Single Line of Descent

Curious phenomenon where there's only one true descendant of the some legendary hero/villain or chosen one. Usually it's only that one person who can save the day or bring about The End of the World As We Know It. Because Destiny Says So, of course. And often it has to be the male line, or whichever keeps the last name. The fact that there's multiple branching into different last names doesn't count genetically for some bizarre reason.

This is curious in itself. Most family trees branch quite a bit due to multiple children having multiple children. In fact, if you look far enough into the past, you reach a point where every human being alive then is either the ancestor of everybody or nobody who is currently alive. Here apparently only one child was born per generation. In older legends, it was explicitly stated that only the firstborn "counts", but the socioeconomic systems that fostered that kind of thinking withered away, leaving only this trope.

Similarly, the sole true descendant is generally treated as essentially equivalent to their ancestor, having the same powers, personality, ethnicity, and so on. Never mind that, if the legendary hero lived twenty generations ago, he had roughly a million contemporaries who are just as closely related to the modern-day version as he.

Note that, in the present generation, if there is another sibling, he or she tends to be recruited by the Big Bad as the Evil Counterpart.

Occasionally it will be explained away that the Big Bad found and eliminated the rest, and the Supporting Leader happened to get to the last one in time.

Possibly related to the Identical Grandson. Only one in a generation can take the "legacy."

The last offspring of a Single Line of Descent is by definition the Last of His Kind.

Anime and Manga

 * In the Anime Blue Seed there was only one (well, two) people left of a bloodline whose lifeforce could destroy the Demonic Invaders.
 * Raideen: Akira Hibiki is a descendant of the ancient people of Mu and he must help Raideen save the Earth. With Akira, the line of descent doesn't extend very far.
 * Naruto: Averted with the Sage of the Six Paths, who spawned the Uchiha, Senju, and Uzumaki clans. Justified in the case of the Uzumaki and Uchiha clans in the Naruto and Sasuke are the only descendants because they are also the only survivors of the clans being annihilated.
 * The Nakatsukasas in Soul Eater. The eldest child is expected to inherit the Morph Weapon Dark is Not Evil/Chaotic traits, and Masamune took issue with the fact he did not (though he got the 'dark' bit right). Odd, in that the Demon Weapons are the result of experimentation and that Tsubaki's family is quite clearly not the only example. In fact, the others have branched out into more modern and outlandish interpretations of the word 'weapon'.

Comics

 * The DCU: Both used and averted with the immortal Vandal Savage, who has multiple descendants whom he harvests for organs, and a person he specifically identifies from amongst them as his daughter Scandal, leader of the Secret Six. According to Scandal, her legitimacy is down to the fact Vandal married her mother.
 * Star Wars Legacy seems to hint that this happened. It's been a hundred fifty years, and the only Skywalkers alive are Cade and his immediate relatives. It's hinted that the Organa Solo line got absorbed into the Antilles Fel line, whose descendant is the Emperor. No mention is made of the Solo-Djo line.
 * In the newspaper comic The Phantom, natives and pirates are led to believe that the masked crime fighter is the same man living for hundreds of years. He is, in fact, the son of the last guy. I don't believe they indicated there was ever more than one child, no girls, and they always were fit to take over.

Films

 * A character in Dogma is the only member of bloodline (through a sibling of the "ancestor" instead of the "ancestor" himself).
 * In Underworld. The Lycans are searching for a human descendant of the progenitor of both werewolves and vampires, but they need one with a specific gene and a wall filled with crossed over photographs tell us that there has been a lot of failures before the events of the movie. But that's because all they have to go on to find that one descendant is his last name, Corwin, which isn't exactly rare or unique. Depending on how long they've been looking for this guy, and killing the ones who don't meet their specifications, the Lycans may be the reason there's only a Single Line of Descent.
 * The Shadow, the Big Bad is the last descendant of Genghis Khan. And now compare this to what is written in the Real Life section.
 * Explained in The Covenant that only the firstborn males in each generation receive powers. There may well be many descendants of the original (male) witches of Salem, but only five males with the Power per generation (there are five families).

