We assume that there is one or two parental samples that will be used to create the next generation. Refer to these as lines 1 and 2. We assume monoecious, diploid individuals. To generate a new individual, one parent is selected from line 1 and one from line 2. If line 1 and line 2 are the same sample (for example, crossing two lines to form an ) then selfing is a possibility. Once the parents have been selected, gametes are produced, one from each parent.
The first step in producing gametes is to simulate recombination. We assume that the number of crossovers on each chromosome is distributed as a Poisson random variable with mean equal to the length of the chromosome in Morgans. A separate random integer is generated for each chromosome subject to the Poisson, and this indicates the number of crossovers on that chromosome. These crossovers are placed on the chromosome subject to a uniform distribution.
Once the crossovers are in place, gametes are generated. Starting with the first chromosome, one of the two homologs is chosen at random. This chromosome is followed until a crossover is encountered, at which point the other homolog is used. At the end of the first chromosome, a homolog from the second chromosome is chosen at random and the process continues. At the end, a gamete is created which contains the markers and QTLs. The gametes from each parent are then combined to form a new individual. Genetic values are calculated from the genotypes of the new individual using Cockerham's general genetic model for the partitioning of genetic variance [CockerhamCockerham1954]. Phenotypic values can then be generated based on the genetic variance and the heritability.