How can I make sure there is only one direct descendent over a thousand years?

Long story short, a thousand years ago a man killed himself halfway through a ritual, which stopped it in half (think Jumanji). In order to complete the ritual, the bad guys need the direct descendant of the original (his wife and kids survived). How can I make sure that there is only one direct descendant after 1000 years?

Note: This was first asked on the Writers Stack Exchange site, but they recommended me ask to this here as well.

• If you mean descent in male upon male line, then having only one of those after 1000 years is not uncommon; most male-upon-male lineages last less than 1000 years. If you also allow descent through women then it's more tricky. – AlexP Apr 30 '17 at 18:45
• I don't think "the father must always be male" is a very hard requirement to meet. – Erik Apr 30 '17 at 19:04
• The father "MUST ALWAYS" be male? Is this optional in your world ? 😂 – EveryBitHelps Apr 30 '17 at 19:04
• @Erik. You beat me to the comment by a few seconds! – EveryBitHelps Apr 30 '17 at 19:05
• Everyone believed Dan Brown when he wrote that book about a single descendant of a certain historical figure. And it was 2000-ish years later. Just go for it. – Mindwin May 2 '17 at 12:27

The problem: if you have multiple descendants in a generation their number of descendants will balloon. If you limit number of descendants each generation to have only 1 male at any given time it is too risky: you risk having your line wiped out when the sole male in the line is in a terrible croquet accident and cannot conceive any more progeny.

A way to narrow it down to 1 at the requisite time is to have there be some manageable number more than 1 at prior times, and then have all but one individual die or be killed prior to or during events of your story. There could be some systematic tracking down of these known individuals, like the systematic killing of heirs to a throne. Or a genocide that gets almost everyone with this ancestry. A genocide would be good because they do happen and could be unrelated to events of the story, but would be really bad luck for the people who hope to complete the ritual and realize what happened to the individuals they need.

Or you could somewhat boringly invoke the magic and have there just be one male in each generation, who never plays croquet and always conceives just one son, who in turn always lives to reproduce. Amazing good fortune.

• Upvoting for the terrible croquet accident, these happen all the time – Kilisi Apr 30 '17 at 22:17
• reminds me of Jet Li in "The One"... – Michael May 1 '17 at 2:07
• Also with this approach, you could hide your character "in plain sight"; something like "after the parents were murdered when he/she was at a young age, he/she lived with a godparent who adopted their name with the knowledge." Never underestimate the mentor/father figure trope. – Anoplexian - Reinstate Monica May 1 '17 at 14:24
• Instead of a genocide, you could have a disease that people with his bloodline are particularly vulnerable to. – Brian McCutchon May 2 '17 at 0:18
• There's also the option of a combined approach: there is a single heir, but if they die without leaving offspring, then it passes to the nearest available relative, like a cousin or someone. – anaximander May 2 '17 at 8:39

You don't necessarily need there to only be one living descendant, given your story purpose. In fact, this would break suspension of disbelief if taken literally, as being simply too improbable. You only need there to be one known living descendant, which is an important difference.

There's a lot of ways to go about this. You could have some disaster wipe out records of family lineage in an area where most of the family's descendants had been, with the only known survivor being in some sufficiently distant area; even if some of the others survived that disaster, they wouldn't be readily identifiable as descendants, especially if they didn't actually know it themselves.

Andon offered another idea in a comment: bastard/illegitimate children. Over a thousand years, this is more or less guaranteed to occur multiple times. They wouldn't be officially recognized as part of the relevant lineage even if it was genetically true, and as such would most likely not make it onto any relevant family trees. End result: lots of descendants with the necessary bloodline, but who would probably in the "present" (the time of your story) never be recognized as having the appropriate individual as an ancestor.

Really, the more surprising thing would be if any lineage at all could be accurately traced back 1000 years without modern technology. Which brings up another possible solution: have one branch of descendants become the royal family of somewhere or other (or nobility, etc.) while the rest of said descendants fade into obscurity as farmers or craftspeople that likely don't recall who their ancestor was five hundred years ago or more.