Literature

 * Not so in JRR Tolkien's The Lord of the Rings, where multiple lines and descendants exist. An example are the kingdoms of Arnor and Gondor, respectively founded by Elendil and his sons, who are descended from a sideline branch of the Numenorean royal family: in both cases there are various people (both properly royal and more mundane ones) appearing and mentioned as descending from the same ancestor as the "main descendant(s)" of that line. Gondor even eventually endured a civil war over the question of inheritance, had problems with multiple potential claimants, and eventually no viable successor could be found who would have pleased everyone, resulting in the Stewards taking over. When the Gondorians first had trouble finding a royal successor, the Arnorian line and kingdom was still fully intact, and the Arnorian king tried to take over (on account of both dynasties being descended from Elendil and being married to the last Gondorian king's daughter) but was rejected. His descendant Aragorn would later succeed where he had failed.
 * By which point, however, Aragorn basically was the last direct descendent of Elendil, thus re-invoking the trope.
 * In the movie of The Da Vinci Code, there is only one surviving member of  bloodline. (In the book, though, the corresponding character has a sibling, and it's stated that they aren't the only line of descent, just the most reinforced and "qualified". That apparently wasn't dramatic enough for the movie, though.)
 * Deltora Quest establishes that by tradition, the ruler of Deltora has only one child, meaning during the time of Deltora Shadowlands, Adin (the first king) has only one heir. If that heir dies childless, the power of the Belt will be lost forever.
 * The Belgariad book series featured the bloodline of the Rivan king, which only had one child per generation for centuries. This is justified due to prophecy keeping the family small so as to be easier to hide from numerous enemies. Seeing as almost the entire family was killed when they were secure on a small island surrounded by guards, this may be a good idea. Interesting in that the subject matter of one of the prequel books covers how the family was hidden/protected.
 * Except in Polgara the Sorceress, wherein Cherek wives of the descendants of the Rivan kings always had lots of babies. Either they all died, or Garion has bunches of n-th cousins running around..
 * The House of Usher is a classic example, as Poe describes them as having produced no side-branches and declined to a point where only two siblings remained. M.P. Shiel's "House of Sounds" used the same idea, with a family that had once numbered in the millions dwindling down to three. A partial subversion, in that the declining bloodline is traced through both sexes, with the Last of His Kind descendent being born to parents deriving from two distant branches of the family.
 * In the Hollow Kingdom Trilogy, both the Elf and Goblin Kings only ever have one son apiece. None of those messy succession debates here, no sirree!
 * Lampshaded in Prelude to Foundation, where a noblewoman claims she should be the Empress because her family descends from an ancient ruling house. A nearby historian remarks that with said dynasty ruling 5,000 years ago, half of the galaxy is their descendants.
 * In Legends of Dune, Camie Boro claims to be the only descendant of the last emperor of the Old Imperium. Given that the Old Imperium fell over 1000 years before, this is not very likely.
 * Played with in the Mithgar series with the "Lastborn Firstborns". A pair of mortal lovers become involved in a quest, but after a point, they're going to have to wait centuries to carry out the next step. They get married and pass their lore and quest items down the generations, hers to her firstborn daughter and then her firstborn daughter and so on, his to his firstborn son and so on. When the destined time finally rolls around, we end up with two characters who each look very similar to the ancestor whose lines of descent they've been following, but are no longer closely related. So they meet up, fall in love, and continue the quest, just like their ancestors.

Live Action TV

 * A rare female example in Charmed. The Charmed Ones are three sisters who are the last decendents of 17th century witch Melinda Warren. Apparently, up until the birth of the protagonists, there never was more than one daughter per generation.
 * Kind of subverted in season 4 when we find out about Paige. But of course nobody had thought of her yet in season 1 when the trope was established.
 * In the Star Trek the Next Generation episode "Sub Rosa", we learn that a "ghost" named Ronin has been bedding Dr. Crusher's female ancestors for centuries, moving from mother to daughter, and is now moving onto Crusher following the death of her grandmother Felisa Howard. The logical flaws start with the fact that all her female ancestors were apparently named "Howard", indicating that Crusher is the first woman in her family to lose her maiden name, despite her living in the twenty-fourth century and the ancestor this started with living in the seventeenth century. Not to mention what would happen if a Howard woman failed to produce a daughter. (Would Ronin have to move onto Wesley after Dr. Crusher died?)

