Implementation details

PowQ generate random datasets of families that segregate a trait and a map of marker, according to the user-specified genetic model and to a file providing the relative location in cM of a number of fully informative markers and the QTL.

The distances between pairs of markers, and a marker and the QTL, are converted to recombination fractions by means of the Haldane mapping function.

Random chromosomes are assigned to founders, assuming Hardy-Weinberg equilibrium within marker and QTL genotypes, and linkage equilibrium between marker-marker and marker-QTL alleles. These chromosomes are segregated through the pedigree according to the relationship specified in the pedigree file and the recombination fractions. During simulations, the matrix of the true proportion of alleles shared IBD at each location between the user-specified subjects is stored.

The generated trait is genetically controlled by an additive polygenic component and a biallelic QTL with additive effects.

The total genetic value for the ith individual is , where is the genotypic value due to the QTL and is the polygenic effect. The QTL additive effect is defined as half the difference between the two homozygotes, as no dominance effects are allowed in this release of PowQ.

The polygenic values for the founders are obtained by a normal distribution with mean zero and variance. The polygenic variance is that fraction of the trait variance within each QTL genotype due to polygenic effects. The trait variance is the same for the three QTL genotypes, since PowQ assumes absence of genotype-environment interactions. The fraction due to polygenic effects establishes the residual heritability value, while the remaining trait variance is attributed to random environmental effects.

The polygenic effect in the offspring is evaluated as the average of the polygenic effects of their parents, plus a random Mendelian deviation sampled from a normal distribution with mean zero and variance , where and are the parents inbreeding coefficients.

The phenotypic value , for the ith individuals is obtained by adding to the total genetic value a normally distributed environmental component with mean zero and variance.

After each simulation cycle the dataset is analysed through a variance component approach, which follows the Merlin implementation. The observed trait heritability, and the QTL effect and LOD-score observed at each marker are stored for the power evaluation and reports.

Changing the random seed will generate a different set of founder chromosomes, segregating pattern, and trait values.