In recent years, have some tragedy happen (a plague sweeps the royal castle, a coup deposes the king and slaughters most of the royal family, a mother dies in childbirth and leaves the king with only a single heir, whatever you can think of) that leaves only one survivor. Fabricate history as you please: perhaps your protagonist is trying to take back the kingdom; maybe they got smart, chose to skip the royal intrigues, and settled down to a simple life (or are the son/granddaughter/whoever of that person). This leaves only one family of the appropriate lineage whose lineage could hope to be verified. Whoever was formerly of that lineage before the royal family came about would be impossible to ascertain, so it doesn't even really matter what became of that chunk of the family tree.

• Also: Bastards. In the original definition. Joe Secondson goes and has fun with some tavern girls who end up with kids, but they're not "Official" and aren't tracked or cared about. And don't forget murder/early death cutting out good chunks of a living family. Pox comes and wipes out 7 of the 8 children and the father. Mother re-marries and has more, but only the one kid has the father's blood. – Andon Apr 30 '17 at 23:44
• @Andon Good point about the bastard angle. As for early death/etc., I covered that under the royal family idea (plague, violent coup, and so on). – Palarran May 1 '17 at 0:24
• I can trace back my lineage in direct male line to 1273, nearly 800 years, so it isn't completely impossible. But I have to admit that the family held a minor noble title since 1634 and prior to that consisted almost entirely out of successful merchants and gold and silver smiths (many prominent guild-members), with a lot of second sons being clergy. Makes the family far more noticeable through the ages than what normally would be the case. And they mainly lived in a city where the archives never got destroyed by fire. There are only 3 remaining male descendants. All other branches died out. – Tonny May 2 '17 at 13:54
• This approach has the downside that, after a thousand years, almost everyone in the general geographical region of the original ancestor will be a descendant of any given person who had children. Family trees branch exponentially (usually), and exponential processes can get really big after 20 or 30 iterations. So the Bad Guys would have the option of just taking random nobodies off the street and attempting the ritual; after a few tries, they'd hit a descendant by accident. – Maxander May 2 '17 at 20:18
• @Maxander That is entirely true, which is why I mentioned the "destroyed records" option: if fire swept through the local library and carried off all the family trees, nobody is going to know to look there for the descendants. If, for example, the one known descendant is currently living in region A and that catastrophe occurred in region B, where A and B are as far apart as Spain and Russia, it's not practical in pre-industrial times to expect the Bad Guys to know about those other descendants. – Palarran May 2 '17 at 20:29

An option is to instead have a "mantle" that gets passed down through the descendants. When the current holder dies (or gets too old or something), it gets passed automatically to another. What matters for the ritual is using the current holder of the mantle. The bad guys just need a way to track or test for the mantle.

This could also allow for some plot bends and twists if the bad guys find the current holder, who dies accidentally in a chase, or know what the bad guys are up to and commits suicide, or something else along those lines. The bad guys need to quick get secure hold on the mantle holder to prevent such setbacks. Could make some useful backstory. Also, they may get the hands on a holder that's too young for the ritual and have to raise them, leading to appropriate complications (like a conscious).

