To what extent does genealogical ancestry imply genetic ancestry?

Recent statistical and computational analyses have shown that a genealogical most recent common ancestor (MRCA) may have lived in the recent past [Chang, J.T., 1999. Recent common ancestors of all present-day individuals. Adv. Appl. Probab. 31, 1002-1026. 1027-1038; Rohde, D.L.T., Olson, S., Chang, J.T., 2004. Modelling the recent common ancestry of all living humans. Nature 431, 562-566]. However, coalescent-based approaches show that genetic most recent common ancestors for a given non-recombining locus are typically much more ancient [Kingman, J.F.C., 1982a. The coalescent. Stochastic Process Appl. 13, 235-248; Kingman, J.F.C., 1982b. On the genealogy of large populations. J. Appl. Probab. 19A, 27-43]. It is not immediately clear how these two perspectives interact. This paper investigates relationships between the number of descendant alleles of an ancestor allele and the number of genealogical descendants of the individual who possessed that allele for a simple diploid genetic model extending the genealogical model of [Chang, J.T., 1999. Recent common ancestors of all present-day individuals. Adv. Appl. Probab. 31, 1002-1026. 1027-1038].