TY - JOUR
T1 - On the Number of Siblings and <em>p</em>-th Cousins in a Large Population Sample
JF - bioRxiv
DO - 10.1101/145599
SP - 145599
AU - Shchur, Vladimir
AU - Nielsen, Rasmus
Y1 - 2018/01/01
UR - http://biorxiv.org/content/early/2018/05/03/145599.abstract
N2 - 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.
ER -