• I think this is the correct answer. There is nothing special about the genetics or the bloodline. The special thing is the interrupted ritual of which there is only one regardless of how many generations pass or how many descendants the original has. Basically, the ritual is a self-sustaining magical construct (acquired sentience optional) that attaches itself to person most similar to its previous bearer after they die. It might even skip generations or leave a person if his personality undergoes drastic change. – Ville Niemi May 1 '17 at 14:53
• +1. The mantle could be a semi-sentient object that chooses a descendent of the original. Perhaps the object was originally owned by the bad guys, it chose the first person, and that person was killed when they managed to sneak the object out of the ritual to their family. The family wants to keep the object out of the hands if the bad guys, but the object will betray them to return to the bad guys unless it's in the possession of its current desire (a descendent of the original). So the family passes it down and figures out who it wants, only one step ahead of the bad guys. – Wayne May 1 '17 at 22:31
• +1 The mantle could even have belonged to the bad guys (one of their ancestors) at one point in history, before leaving because of a drastic change in personality, as suggested by @VilleNiemi. The bad guys are trying to steal back what they lost by lack of virtue. As such, the mantle would have to bestow some desirable power/trait worth fighting for, not just burden the virtuous holder. – CactusCake May 2 '17 at 21:41
• Watch the Star Trek: TNG episode "Sub Rosa" for an example of a sentient "mantle". – Robert Columbia May 6 '17 at 23:27
• If the magic is inherited only in the male-upon-male line (as, for example, royal crowns and titles of nobility in many western European countries, see Salic law), then this is not hard to believe; most male-upon-male lineages don't even last 1000 years.

• If the magic can also be transmitted through women even if it manifests itself only in men (as, for example, titles of nobility in England) then things are much more tricky, because after 50 generations just about everybody is related to everybody -- that is, if a person has any mixed-line descendants after 50 generations then they tend to be an ancestor of a very large part of the population. There may be one case where after 50 generations there is only one mixed-line descendant but that's rare.

But you don't need to explain it; make it one of the mysteries of the story. Indeed, the normal expectation would be that after 50 generation the original magic man would either be an ancestor of pretty much everybody in the area, or else have no descendants at all. That there is only one descendant is an unexpected twist, forcing the opponents to concentrate on that one last carrier of (a small part of the) magic DNA.

In the comments, user jamesqf raises the question of illegitimacy. He is of course right, the true biological male-upon-male lineages (if any), and the legally documented male-upon-male line (if still extant) are two different things. Humans are prodigious at making sure that genes flow and mix within the species; after 1000 years even groups which start with specific physical traits and which put a very strong emphasis of in-group marriage tend to look pretty much like everybody else in the area. As a well-known example, many Israelis of European descent look like Europeans and not like Levantines or Middle-Easterners, although their officially documented ancestors came from Palestine...

Tangentially, the last of the line is a common enough trope which doesn't need that much explanation; consider famous works such as Fenimore Cooper's The Last of the Mohicans, or Alexander Fadeyev's The Last of the Udege. (In reality, unlike the Mohicans, the Udege are still extant, barely; there are less than 2000 of them in the Russian Far East.) For fun, you may search for the phrase "last descendant" on Wikipedia...

• After 50 generations the original DNA would be pretty diluted, I'd have thought. I'm not sure you could even do a DNA match over such a long ancestor chain - you'd need to check that with someone knowledgeable in the field. And identifying someone (through e.g. paperwork) as an ancestor over a thousand years is something possible only under exceptional circumstances (even royal lines are lost on these timescales), – StephenG May 1 '17 at 1:04
• Re "most male-upon-male lineages don't even last 1000 years", you've got two problems here. First, men - especially kings and others with plentiful resources - tend to have a number of undocumented offspring. Consider the number of Fitzroys in British history, for instance. Second, women - even queens - do sometimes have sex with men who are not their documented husband, and sometimes produce children as a result. So the only possibly reliable way to find that one descendant would be massive DNA testing. – jamesqf May 1 '17 at 4:31
• @jamesqf: I expanded the answer a little, addressing those concerns. – AlexP May 1 '17 at 7:43
• @AlexP: Though WRT Israeli/Palestine, you also need to recall that a good many ancestors of the present-day Palestinians came to Palestine long after the Diaspora. Then there's the dilution factor: go back N generations, and you have 2^(N-1) male ancestors - some of whom (many if you go back far enough) are the same person. – jamesqf May 1 '17 at 18:12
• @StephenG I assume the "magic gene" is carried on the Y-chromosome, that way it persists down the male linage and does not "dilute" exponentially. It would still slowly change due to mutations.. – k-l May 1 '17 at 20:59

Perhaps I'm overlooking something but, if you're allowing magic, perhaps part of the curse of the half-completed ritual is that you're only able to conceive one child. Of course this has to skip the first guy who killed himself but maybe it cursed his blood-line.

