Supplementary materials for A study on Mapping Quantitative Trait Loci in the Advanced Populations Derived from Two Inbred Lines Derivation of Genotypic Distribution for Three Genes under Self and Random Mating

Consider the genome structure of gametes in an advanced F t population descended from two inbred lines. these eight gametes can produce 36 diierent zygotes (27 discernible genotypes in practice). Assume that r, r 1 , and r 2 denote the recombination rates between A and C, betwe e n A a n d B a n d b e t ween B and C, respectively. Let 1 and 0 represent the capital and small-letter alleles, respectively, t o count the number of capital allele, so that the conngurations of the eight t ypes of gametes can be However, the relation between gametic frequencies and recombination rates becomes complicated in the advanced populations after further sellng or intermating as the genomes have undergone multiple runs of meiosis. If population is mating randomly, the gametes produced by a n y t ype of zygotes (individuals) can randomly fertilize each other across diierent individuals. If the population is self-fertilized, the gametes of an individual are randomly mating within individual, but they are not allowed to seminate the gametes from diierent individuals. The procedures to obtain the transition formulas of genotypic frequencies from current to next generation under self and random mating are outlined below. Random mating: If mating is random in a population, the uniication of the eight g a m e t e s can produce 27 possible zygote genotypes, and the frequency of a zygotic genotype is equivalent t o the product of the two gametic frequencies in the previous population. The genotypic distribution of a population is completely determined by the gametic distribution in the previous generation,