Proportion of genes survived in offspring conditional on inheritance
of flanking markers
S.W. Guo
Genetics, 138(3),953-962 (Nov 1994)
Abstract
In mammalian genetics and perhaps in human genetics as well, it is
an interesting question as to how many offspring are needed in order
to have a desired chance of preserving part of the entire genome of
an individual. A more practical and perhaps more important question
is: given k children and DNA marker data on a particular region of
interest, what proportion of one's genes has been actually passed on
to his children? To answer this question, I define the concept of
identity by descent proportion, or IBDP for short. The IBDP is
defined to be the proportion of genetic material shared identical by
descent by a group of relatives in a specified chromosomal region. I
provide a novel approach to computing the mean and variance of IBDP
for k (> or = 2) half-sibs based on marker data, thus providing a
means to compute the mean and variance of proportion of genes
survived. 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 will
show that IBDP can be written as a stochastic integral and that the
computation of the EIBDP can be reduced to evaluating an integral of
some elementary functions. Numerical examples are provided to
illustrate the calculation.
Allele-sharing linkage analysis