Of course there is the danger that the first born could be killed...but maybe the curse protects them to a certain degree too, even prolonging life if they have yet to have any children.

• Good idea, but it’s highly unlikely that every male child would survive for 50 generations. – Michael May 1 '17 at 7:21
• @Michael Yeah I thought that which is why I added the bit about the curse protecting them to some degree. You don't want it over powered but maybe they're more resistant to diseases, a little stronger that normal, recover when maybe all else said they should have died. – FreeElk May 1 '17 at 10:23
• Making them immortal until their first son would be interesting. – Michael May 2 '17 at 12:33

Most answers are quite complex, I suggest a simple solution:

The firstborn enherits the magical properties of the parent, wether it's a boy or a girl. Because you're talking about magic, you can thicken it by adding that the person with the magical properties has a higher charisma, which attracts a partner with the urge to reproduce.

I just came up with: You could easily redirect the user, build up to the great moment and then.... Nothing. Because everybody assumed person A to be the firstborn, but there was a hidden person B!

• And there's the plot for your sequel – Don_Biglia May 2 '17 at 13:56

To limit the number of offspring, use marriage within the lineage. This is something observed in practice and called Pedigree collapse. Without such family marriages, anybody would have around 2^30 (1,073,741,824) ancestors 1000 years ago, exceeding the world population at that time.

Limit the lineage geographic mobility and restricted it to as small area. You can then use local major events to limit the number of survivors : epidemics, conflicts, etc. This pressure will create a bottleneck and reduce the lineage, allowing you to end-up with one remaining person quite easily.

There isn't a great solution to force having just one descendant from a Worldbuilding perspective. But there are a couple other things that you could do.

1. The simplest is that each generation chooses to have one and only one descendant deliberately. So there are only ever two to five descendants alive at a time (child, parent, grandparent, etc.). This person's parent, etc. are dead.

2. Change up the requirement. It's not any descendant. It's the current heir. So they either need this guy or they need to kill him off so that it goes to the next heir. Sort of Slayer rules (from Buffy the Vampire Slayer). Perhaps they don't know who the next heir is or even who all the heirs might be. So they'd prefer this guy, who is the current heir.

3. Create a countering force that wants to prevent the ritual from finishing. They've been popping off descendants. There's only one left. They may have been operating for a long time.

4. Highlander rules. There can be only one. They had to kill off the other descendants to concentrate the magic in just one.

These are all more plot-based than I'd like for this venue, but that's somewhat of a characteristic of the problem.

• An alternate take: all male heirs must fight to the death for the right to succeed. The losers are killed or castrated in order to prevent future claimants. This happens after the youngest male in that generation reaches puberty, but not too late so that the father can spawn another son should all the combatants die (or fall victim to a low blow from the losing party) – nzaman May 2 '17 at 12:11

The simplest method is often the best...

If there was some particular specific combination of genetics which had to be present: rare, double recessive gene required say (something to the effect of like a red head with straight hair, no freckles, attached ear lobes, and blue eyes)... then it would be entirely likely to have only one valid descendant, regardless of how many total descendants there may be.

