I've been reading a lot of young-adult fiction this summer, looking for things to read to Bunny at bedtime, and also scoping out her options for books with positive social messages (gender roles, diversity, etc.) when she is old enough to read herself. Ancestry, and the talents/privileges/burdens that come with ancestry, are frequently a theme in these books. Fantasy is particular prone to this - all those poor orphan boys with their hidden destiny to take their "rightful" place on their great-great-great-great-great-great-great-great grandfather's throne.
The last two books I've read happen to fall into this category. Rick Riordan's The Kane Chronicles, follows two young siblings who are the most powerful magicians born in millenia, because they are born from two separate lines of Egyptian pharaohs; their father was a descendant of Narmur, while their mother was a descendant of Ramses the Great. They've inherited their predecessors' magical powers, and hey! the boy even looks like the portrait of Narmur on the famous palette!
Now, let's see, Narmur lived about 5,000 years ago, which is about 250 human generations. If none of their ancestors married other descendants of Narmur (more on that later), then Narmur contributed about 1/1.8x10^77 of the child's genome. Wow, them's some powerful genes!*
My second case in point can also be attributed to Mr. Riordan. Scholastic printed ten books in the 39 Clues series, all written by different authors, but Riordan was the author of the first book, and created the overall story arc. In this series, two young siblings are members of a powerful family that have contributed most of the important historical personages of the last 500 years. There are four branches of the family, from four original siblings, and the branches have distinct talents and personalities. Descendants of Jane, for example, are artistic geniuses (Mozart, Charlie Chaplin, etc.), while descendants of Luke are brilliant strategists (Napoleon, etc.).
Ignoring the improbability of a deep, yet meaningful, family connection between such diverse people as Benjamin Franklin and Toyotomi Hideyoshi, let's think about the logic of four separate branches of the family lasting 500 years. Around 25 human generations have passed in those 500 years. A person living today would have around 2^25 ancestors that were alive 500 years ago, or 33,554,432 people. The current world population is estimated at 6.9 billion. So, if everyone alive today had separate ancestors, there would have had to have been 2.3x10^25 people 500 years ago. Obviously, that's not the case. Estimates put world population 500 years ago at only 500 million. So any two people likely share a large percentage of their ancestry, whether they know it or not. This is particularly true for people of European descent, as is (of course!) the fictional family. Today, the population of Latin America, North America, Europe, and Australia is largely European, but Europe had a population of only 50 million or so in 1500. In other words, even if you accept the idea that each sibling of a certain family had personality traits and talents that they passed on to all of their descendants, those descendants would be so heavily mixed by now that every descendant of one sibling is probably a descendant of them all.
You know how every U.S. president is eventually found to have a European king in his background? That's not because kings' distant offspring are more likely to be presidents (although they might, for various reproductive and economic reasons), but rather because everyone likely has a king in their background. Almost all Europeans are probably related to Charlemagne. There just aren't enough medieval Europeans to account for our ancestry, otherwise.
*That number is not realistic for a variety of reasons, but you get my point.