TY - JOUR
T1 - On the number of siblings and p-th cousins in a large population sample
AU - Shchur, Vladimir
AU - Nielsen, Rasmus
PY - 2018/11/1
Y1 - 2018/11/1
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 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-(22p-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.
AB - 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 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-(22p-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.
U2 - 10.1007/s00285-018-1252-8
DO - 10.1007/s00285-018-1252-8
M3 - Journal article
C2 - 29876645
SN - 0303-6812
VL - 77
SP - 1279
EP - 1298
JO - Journal of Mathematical Biology
JF - Journal of Mathematical Biology
IS - 5
ER -