Gametogenesis processes and multilocus gene identity by descent

With few exceptions, the determination of unconditional probability of genes shared identical by descent (IBD) by relatives can be very difficult, especially if the relationship is complex or if multiple loci are involved. It is particularly difficult if one needs the IBD probability in a explicit form, expressed in terms of interlocus recombination fractions. In this paper, I will further extend the concept of gametogenesis process introduced elsewhere and indicate that it completely determines the gene IBD events of interest in pedigrees. I will demonstrate that the gametogenesis process not only serves as a convenient conceptual framework in considering IBD events in pedigrees but also provides a simple yet powerful tool to solve a wide range of seemingly difficult problems. In particular, I consider the problem of multilocus IBD probability for relative pairs, k siblings, and a group of pedigree members. In addition, I consider the problem of multilocus autozygosity probability and the problem of gene preservation in close relatives.