Ancestor Paradox

[Jose AR]

I couldn't sleep the other night because I was thinking about my long line of ancestors. I have been thinking about the growth of numbers when you double a number over and over. The number grows very big after not that many repetitions. So I have 2 parents, 4 grandparents, 8 greatgrandparents, and so on. So in 60 generations, about 2000 years, the number is too big to be true. I know that populations grow over time, but with this thinking the population grows the further back you go. I figure the answer has to do with cousins but can't see how. Also, new species (humans) probably start with very small isolated populations, but are subject to the same paradox. Can anyone help me with this?
Jose

[Tank]

Do you have a link to the explicit details of the paradox you are trying to resolve?

[Ecurb Noselrub]

Part of the paradox can be resolved by considering the tribal nature of earlier generations.  There was probably a much higher incidence of what we would refer to today as "incest" during those times. So you would probably find, for example, that one level 10-great grandfather was the father of more than one of your level 9-great grandparents.  That would cut down on the required number of ancestors somewhat.  If you started with a bottleneck of one woman, for example, such as "Mitochondrial Eve" 200,000 years ago  (see article on her at  http://www.sciencedaily.com/releases/2010/08/100817122405.htm )  , all current humans might come from her.  This means that, of necessity, there was "incest" at probably multiple levels downstream from her (using "incest" not in a legal or moral sense).  That cuts down on the total number of required ancestors.  Am I making sense?

[Pharaoh Cat]

There was probably a much higher incidence of what we would refer to today as "incest" during those times.

In fact I think the Ancestor Paradox demonstrates the logical necessity that not too long ago, incest as we currently define it must have been commonplace.

[xSilverPhinx]

Besides tribal inbreeding there were also bottleneck moments in certain times and places that shaved off a portion of the population, us coming from a relatively small group of them. There is waaaaaay less genetic variation in humans than in the chimp population, for instance, because of this.

[Whitney]

ya, basically if you go far enough back you find out that we were all related...so it's not a paradox.

[Buddy]

ya, basically if you go far enough back you find out that we were all related...so it's not a paradox.

I don't know the thought of being related to Asmo is pretty terrifying. 

But these guys are right, most of our ancestors were likely in an incest thing a long time ago.

[Tank]

ya, basically if you go far enough back you find out that we were all related...so it's not a paradox.

I don't know the thought of being related to Asmo is pretty terrifying. 

But these guys are right, most of our ancestors were likely in an incest thing a long time ago.

Given your Scandinavian heritage you're definitely related to Asmo.

[Asmodean]

I don't know the thought of being related to Asmo is pretty terrifying.  

Well, The Asmos come from Planet Asmodea, which is not even in this galaxy... Or so I'm told   AND they are of a massively mixed heritage.

[OldGit]

There is a very small town not far from my home, where they all look the same.  Everybody is everybody else's cousin, not to mention brother, father and uncle.  My impression is, it's not very helpful genetically.

[Jose AR]

I don't have any links, cause I just thought about it. We think about this idea as if it was in the past; but extrapolating into the future, my greatgrandchildren at the 10th tier will have 2048 ancestors. This will take about 200 to 300 years. If the world population then is about the same as now, say, 6 billion, then there should be 12 trillion people alive now! obviously I don't understand what's going on or where the error is. Is there that much incest? I know Darwin married his cousin. Is human sexuality harem based? (if that even changes the math). If incest was the answer to the paradox shouldn't we all know about cases of people who mate with second or third cousins? The solution can't be (I don't feel) that in the distant past incest was common, because in the present I have children who will marry single individuals who have 2 individual parents.

Am I crazy?

[Davin]

I don't have any links, cause I just thought about it. We think about this idea as if it was in the past; but extrapolating into the future, my greatgrandchildren at the 10th tier will have 2048 ancestors. This will take about 200 to 300 years. If the world population then is about the same as now, say, 6 billion, then there should be 12 trillion people alive now! obviously I don't understand what's going on or where the error is. Is there that much incest? I know Darwin married his cousin. Is human sexuality harem based? (if that even changes the math). If incest was the answer to the paradox shouldn't we all know about cases of people who mate with second or third cousins? The solution can't be (I don't feel) that in the distant past incest was common, because in the present I have children who will marry single individuals who have 2 individual parents.

Am I crazy?

Do a lot of geneology, you'll find that many people have common ancestors. This is a problem of trying to think things through when the facts will set you straight.

[xSilverPhinx]

I don't have any links, cause I just thought about it. We think about this idea as if it was in the past; but extrapolating into the future, my greatgrandchildren at the 10th tier will have 2048 ancestors. This will take about 200 to 300 years. If the world population then is about the same as now, say, 6 billion, then there should be 12 trillion people alive now! obviously I don't understand what's going on or where the error is. Is there that much incest? I know Darwin married his cousin. Is human sexuality harem based? (if that even changes the math). If incest was the answer to the paradox shouldn't we all know about cases of people who mate with second or third cousins? The solution can't be (I don't feel) that in the distant past incest was common, because in the present I have children who will marry single individuals who have 2 individual parents.