Tabletop Games

 * Strongly averted in Legend of the Five Rings where the direct descendents of the two dozen or so gods and heroes that founded Rokugan number in the tens of thousands. And that's not counting the two million or so samurai that carry those gods' and heroes' names through fealty. It does appear in the first Imperial line, but only because when a new Emperor takes the throne, all of the other candidates must renounce their family name and be adopted into one of the secondary Imperial families. Interestly, this does lead to the logical conclusion of the Imperial family being wiped out in the first story arc. An heir turns up Moses in The Bullrushes-style in the third arc... but he's the new Big Bad.

Video Games

 * Averted in the Assassin's Creed series, where Ezio and Altair are from different parts of Desmond's family tree.
 * In the Castlevania series, only the Belmont family has the power to vanquish Dracula when he rises every 100 years (though there have been many exceptions). Each time he rises, there are only one or two Belmonts around to do the job.
 * The Morrises, a family that stepped up to the plate to battle Dracula when the Belmonts went missing, are said to be related to the Belmonts. The relation isn't pure, however, and they aren't able to effectively wield the Vampire Killer whip without significant cost to themselves.
 * Exception: The plot of the cell phone game Castlevania: Order of Shadows involves three Belmont siblings, two of them women. But only the guy gets to take on Dracula, and the game isn't considered canon anyway.
 * It is stated that the villagers in Castlevania: Order of Ecclesia are of the Belmont lineage, but don't have their last name.
 * In The Elder Scrolls IV: Oblivion, the realm is protected from the land of the Big Bad by Dragonfires, product of a pact between the Dragons and the Septim family. At the time of the game, the last Septim to be king is assassinated, laying the ralm open to invasion by the Daedric forces. The main plotline of the game involves finding the hidden son of the last Septim and getting him the Phlebotinum he needs to start the Dragonfires again. Or, at the very least, to stop the invasion...
 * Though it's an aversion as well: the murdered Emperor had other sons, three of them, in fact, all of whom were taken out in similarly nefarious assassinations shortly before the game begins (making the Cyrodiilian Secret Service the worst bodyguards in history). Martin survived because, as the bastard son of the Emperor, his existence was kept so secret that even he didn't know who he was.
 * Incidentally, if you sit down and read the in-game books, neither Martin nor Uriel Septim are actually blood descendants of the person who made the original pact in the first place. The original pact was between Akatosh and the Slave Queen Alessia. The Septims (ostensibly) descend from Tiber Septim. Firstly, Tiber Septim wasn't related to Alessia, and secondly, such levels of in-fighting, fratricide, and incest characterise the Septim dynasty that it's unlikely Martin is even related to Tiber. This is validated in-game when
 * Done in Chrono Trigger, where only the Royal Family of Guardina is said to be descended from Ayla and Kino, ancestors some 65 million years back. Then again, over the course of 65 million years, pretty much everyone can trace their lineage to them at some point.
 * In The Lost Crown, William Ager was a villainous example. Unusual in that he died of tuberculosis with no heir to pass on the family secrets to, hence let down both Destiny and centuries of bloodthirsty tradition.
 * Fire Emblem's Jugdral timeline has holy blood passed down from the Crusaders. Word of God explains that if the child of someone with "major" blood (and is able to use the Crusader's Ancestral Weapon) gets "minor" (just some stats bonus) or "major" blood is completely random (birth order and sex play no part) and that the blood can be determined by a birthmark, this doesn't explain why only nobility seems to have even minor blood.
 * Averted all over the place in Blaze Union., the descendant of Gill the legendary dragonslayer, mentions repeatedly that she's from the secondary line. Characters also discuss that due to the Imperial bloodline being so diluted and spread throughout the people, it's not unusual for children qualifying as Brongaa's descendants to be born in all walks of life; the interesting thing about Gulcasa is that he's the first pureblood to be born in centuries.
 * Also averted in Tales of Symphonia, where the family of the Chosen is huge, has many branches, and is scattered all over the world so that if something happens to one branch, the bloodline will still exist.
 * In Dragon Quest VIII, the Big Bad is tracking down the descendants of the Seven Sages who originally sealed him away, as their deaths are the only way to release his original body. The game establishes that only one descendant in each most recent generation is the heir (as Jessica's brother Alistair held the bloodline whereas Jessica just received magical strength), but that all goes to hell when it comes to Marta. She's still the holder of the bloodline even though she has a freaking son. It really makes no sense.
 * Inverted in Fable 3, only the youngest of the Hero of Bowerstone's two children gets any Hero powers.