• +1. And this isn't an unusual trope: there is some characteristic that is recessive and: 1) it's hard to tell if you actually have that characteristic -- particularly given that it's probably viewed as a myth or a scary story your great grandmother used to tell her kids, and 2) may take generations to show up. – Wayne May 1 '17 at 22:22
• As a side note, my list was non-random: all of the traits I listed are recessive in nature, based on my research... now imagine trying to get all of those recessive traits onto a single person! – nijineko May 2 '17 at 2:58
• Exactly, and I'm suggesting an enhancement: not only are the traits recessive, but the result isn't visible externally, and may not manifest without some kind of intervention. – Wayne May 2 '17 at 13:49
• Ah, yes, quite so. My examples were intended as just that, examples. I like the non-visible trait as well, actually. – nijineko May 3 '17 at 1:17

If the magical ability is passed along through the female line by mitochondrial DNA or in the male line by the Y chromosome, then only someone in the female line or the male line will do. And it is quite reasonable for someone to have exactly or almost exactly the same mitochondrial DNA or Y chromosome as their ancestor a thousand years and about 30 to 40 generations ago.

And of course the number of a person's descendants in male only or agnatic descent or in female only or matrilineal descent will be much smaller, often a tiny fraction, of his descendants in mixed male and female descent.

If it is consistent with your plot, the characters who want to complete the ritual may have to leave that world for almost 1,000 years if they are aliens or demons instead of human cultists. Then when they return they may innocently ask where they can find the son of the person who committed suicide and learn that humans only live for about 70 years, and almost nobody can trace their ancestry back 1,000 years. Oops!

Then they may have to frantically research human heredity to find out if they have to search for male line descendants, or female line descendants, or if mixed male female line descendants will do. They may find that they have to trace female line descendants and humans only keep track of male line descendants, or vice versa.

Some lineages get smaller and smaller each generation, until they die out. Some lineages get bigger and bigger each generation until they become enormous. Some lineages get bigger over generations and then get smaller over generations and then get bigger again in a cycle. So someone trying to trace a lineage may find that the descendants grow in number to several dozen and then shrink to only one and then grow in number to dozens and then shrink to only one again, and may fear that the numbers may shrink to zero sometime.

And if someone needs the rightful heir of someone who lived 1,000 years ago there are many different types of inheritance rules and someone may have different heirs according to different inheritance rules. For example male-preference primogeniture and male only or agnatic primogeniture are two different rules. And in one case for about 450 years the same persons were heirs to one dynasty by male-preference primogeniture and heirs to another dynasty by agnatic primogeniture, but over sixty years ago the two sets of heirs separated at last.

And single line of descent trope:

http://tvtropes.org/pmwiki/pmwiki.php/Main/SingleLineOfDescent[2]

Added 0-18-2017. Because humans have 2 genders and it takes 2 to reproduce it is necessary for the average couple to have at least 2 children to maintain the population level.

A fictional gender less species might have each person who reproduces have only one child since they need only one parent. Thus there could be only one direct descendant over a thousand years if it is a nonhuman species or future humans modified by science.

It gives a rather elementary discssion of the mathematical improbability of someone having one, and only one, descendant alive after 2,000 years.

• I may add that some Chinese families trace their ancestry - accurately or not - back to the Yellow Emperor almost 5,000 years ago and a few Japanese, Armenian, Georgian, Welsh and Irish families go back to about 500 AD. – M. A. Golding May 3 '17 at 18:01
• And also see my answer here: movies.stackexchange.com/questions/106330/… - where I elaborate a bit on the mathematical improbabillty of having one and only one descendant after 2,000 years. – M. A. Golding Jan 18 at 22:24

One is the lonliest number.

You'd expect the number of descendants to either diverge to a large fraction of the entire population, of disappear completely. This will be true of almost any way to describe "descendant", unless there is a serious feedback loop.

The hard part is avoiding extinction; I can give you a dozen feedback loops that keep the number from diverging. For example, the good old highlander trick, where people with the gene can detect each other and are compelled to kill each other for whatever reason.

The problem is that once the values are small, random flux means that there is a increasingly decent chance at extinction. 1 is a very small number.

We could go with feedback loops in each direction. Imagine the line has a reserve of magical luck. But this gets diluted when there are more of them, and the one with more luck actually imposes bad luck on the other members of the line in order to give more luck to its source.

