The information contained in multiple sibling pairs

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Abstract
In a sibship of size s, s(s − 1)/2 sib pairs can be formed, but these pairs are statistically dependent when s > 2. This study examines how much independent information is obtained when all possible pairs are used to evaluate the sharing of genes identical by descent. A logarithmic measure of information, Σpilog2pi [Shannon, 1948], is used. The basic unit of information is the binomial “bit,” or the amount of information in the toss of a fair coin. It is shown that a single independent sib pair contains 1.5 bits. The complete sibship contains a total of 2s−3 + (1/2)s−1 bits, or (2s−3 + (1/2)s−1)/1.5 pair-equivalents of information. The information is reduced if all sib genotypes do not occur with equal probability.