Web Comics

 * Subverted in Girl Genius. Part of the plan of Zola (the fake Heterodyne) is to ally with and marry a direct descendent of Andronicus Valois, the Storm King. When Gilgamesh skeptically points out that, if the legends are true, half of Europe is descended from the Storm King, she angrily specifies that it's a descendent who the Fifty Noble Families of Europe will recognize.
 * Later, when she explains more of the plan to him, she specifies why this one's confirmed,
 * Subverted in Digger. The ghost of Helix, a wombat who's been dead for a thousand years, give or take, immediately pegs Digger as a descendant. He had nine sons a thousand years ago, so it's more likely than not.
 * Parodied in The Adventures of Dr. McNinja, where a demon can only be slain by one of "pure Belstein blood". There is only one left, who's deformed and in a wheelchair due to generations of inbreeding.

Real Life

 * Enforced in China by the government's one-child policy, to keep the already humongous population from completely exploding. It's been estimated that without this policy, there would be 400 million more Chinese people.
 * This trope is seriously averted with Genghis Khan: about 0.5% of the male population of Earth descends directly from Genghis Khan or his male relatives. Douglas Adams spoofs this in Hitch Hikers Guide to The Galaxy.
 * Not a spoof at the time, as the true scope of Genghis's genetic legacy didn't come to light until after Adams passed away. He was just making a funny contrast between Prosser and the Great Khan. That makes this Hilarious in Hindsight.
 * Also, the book specifies that he was a "direct male-line descendant" of Genghis Khan, apparently meaning the more improbable lineage in which the long chain from Prosser to Genghis Khan consists only of men.
 * Some 30% of Europeans have Charlemagne, or Charles the Great, as their ancestor. Charles was not a first-class fornicator - he had ten children - but all his offspring survived and had in turn children.
 * This is averted with pretty much anyone who had descendants, if you go surprisingly not far back in history. A paper in Nature demonstrated that if a person has four or five grandchildren, either their line tends to die out within a few generations, or the number of descendants begins to increase exponentially. Someone living two or three thousand years ago will either have no descendants at all alive today, or be an ancestor to a lot of people.
 * Averted with Sophia of Hanover who has over 5000 legitimate descendants. Out of these, all who are not Catholics or married to Catholics (still over 1000) are in line to the British throne.
 * Due to the fact that the members of European royal families tended to marry members of other European royal families, just about every royal in Europe is descended from her.
 * Due to the fact that her descendants were mostly royalty, and that royal men tend to have at least one mistress, there are even more illegitimate descendants. William IV of the UK alone had ten illegitimate children by his mistress, the actress Dorothea Jordan (he would have married her, but there would have been an uproar; remember Edward VIII? Now put that a hundred years earlier). Among those illegitimate descendants is David Cameron.
 * Sometimes intentionally attempted by dynasties to limit the number of people vying for the throne, land or fortune. Different cultures handled this in different ways:
 * In Europe, this often came in the form of sending surplus sons off to monasteries and various church jobs, ensuring no legitimate children. Alternately, younger sons would be sent to the army, where they would fight (and in many cases hopefully die on the battlefield); this, incidentally, is where we get the term "cadet" for a trainee officer ("cadet branch"=junior line of a noble house). If the line were about to expire, a monk or priest in such a position might be permitted to leave the Church and marry.
 * In Ancient Mesopotamia, aristocratic sons could end up as castrated but high-ranking officials at court. The Chinese sometimes did much the same thing.
 * In the Ottoman Empire, the successor was entitled to have all his brothers and half-brothers strangled upon being chosen.
 * Royal relatives in Ethiopia used to live in Gilded Cage prisons on top of high buttes in the wilderness, to ensure their genetic lines remained strictly under the reigning monarch's control.