Main symbols used

nNumber of phenotypic records
mNumber of individuals in the pedigree
yPhenotypic records, dimension n
MMarker information, contains the alleles for each individual and marker; dimension m × no. of markers × 2
S0Identity-by-descent status of the QTL allele of the base generation individuals with the causative mutation; it can take values wild (+) or mutant (-) allele, dimension 2 × no. of base generation individuals
aAdditive QTL effect; the average value of individuals with genotype (+/+) - (-/-) is 2a
dDominance effect; phenotypic value of individuals with genotype (+/-) or (-/+)
uInfinitesimal genetic value; it contains all genetic effects except the QTL under study, dimension m
βFixed (noise environmental) effects, dimension the sum of levels for each fixed effect
Embedded Image Infinitesimal genetic variance
Embedded Image Residual variance δ QTL position, in morgans
tTime (no. of generations) since mutation
T2 × m matrix with QTL segregation indicators. The genotype of all individuals is unambiguously determined by T and S0
HMarker phases; contains indicator variable to identify whether the allele in vector M is of paternal or maternal origin; dimension m × no. of markers