The sole descendent thus has lots of luck, and survives. When there are more, the stronger bearer of the luck gene kills off the weaker members, unless they are focused on the survival of the stronger bearer. Luck remains concentrated, a single descendent is a given.

The "luck" could be something more sinister. Imagine if there is a demon who is watching over the line, and an order of assassins trying to thin it out. When the demon is distracted they succeed; when the demon is protecting one mortal, they don't stand a chance.

Another possibility is that the ritual requires a specific combination of bloodlines. What if there wasn't just one person in the ritual, but a set of them?

In order to complete the ritual, you need someone who is a descendant of all of them, as there is a limit on how many more people can join the ritual, and a requirement that every bloodline be present.

So the last remaining descendant could instead by a really careful breeding effort by the organization in question. They would have to find validated direct descendents of each of the bloodlines, perform specific costly rituals on them to "bring the blood back up", then breed them.

Such an effort would take literally generations of effort. Things would go wrong along the way.

Toss in a time based limitation (celestial alignment? 1000 year deadline?), and it might not be the sole descendant but rather the only viable candidate.

• I did a simulation once dealing with "percent of the population that is genetically related to an individual." My starting parameters had said individual having 3 offspring in a population of 100 total members. Hitting 100% saturation took hardly any time at all (12-15 generations). Even scaling back the initial percentage ("3%" to more like "0.03%") and trying to restrict spread, the end result was still total saturation in about 15 generations. TL;DR I have a character who is the literal father of his species. – Draco18s no longer trusts SE May 1 '17 at 21:18

Magical Curse

Maybe the line is cursed such that only one child ever survives to age of maturity. All others die of not-quite-believable, but not-quite-impossible circumstances like disease or accident. This could be a side effect or backlash from cancelling the ritual. Or it could be related only tangentially.

Attacks

If there is a faction trying to find the living heir, maybe there are other faction(s) trying to stamp out the line and prevent the ritual. Maybe they've sold out their morals to the cause and are willing to kill children, even. But maybe, just maybe, some small faction within this group wants to keep one heir alive "just in case." They're watching over that heir, but destroying the rest of the family line. Or the group wanting to complete the ritual has fought desperately over the centuries to preserve the line from the assassins, and now that this is the last one left, they must complete the ritual before it is too late.

Why must there be only one?

Maybe there's only one known heir. Maybe others exist that are sufficient for the ritual, but this one person is the only heir they can prove lineage for. Maybe the family was split up in an orphanage, and the records were lost. So there's another heir... maybe... somewhere. But no one knows about him or her. Or their could be bloodline heirs but not legal heirs via children born out of wedlock. Again, their existence may not be known with sufficient accuracy to confirm their relations. But someone might know. Or be desperate enough to try them in the ritual anyway.

Actually having only one living person who is a direct descendant on the male line is easier than you might think.

1000 years is approximately 33 generations. While i'm currently a bit unsure about the math, the basic idea is the following:

A mal descendant can have 0-n children. It is easily conceivable that any given male descendant has only female offspring. This ends that line for this given descendant.

Over 33 generations, you can of course have any number of male descendants, but that includes 0 an 1, too.

So, there need not be any magic, no secret societies need to be involved, no wrath of any deity of your coice, even murphy doen't have such a hard job achieving the goal you have in mind.

Basic chance can easily achieve what you have in mind.

For a plot twist, it might even be that your current events are triggered by the fact that the only other male descendant died without having male offspring, thus just reaching the point where there's only one left.

So, long story short: Since it's not uncommon and not difficult to achieve, the mere fact that it happened should be credible enough.

• Why do you assume descents of females don't count? Having only daughters merely means your family name dies out (and even then, only in patrilinear societies), but, a priori, not your magical properties, since you still carry the blood/genetic heritage of that original ancestor. Since OP does not indicate that magic is transmitted via the Y chromosome, I wouldn't assume a male-only lineage as the sole possibility for a unique descendent. – Adrien May 2 '17 at 12:49
• @Adrien you are right... I somehow thought the question was abount the male lineage. But checking again i find that i am mistaken. I will thinkk about re-wording my answer, or deleting it, as soon as i find the time. – Burki May 2 '17 at 12:55

No magic is needed. There's always a conspiracy.

