Computation of identity-by-descent proportions shared by two siblings

Am J Hum Genet. 1994 Jun;54(6):1104-9.

Abstract

I provide a novel approach to computing the mean and variance of the proportion of genetic material shared identical by descent (IBD) by sibling 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 computation of its mean and variance can be reduced to evaluation of an integral of some elementary functions. In addition, I show how Goldgar's model can be extended to include dominance effects. Several examples are provided to illustrate the calculation.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, P.H.S.

MeSH terms

  • Analysis of Variance
  • Chromosome Mapping / methods*
  • Chromosome Mapping / statistics & numerical data
  • Chromosomes, Human
  • Genetic Linkage*
  • Genetic Markers
  • Humans
  • Markov Chains
  • Models, Genetic*
  • Models, Statistical*

Substances

  • Genetic Markers