The existence and abundance of ghost ancestors in biparental populations

In a randomly-mating biparental population of size N there are, with high probability, individuals who are genealogical ancestors of every extant individual within approximately log2(N) generations into the past. We use this result of J. Chang to prove a curious corollary under standard models of recombination: there exist, with high probability, individuals within a constant multiple of log2(N) generations into the past who are simultaneously (i) genealogical ancestors of each of the individuals at the present, and (ii) genetic ancestors to none of the individuals at the present. Such ancestral individuals-ancestors of everyone today that left no genetic trace-represent 'ghost' ancestors in a strong sense. In this short note, we use simple analytical argument and simulations to estimate how many such individuals exist in finite Wright-Fisher populations.