Within a sample from a population, the distribution of the number of descendants of a subsample's most recent common ancestor

Sample n individuals uniformly at random from a population, and then sample m individuals uniformly at random from the sample. Consider the most recent common ancestor (MRCA) of the subsample of m individuals. Let the subsample MRCA have j descendants in the sample (m⩽j⩽n). Under a Moran or coalescent model (and therefore under many other models), the probability that j=n is known. In this case, the subsample MRCA is an ancestor of every sampled individual, and the subsample and sample MRCAs are identical. The probability that j=m is also known. In this case, the subsample MRCA is an ancestor of no sampled individual outside the subsample. This article derives the complete distribution of j, enabling inferences from the corresponding p-value. The text presents hypothetical statistical applications pertinent to taxonomy (the gene flow between Neanderthals and anatomically modern humans) and medicine (the association of genetic markers with disease).