The models of coalescent theory for diploid organisms are wrongly based on averaging over reproductive, or family, relationships. In fact, the entire set of relationships, which may be called the population pedigree, is fixed by past events. Because of this, the standard equations of population genetics for probabilities of common ancestry are incorrect. However, the predictions of coalescent models appear surprisingly accurate for many purposes. A number of different scenarios will be investigated using simulations to illustrate the effects of pedigrees on gene genealogies both within and among loci. These scenarios include selective sweeps, the occurrence of very large families, and population subdivision with migration.