Geneology and/or math question.

[Third Eye Open]

Not sure what kind of math to do for this, so if anyone can give me a ballpark answer or any tips on how to figure it out that would be much appreciated!

I want to know how many descendants an immortal person would have if they sired an average of one child every 30 years for 1000 years. The children themselves would have the same likelihood as any other children of surviving to have children themselves (what that chance is, i don't know, but it probably gets a lot higher as we approach present day). So if we started 1000 years ago, how many descendants would this person have today? Ten thousand? Ten million?

Alternately, if the above number turns out to be high, what if instead of measuring descendants we were measuring people who had some special trait passed on by the immortal person (not immortality). This trait would be passed on to children 100% of the time, but only males would be able to pass it to the next generation, so if someone had a single female child, that line would lose the trait. Ballpark estimates for number of people with said trait after 1000 years?

 

[Molinaro]

Off the top of my head, I would say 42.

I'd need a bit more time to come up with something more accurate.

 

[I Ratant]

ISTR something like this about vampires, with one biting a person a month, and that person biting a person a month... In a very short period... hundred years? everyone living would be a vampire.

 

[Wowbagger]

Immortal people can't sire children until they cut off the heads of all of the other immortal entities. And, they cease to be immortal at that point, anyway.

That is why I wear a neck sheild.

 

[LostAngeles]

So we need to know a few things:

Are we looking for the total number of descendants and not living descendants after x time?

Are the children also immortal?

This will help us set up the basic model. Also, we're presuming that these children are not mating amongst themselves, yes? (Give a yes or no answer to this. We just want to start off with a basic model and we'll adjust it as needed)

 

[Smackety]

Somewhere around 2^30. What is that - a billion?

 

[Smackety]

Double

 

[Third Eye Open]

So we need to know a few things:

Are we looking for the total number of descendants and not living descendants after x time?

Are the children also immortal?

This will help us set up the basic model. Also, we're presuming that these children are not mating amongst themselves, yes? (Give a yes or no answer to this. We just want to start off with a basic model and we'll adjust it as needed)

Living descendants only. The children are not immortal, and have no special privileges.

For ease, the children will not be mating with each other.

 

[sol invictus]

I want to know how many descendants an immortal person would have if they sired an average of one child every 30 years for 1000 years. The children themselves would have the same likelihood as any other children of surviving to have children themselves (what that chance is, i don't know, but it probably gets a lot higher as we approach present day). So if we started 1000 years ago, how many descendants would this person have today? Ten thousand? Ten million?

Let's first ask how many descendants someone in 1000 CE had. Suppose on average each parent has 3 children that survive to reproduce. Then the number of descendants of an average person would be 3^n, where n is the number of generations.

But in 1000 years there have been 40 generations or so, and 3^40 is much, much larger than the current population of the earth. Which means any given person in 1000AD is the ancestor of a significant fraction of the world's population today.

And in fact you don't have to go back much longer than that before everyone whose line didn't die out was the ascestor of everyone alive today, particularly if you're willing to restrict to one region of the world.

So I don't think the immortality is that important - even an ordinary person in 1000 AD has either zero or a mind-boggling number of descendants today.

 

[Uncayimmy]

Let's first ask how many descendants someone in 1000 CE had. Suppose on average each parent has 3 children that survive to reproduce. Then the number of descendants of an average person would be 3^n, where n is the number of generations.

But in 1000 years there have been 40 generations or so, and 3^40 is much, much larger than the current population of the earth. Which means any given person in 1000AD is the ancestor of a significant fraction of the world's population today.

And in fact you don't have to go back much longer than that before everyone whose line didn't die out was the ascestor of everyone alive today, particularly if you're willing to restrict to one region of the world.

So I don't think the immortality is that important - even an ordinary person in 1000 AD has either zero or a mind-boggling number of descendants today.

And thus we have pedigree collapse.

Wiki: The catch is that ancestors along the way married their relatives, intentionally or without knowing it. This is pedigree collapse; the closer the cousin, the bigger the percentage of the collapse. The greatest change is when two siblings marry, a 50% collapse. When first cousins marry, it is a 25% collapse, and so on.

