Effect size and error variance {qtlDesign} | R Documentation |
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.
error.var(cross,bio.var=1,gen.var=0,bio.reps=1) gmeans2effect(cross, means)
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. |
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.
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.
Saunak Sen, Jaya Satagopan, Karl Broman, and Gary Churchill
Sen S, Satagopan JM, Churchill GA (2005) Quantitative trait locus study design from an information perspective. Genetics, 170:447-64.
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))