qtlDesign (version 0.953)

Variance and effect size: Effect size, proportion variance explained, and error variance calculations

Description

The function error.var estimates the error variance using estimates of the environmental variance and genetic variance. The effect segregating at a locus, can be calculated using gmeans2effect These are key inputs for power calculations. The function prop.var calculates the proportion of variance explained by a locus given the effect size and error variance.

Usage

error.var(cross,env.var=1,gen.var=0,bio.reps=1)
gmeans2effect(cross,means)
prop.var(cross,effect,sigma2)

Value

For error.var the value is the estimated error variance based on the assumptions mentioned above. For gmeans2effect

the value depends on the type of cross. For RI lines it is simply the additive effect of the QTL which is half the difference between the homozygote means. For intercross, it is a vector giving the additive and dominance components. The additive component is half the difference between the homozygote means, and the dominance component is the difference between the heterozygotes and the average of the homozygotes. For the backcross, it is a vector of length 2,

c(a-h,h-b), which is the effect of an allelic substitution of an "A" allele in the backcrosses to each parental strain.

Arguments

cross

String indicating cross type which is "bc", for backcross, "f2" for intercross, and "ri" for recombinant inbred lines.

env.var

Environmental (within genotype) variance

gen.var

Genetic (between genotype) variance due to all loci segregating between the parental lines.

bio.reps

Number of biological replicates per unique genotype. This is usually 1 for backcross and intercross, but may be larger for RI lines.

means

Vector of genotype means in the form c(a,h,b), where a is the mean of the "AA" homozygotes, h is the mean of the "AB" heterozygotes, and b is the mean of the "BB" homozygotes.

effect

The QTL effect which depends on the cross. For backcross, it is the difference in means the heterozygote and homozygote. For RI lines it is half the difference in means of the homozygotes, for intercross, it is a two component vector of the form c(a,d), where a is the additive effect (half the difference between the homozygotes), and d is the dominance effect (difference between the heterozygote and the average of the homozygotes). The genotype means will be -a-d/2, d/2, and a-d/2.

sigma2

Error variance.

Author

Saunak Sen, Jaya Satagopan, Karl Broman, and Gary Churchill

Details

The function error.var estimates the error variance segregating in a cross using estimates of the environmental (within genotype) variance, and the genetic (between genotype variance). The environmental variance is assumed to be invariant between cross types. The genetic variance segregating in RI lines is assumed to be double that in F2 intercross, and four times that of the backcross. This assumption holds if all loci are additive. The error variance at a locus of interest is aproximately $$\sigma_G^2/c + \sigma_E^2/m,$$ where \(\sigma_G^2\) is the genetic variance (gen.var), \(c\) is a constant depending on the cross type (1, for RI lines, 1/2 for F2 intercross, and 1/4 for backross), \(\sigma_E^2\) is the environmental variance (env.var), and \(m\) is the number of biological replicates per unique genotype (bio.reps).

The function gmeans2effect calculates the QTL effects from genotype means depending on the cross.

The function prop.var calculates the proportion of variance attributable to a locus given the effects size(s) and the error variance. The definition of effect size is in the output of gmeans2effect (see below).

References

Sen S, Satagopan JM, Churchill GA (2005) Quantitative trait locus study design from an information perspective. Genetics, 170:447-64.

See Also

powercalc

Examples

error.var(cross="bc",env.var=1,gen.var=1,bio.reps=1)
error.var(cross="f2",env.var=1,gen.var=1,bio.reps=1)
error.var(cross="ri",env.var=1,gen.var=1,bio.reps=1)
error.var(cross="ri",env.var=1,gen.var=1,bio.reps=10)
gmeans2effect(cross="f2",means=c(0,1,2))
gmeans2effect(cross="f2",means=c(0,1,1))
gmeans2effect(cross="bc",means=c(0,1,1))
gmeans2effect(cross="ri",means=c(0,1,1))
prop.var(cross="bc",effect=5,sigma2=1)
prop.var(cross="f2",effect=c(5,0),sigma2=1)
prop.var(cross="ri",effect=5,sigma2=1)