This, of course, is not to be confused with being your own grandfather.

You know the old song, right? I marry a widow. Her daughter marries my father. That made my dad my son-in-law. Then I had a son. That made my son my father's brother-in-law. This, of course, made my son my uncle. And since he is my uncle, that makes him the brother of my wife's daughter. She, therefore, is my stepmother.

So, then my dad and my wife's daughter, who is also my stepmother, had a son. Being my step-daughter's son, that made me a grandfather!

And if you think about it, my wife is also my stepmother's mother. That makes her a grandmother to both me and my grandson. But since I'm her husband, that makes me a grandfather. Thus I am my own grandfather.

Q.E.D.

 

[Third Eye Open]

Let's first ask how many descendants someone in 1000 CE had. Suppose on average each parent has 3 children that survive to reproduce. Then the number of descendants of an average person would be 3^n, where n is the number of generations.

But in 1000 years there have been 40 generations or so, and 3^40 is much, much larger than the current population of the earth. Which means any given person in 1000AD is the ancestor of a significant fraction of the world's population today.

And in fact you don't have to go back much longer than that before everyone whose line didn't die out was the ascestor of everyone alive today, particularly if you're willing to restrict to one region of the world.

So I don't think the immortality is that important - even an ordinary person in 1000 AD has either zero or a mind-boggling number of descendants today.

Thanks Sol! You always seem to have the answers.

 

[casebro]

Sort of makes genealogy pointless, don't it?

 

[LostAngeles]

Let's first ask how many descendants someone in 1000 CE had. Suppose on average each parent has 3 children that survive to reproduce. Then the number of descendants of an average person would be 3^n, where n is the number of generations.

But in 1000 years there have been 40 generations or so, and 3^40 is much, much larger than the current population of the earth. Which means any given person in 1000AD is the ancestor of a significant fraction of the world's population today.

And in fact you don't have to go back much longer than that before everyone whose line didn't die out was the ascestor of everyone alive today, particularly if you're willing to restrict to one region of the world.

So I don't think the immortality is that important - even an ordinary person in 1000 AD has either zero or a mind-boggling number of descendants today.

Yeah, I was thinking this way too much.

 

[Beerina]

ISTR something like this about vampires, with one biting a person a month, and that person biting a person a month... In a very short period... hundred years? everyone living would be a vampire.

Well, it's also similar to an issue I was thinking about a few years back when it turns out "most" of humanity is a descendant of Genghis Khan or some such.

Well, if there are 4 generations per century, then working backwards, we have:

You
2 parents
4 gps
8 ggps
----- century
16
32
64
128
----- century
and so on

So that's 2**4 people per century. 2000 years is 20 centuries = 2**80 = 1.2 heptillion ancestors around the time Jesus was born.


And that's patently ridiculous.

So therefore, there was much crossing over long before then, which is also obvious since 43rd cousins not marrying for taboo reasons is highly unlikely, much less people tracking such things.


And from that it is tertiarily obvious that just about everyone today should be a descendant of just about everyone back then, in one way or another.

 

[Wolrab]

Now that that is settled, here is my horticulture and/or physics problem....

 

[I Ratant]

And considering the devastation the Black Death created in Europe, wiping out most everyone, reducing the available breeding stock, it's probably fair to presume that everyone with a European background is related.

 

[sol invictus]

And considering the devastation the Black Death created in Europe, wiping out most everyone, reducing the available breeding stock, it's probably fair to presume that everyone with a European background is related.

I think it's much stronger than that: everyone is related, and surprisingly closely.

Go back far enough, and you'll find an individual that every human currently alive is descended from. I believe the best estimates are that the most recent such individual lived between 2000 BCE and 1000 CE. That makes us all 50th cousins or so.

Go back a back further, and you'll reach a point where everyone alive then either has zero descendants or is an ancestor to everyone alive today. I think the estimates for that are around 5000 BCE.

Not very long ago at all....