Evaluation of identity-by-descent probabilities for half-sibs on continuous genome

A new method is provided for exact evaluation of the distribution of the amount of genetic material, from a chromosomal segment, shared identical-by-descent by a finite number of half-sibs. The interest in such distribution stems from its relation to the distribution of genetic material from chromosomal segments of an individual surviving to the next generation. The new method is superior to the existing one which has recently been suggested by Stefanov [V.T. Stefanov, Distribution of the amount of genetic material from a chromosomal segment surviving to the following generation. J. Appl. Probab. 41 (2004) 345]. It allows both faster computation and a large number of half-sibs. Relevant software codes are provided for automated implementation of such evaluations.