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On the Number of Siblings andp-th Cousins in a Large Population Sample

Published Web Location Commons 'BY-NC-ND' version 4.0 license

1. The number of individuals in a random sample with close relatives in the sample is a quantity of interest when designing Genome Wide Association Studies (GWAS) and other cohort based genetic, and non-genetic, studies. In this paper, we develop expressions for the distribution and expectation of the number of p -th cousins in a sample from a population of size N under two diploid Wright-Fisher models. We also develop simple asymptotic expressions for large values of N . For example, the expected proportion of individuals with at least one p -th cousin in a sample of K individuals, for a diploid dioecious Wright-Fisher model, is approximately 1 − e −(2 2 p −1 ) K/N . Our results show that a substantial fraction of individuals in the sample will have at least a second cousin if the sampling fraction ( K/N ) is on the order of 10 −2 . This confirms that, for large cohort samples, relatedness among individuals cannot easily be ignored.

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