%0 Journal Article
%A Shchur, Vladimir
%A Nielsen, Rasmus
%T On the Number of Siblings and *p*-th Cousins in a Large Population Sample
%D 2018
%R 10.1101/145599
%J bioRxiv
%P 145599
%X 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 ā eā(22pā1)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 10ā2. This confirms that, for large cohort samples, relatedness among individuals cannot easily be ignored.
%U https://www.biorxiv.org/content/biorxiv/early/2018/05/03/145599.full.pdf