Am I crazy?

You have to remember that before fast travel was easy, people mostly were born and died in their small rural villages. Not like these days were you aren't as restricted to one small geographical area, and people are more individualistic. Tribal/village inbreeding did occur, and chances are, many of your ancestors are your ancestors many times over, especially the further back you go. 

There is a very small town not far from my home, where they all look the same.  Everybody is everybody else's cousin, not to mention brother, father and uncle.  My impression is, it's not very helpful genetically.

No, it's not. The more variation there is, the better for the species as a whole.

[Pharaoh Cat]

I don't have any links, cause I just thought about it. We think about this idea as if it was in the past; but extrapolating into the future, my greatgrandchildren at the 10th tier will have 2048 ancestors. This will take about 200 to 300 years. If the world population then is about the same as now, say, 6 billion, then there should be 12 trillion people alive now!

No.  Population is increasing over time, not decreasing.  No logic can be valid that implies a falsehood.  If our logic implies population is increasing as we move backward in time, then our logic isn't valid, because it implies a falsehood.  But let me hasten to add that I know you realize this.  Otherwise you wouldn't ask if you're crazy.

The truth has to be that most of my ancestors have more descendants than I have ancestors.  This has to be true since population is increasing.  And lo and behold, I can find evidence very quickly.  For example, I have exactly four grandparents.  Yet my four grandparents, taken together, have considerably more than four or even two to the fourth power (sixteen) descendants.  The first generation alone was ten kids.  The next generation (my generation) is twenty-seven.  Ten plus twenty-seven equals thirty-seven.  Thirty-seven is more than four and is even more than sixteen.  Any way you look at it, population increased.

I wish I was more adept at math so I could eliminate the nagging conundrum you originally posed.  A skilled mathetician could, without a doubt, eliminate it.  I know this because the truth conflicts with what the conundrum implies, so the logic underlying the conundrum cannot be valid.  I look forward to someone with a head for math stepping in to resolve the dillemma for the rest of us.

[keithpenrod]

Having read the entire thread and being a mathematician, I'm not sure what the question is.  I'd be glad to help out, but I'm not sure what's being asked.  Let me try a couple explanations and see if I can avoid striking out.

If the question is: "How can I have 1024 ancestors 10 generations back when population is increasing over time, not decreasing?" then I think PC gave one really good response: your ancestors have more descendants than you have ancestors.  But this is only part of what's going on.  Incest is only one other possible explanation. 

But, think about it this way: being 10th cousins with your spouse is not typically considered incest.  I'm only assuming, but I believe that most biologists would say that being 3rd or 4th cousins (or more distantly related) would be enough genetic difference to qualify as non-incest.  So, when you list out your pedigree chart to the 10th generation past, you would list 1024 people in that one generation, but half of them could be the same people listed over again--not because of incest, but because people have common ancestors (perhaps 4th or 5th cousins, or something). 

So, in other words, you have 1024 different ways to go back 10 generations, but that doesn't mean that 1024 distinct people were your 7th-great-grandparents.  If each of your ancestors was required to be unique, then the logical conclusion would be that the population would halve with each generation and therefore would be extinct in a very short time.  (For example, our current world population of 7 billion would be extinct in 33 generations.)  Therefore, the only logical conclusion is that the further back you go in your pedigree, the more repetition of ancestors you'll find. 

In fact, if you spend any good amount of time in doing genealogy work, you'll find that you might have one ancestor that's a 6th-great-grandpa on one line and a 7th- or 8th-great grandpa on another line.  This is easily accounted for when parents have children several years apart.  I have cousins who are very young--the same age as some of my nieces and nephews--because my father was the oldest of 13 children.  He was done having children in 1986, but some of his younger siblings hadn't even married by that time.  Now that his children (my siblings) are grown and having their own children, his own siblings are as well.  Anyway, do this multiple times and you can see how easily you can skip a couple generations in one line of ancestry. 

Also, once you have two ancestors who are the same (for the sake of simplicity, let's just say you have a 7th-great-grandpa that shows up twice in your pedigree), then every generation back along those two lines will be the same as well.  So, in the 10th generation back, you have those two who are the same, but in the next generation back you have at least 4 that are the same, and the next generation at least 8 just because of those two that were the same in the 10th generation.  But remember that you'll keep finding new common ancestors, so 8 is only the bare minimum that must be the same at the 12th generation.  Therefore, the number of common ancestors you see in your line will increase at a rate of at least double each generation, which is enough to keep up with the rate that your total number of ancestors is increasing.  Therefore, in very short time you'll have tons of repetition.  So, in the 20th generation back, for example, you'll list about 1 million ancestors, but you'll expect at least half of them to be repeats of each other.