Relationship Information Contained in Gamete Identity by Descent Data

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Abstract
We consider idealized gamete identity by descent (IBD) data which consists of the lengths of IBD and non-IBD regions along the genome for gametes segregating from two related individuals. Information on the relationship between the individuals is contained in the pattern of lengths, with the power of the likelihood ratio test to reject one relationship in favor of another giving a measure of the information contained in the data. We model crossovers with a Poisson process and, under this assumption, present a novel Monte Carlo method for calculating the likelihood of a particular relationship for a given data set. The method provides a way to calculate the information content of data and find the maximum power that tests of relationship can achieve. Simulated data from cousin and greatgrandparent-greatgrandchild relationships is analyzed as an example.