Some definitions:
Y-chromosomal Adam: The most recent male-line ancestor of all humans now living. Thought to have lived about 60,000 years ago in Africa.
Mitochondrial Eve: The most recent female-line ancestor all all humans now living. Thought to have lived about 140,000 years ago in East Africa.
Pedigree Collapse: Theoretically, you have 2 parents, 4 grandparents, 8 grandparents, etc., the number doubling for each generation you go back. These numbers rapidly become very large. You have, theoretically, 128 fifth-great-grandparents, 4096 tenth-great-grandparents, 131,072 fifteenth-great-grandparents, 4,194,304 twentieth-great-grandparents, 134,217,728 twenty-fifth-great-grandparents, and 4,294,967,296 thirtieth great-grandparents. Your thirtieth great-grandparents may have lived, on average, about a thousand years ago, at a time when there were far fewer than 4 trillion people in the world.
Pedigree collapse means that you have more than one descent from many of your ancestors. Theoretically, I have 64 fourth-great-grandparents, but those 64 slots are filled by only 62 people, because my maternal grandfather's parents were second cousins; I have two descents from Gutridge and Bridget Garland, and at least two from each of their direct ancestors. John's parents are fifth cousins once removed; he has two descents from Jacob and Elizabeth Hallman and from each of their direct ancestors. My 7th-great-grandparents, Hans Jerg and Elisabeth Rominger, were half-first-cousins; they had a grandmother in common, but different grandfathers. All their descendants have two descents from their common grandmother, Barbara Koch, but only one descent from each of her husbands.
Whether it can be documented or not, all people have this kind of pedigree collapse in their ancestry. If two siblings marry, as in the Ptolemy Dynasty of Egypt, pedigree collapse is rapid and dramatic. If two first cousins marry, as in the case of Queen Victoria and Prince Albert, it's less dramatic, but still pronounced. It's estimated that as many as 80% of all marriages have been between second cousins.
Most Recent Common Ancestor: The most recent person who was an ancestor (in any line) of any designated group. The MRCA of Western Europeans is thought to have lived about a thousand years ago. There's greater doubt about the MRCA of all humans, because it depends on whether or not there are isolated groups still extant that are very distantly related to everyone else in the world. If so, the MRCA of all humans now living probably lived 10,000 to 40,000 years ago. If not (which I think is more likely), the MRCA of all humans now living probably lived within the last 5,000 years, and possibly as recently as 2 or 3,000 years ago. Everybody now living is probably descended from both Confucius and Nefertiti, and it's thought that no human now living is more distantly related to any other human now living than 50th cousin.
Identical Ancestors Point: The farther back we go in time, the more common ancestors we have, and if we go back far enough, we reach a point where everybody living at that time is either the ancestor of everybody now living, or of nobody now living (because they had no descendants or their descendants died out). That point is the identical ancestors point, and it may have occurred as recently as 5,000 years ago. Every human who lived before the IAP is either an ancestor of all of us or an ancestor of none of us.
