- ## No. alleles: 5 ## No. individuals: 1 ## Hardy-Weinberg probabilities: ## * p(1, 2, 3, 4, 5) = (.2, .2, .2, .2, .2) ## * p(11, 12, 13, ...) = (p(1)^2, 2p(1)p(2), 2p(1)p(3), ...) ## Individual genotype probabilities: ## * p(11, 12, 13, ...) = gp / 2 ## p(12) = p(12) + .5 (hwp <- rep(.2, times=5) %*% t(rep(.2, times=5))) hwp <- c(hwp[upper.tri(hwp, diag=TRUE)]) (hwp <- hwp[1:(length(hwp) - 1)]) gp <- hwp / 2 gp[2] <- gp[2] + .5 gp gpi(gp=gp, hwp=hwp) ## --- Simulate gp for n alleles and i subjects --- n <- 3 i <- 10 kAll <- (n*(n+1)/2) # without -1 here! k <- kAll - 1 if(require("gtools")) { gp <- rdirichlet(n=i, alpha=rep(x=1, times=kAll))[, 1:k] hwp <- as.vector(rdirichlet(n=1, alpha=rep(x=1, times=kAll)))[1:k] gpi(gp=gp, hwp=hwp) }