The direct descendant was always known (and enforced)

The bad guys know they need to wait exactly 1000 years for the ritual to complete, and that exactly one descendant must survive: the "magic" will thin among all the descendants. So they have watched your family over 1000 years waiting for this moment. They tracked your family, allowed a safe number of descendants to be alive at a moment given, to be killed if that number increases. In times of war or plagues, the bad guys kept your ancestor(s) safe in a remote island.

Maybe the nice guy who help your grandpa flee from that Warsaw guetto isn't such a nice guy after all!

Now the time to finish the ritual has come, and finally only one ancestor is necessary. The rest can be killed safely.

If that's too much for your bad guys to do, let that be done by the other group, which also know of the ritual and want to finish it for a different, maybe lighter, reason.

The shadowy organization could have been hunting this family for the past thousand years. Members will manage to evade the organization for some time, long enough to pass on their genes, but eventually the organization finds them and they either die fighting them or follow in their ancestors' footsteps and kill themselves to deny them. Always being on the run will make it more difficult for your bloodline to have multiple children, and could lead to a lot of children being born after their fathers have mysteriously died (or left on the doorstep of an orphanage by a mother who knows she can't raise them in safety) and having no knowledge of their bloodline until they come of age and they begin to manifest strange mystical powers (which the shadowy organization has some kind of artifact or ritual to alert them to). Then the shadowy organization comes and rousts them from their happy life and pregnant sweetheart (or sweetheart who got them pregnant as case may be) and begins the cycle anew.

The 'Good Guys' killed your family.

If the Bad Guys need someone alive in your line, then there are going to be a faction of Good Guys who don't want them to succeed. The logical (and less than moral) way to do this is to kill the whole family. You are obviously the son who was hidden away in secret with the shepherd family, so the Good Guys didn't know that you existed. Now, however, someone has uncovered your true identity, and a Wise Old Man has informed you that you must reclaim your lost heritage.

This is often handled by having the inheritance be a thing that's handed down - the one who holds the golden key that has in its handle the scroll with the ritual written on it, or whatever.

Then it doesn't really matter about who inherits what, and whether the firstborn's firstborn survived to have descendants, and so on, because that's already all handled by lawyers who have experience in that stuff, and the golden key will get into the right hands, or at least the best-appointed ones.

===

Birthmarks or other physical traits are similar, though perhaps a little hokey. But assuming they're genetic, but can skip generations, and members, you can have a reasonably small population affected. Particularly if you only get the mark if you have two copies of the gene, so only people in a fairly small community will get it - or people who are the result of incest.

So you'd have the whole tribe of people with the trait wiped out, only for the trait to arise in a single unrelated person many years later.

https://en.wikipedia.org/wiki/5-alpha-reductase_deficiency can be caused by a genetic trait that works this way; it causes children to be born apparently female, but become male when they reach puberty. There was a case in London where a young lady discovered she had this condition only on her wedding night! She had no connection to existing known populations with this trait, but on investigation it was discovered that her mother was also her sister, which granted her two copies of the gene, from her father/grandfather.

Although answers hinting to this have been given already. I believe it's worth following this line of thought.

In my personal opinion, wiping out the entire family is the best way to make it widely-known and make certain there are no survivors/only one survivor.

Thinking about it that way, there are quite a few cases we can create.

1. The bad guys kill the relatives, leaving only one (whether it's to secure possession of his power, or anything else, I'm sure you can think of a reason why they'd do that).

2. A widespread disease, resulting in the death of several people in his family line. (Considering your original progenitor had had "kids" and not a single one, make it country-wide, or even worldwide).

