COMPUTATION OF IDENTITY-BY-DESCENT PROPORTIONS SHARED BY 2 SIBLINGS

I provide a novel approach to computing the mean and variance of the p roportion of genetic material shared identical by descent (IBD) by sib ling pairs in a specified chromosomal region, conditional on observed marker data. I first show that each chromosome in an offspring can be represented by a two-state Markov chain, with the time parameter being the map distance along the chromosome. On this basis, I show that IBD proportion can be written as a stochastic integral and that the compu tation of its mean and variance can be reduced to evaluation of an int egral of some elementary functions. In addition, I show how Goldgar's model can be extended to include dominance effects. Several examples a re provided to illustrate the calculation.