qtlDesign (version 0.81)

Effect size and error variance: Effect size and error variance calculations

Description

The function error.var estimates the error variance using estimates of the biological variance and genetic variance. The effect segregating at a locus, can becalculated using gmeans2effect These are key inputs for power calculations.

Usage

error.var(cross,bio.var=1,gen.var=0,bio.reps=1)
gmeans2effect(cross, means)

Arguments

cross

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

bio.var

Biological (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.

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.

Details

The function error.var estimates the error variance segregating in a cross using estimates of the biological (within genotype) variance, and the genetic (between genotype variance). The biological 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 $$\gamma^2/c + \tau^2/m$$, where $\gamma^2$ 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), $tau^2$ is the biological variance (bio.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.

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",bio.var=1,gen.var=1,bio.reps=1)
error.var(cross="f2",bio.var=1,gen.var=1,bio.reps=1)
error.var(cross="ri",bio.var=1,gen.var=1,bio.reps=1)
error.var(cross="ri",bio.var=1,gen.var=1,bio.reps=10)
gmeans2effect("f2",c(0,1,2))
gmeans2effect("f2",c(0,1,1))
gmeans2effect("bc",c(0,1,1))
gmeans2effect("ri",c(0,1,1))