3. The ritual itself could have side-effects since it's been stopped halfway through, and his family members would suffer from some sort of curse that has effects leading to there being only one to a few survivors.

4. One of the descendants had a bastard son, an accident/genocide wipes out ALL of the main family, and the bastardized kid's existence comes to the bad guys' knowledge. This could have quite a few variations in and of its own.

Well, I'm sure there could be a more practical way to go on about this, but that's my two cents.

It all begins with HOW we can know he's the right one

The premise of the question relies on 'the bad guys' only being able to locate or confirm one direct descendant, rather than there necessarily only being one direct descendant in existence. This isn't all that hard:

1. It's all about genetics - If they're searching for a particular genetic marker in common with the original ancestor, it's not implausible that only one male descendant now has that particular special marker. There can be lots of other descendants, but the rest will all be 'the wrong one'.

2. It's all about traceability - Maybe nobody knows anything about the genetics of this ancestor. But perhaps your character's the only individual who can be proven to have a genetic link back to the original man. Sure, there could be many others in existence, but if there is only one anybody can actually identify, then they may as well be the only descendant.

3. It could be all about geography - you could have all of the descendants in a remote geographical area, and then the single main character becomes the only one who is in an accessible region to the 'bad guys', or the only one who escapes from the region where the rest are living.

4. Loose ends are sometimes more plausible than tied up ones - perhaps we can't perfectly tie it all up so that the situation is intuitively plausible with just one descendant. If we make the solution practical rather than perfect, then that could help out with developing the plot later. If the main character or the 'bad guys' can't be 100% certain that there isn't another descendant, this could provide for a useful plot device later on.

"How can I make sure that there is only one direct descendant after 1000 years?"

Scientifically you can not. Just magic is applicable here. But there are real world situations when "there is only one direct descendant after 1000 years". In instance: there are some animal species that have only one individual let in the whole earth. Yes, they are close to total extinction. May be this, and chiefly this, urged the bad guys to finish the unfinished ritual :)

I agree with Will on most that you can't risk having only 1 decendant over the full time period. To keep your family line small you could work with the "greater good" trope - create a cult that knows about the ritual and its requirements. They know that the only way to prevent the ritual from ever being completed is to erradicate the people of that bloodline, and they want to prevent it at any cost. They don't have to be malevolent either: In their eyes, killing all decendants they can find is just the only option. They are prepared to sacrifice one family to stop the destruction the ritual could bring. As for how they know if they've found a decendant, I would use something like a crystal - an object with the properties of the ritual (maybe one that was used in it?) that reacts to the blood of the family line.

What is the story importance of having only one direct descendant?

My guess is that this guy is a main character so you don't want to mess around with a dozen other potential candidates.

The probability that there really is exactly one is tiny. It would not be believable no matter how you explain it.

But the ritual is magic. The requirement can be more precise than "direct descendant". It could be the "most" direct descendant by some measure (e.g. following the oldest son in the line, unless it's a dead end, then follow the next one, etc.) Essentially: Think along the lines of succession. There is a crown prince, but if something happens to him, someone else will become the new heir to the throne.

This way, there can be many descendents, but only one of them at any given time is "qualified". If he dies, the next one is. Unless the family has its tree documented very well, it is quite likely that the current guy X is irreplacable to the bad/good/whatever guys because it would take forever to track down the next one in line.

If each descendant has one descendant on average, that is good enough. For example: if each descendant has equal chances of have 0, 1 or 2 children, the average is 1, which keeps the population stable.

I simulated this in Python. Starting with 2 descendants and simulating for 33 generations, in about 10% of the cases is there any descendant after 33 generations and in about 5% of those cases is there exactly one descendant.

Here is an example of a list that it generated:

[2, 3, 4, 6, 4, 6, 7, 6, 7, 6, 8, 8, 8, 8, 13, 10, 12, 12, 11, 9, 8, 6, 8, 8, 7, 4, 4, 6, 6, 5, 5, 7, 3, 1]