Proportion of Genes Survived in Offspring Conditional on Inheritance of Flanking Markers

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RESUMO

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 or 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 (>/=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.

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