Í'm pretty sure you are wrong about an individual having equal numbers of male/female ancestors, because you have not taken into account that the ancestor tree does not double every generation you go back. In fact, at certain points in history it will almost certainly get narrower. This represents multiple instances of one man or woman being an ancestor to many different ancestors of the individual concerned. Given your assumptions about populations - which are probably correct in general - I would expect if you go back say 100 generations, you will find fewer men who are ancestors of the "fuller" (nearer the expected power of 2) number of intermediate ancestors than women of that same generation.
I don't think that is correct, Iain. Each individual has 2 unique parents, 4 unique grandparents, 8 unique great grandparents, etc. The only situation where the individual could have fewer female ancestors than male is in the situation that Matt posited above: where one male ancestor has sired female offspring in more than one generation (i.e. your father is also your grandfather). Given the time required for a human female to reach the age of fertility and the life span of human males, an especially morally reprehensible man could sire, at most, offspring of his own daughter, granddaughter, etc. in about 5 generations. Looking back over those 5 generations, the individual descendant would have 5 female ancestors but only 1 male ancestor. However, looking back over 100 generations, the individual would have 100 female ancestors and 96 males ancestors. And over 1,000 generations, 1,000 female ancestors and 996 male ancestors. So the ratios approach the 1:1 female to male ratio that Heather is suggesting the further back you go.
No, the "unique" has to give way pretty quickly. After around 36 generations, the number of my ancestors would exceed the total number of humans who have ever lived (around 100 billion). There has to be considerable overlap, and I second Iain's conjecture that overlap is more pronounced for male ancestors.
The unique gives way very easily over generations. Start with someone say 20 generations back. His children probably knew they were siblings or half siblngs. Next generation - lower chance they knew they were all cousins. By the time you get 5 generations down, you are going start to have his descendents having childrent together. 10 generations down and it will be happening a lot because nobody will know they share that common ancestor. For Heather's theory to be correct, you need a mechanism to ensure that 'inbreeding' multi generations down is perfectly balanced. But she makes good arguments that it probably is not.
My simplest model: it starts with one m/f pair. A pair always produdes mmff offspring. Half of the m's do not reproduce, the other half get two f's each. Mating is only within a generation, and random.
The maximum number of male ancestors in the single generations is 1, 1, 2, 4, 8, 16, ...
The maximum number of female ancestors in the single generations is 1, 2, 4, 8, 16, 32, ...
An individual in generation 6 (64 individuals) can have between 5 and 7 male ancestors (7 = 1+1+2+2+1; you multiply by 2 until you run into the maximum), but between 5 and 10 female ancestors (10 = 1+2+4+2+1). It is too late here now to work out the probabilities...
Are you saying you think there are examples of individuals who are the product of two eggs or two sperm? Because that is what it would take for any one individual to have an unequal number of male or female ancestors. Somewhere in their genetic lineage someone would have had to result from two fathers or two mothers—a biological impossibility as far as I'm aware.
No. all it takes is for people who are distant cousins (ie several generations down from a common ancestor) - who probably dont even know they are related, to have a child together. Rinse and repeat.
Hm, the rare incest situation is clear to me, but the fact of a common ancestor generations back is not. I think I’d have to see it mapped to see your point.
2 parents, 4 grandparents, 8 great grandparents, 16 g-g-grandparents, 32 the generation before (gggs). It is highly unlikely the parents have any idea who their gg grandparents were, let alone the gggs. If that's nto enough just add a few additional generations.
Now, imagine 1 of the G4 men has children by 2 different (G4) women. Both of those children are among the 32 GGGs. There may be knowledge or suspicions they are related, but go forward a few gens, perhaps all the way to the parents, and nobody will know. Now you have 32+16+8+4+2+1 women ancestors, and 31+16+8+4+2+1 men.
Now you know how it can skew without obvious inbreeding.
So - the question is: how often is that likely to happen? How likely that a man fathers children by different women compared to women bearing children to different men - over all of history? I would guess it is definitely not 50-50, so variants of the above scenario happen more often to reduce the number of men in the ancestor tree. If nothing else, we know of a number of cultures where polygamy was normal, we know that wars often result in male invaders raping women, and we know that it was not unusual for women to die in childbirth and for men to take a second wife. I imagine plenty of powerful men fathering children by servants, but far fewer women doing the same. There are probably loads of men who never fathered a child because of dying in wars, or hunting etc before they managed it, or never getting sufficient socio-economic status to balance things out in terms of couples.
What about the case where the the same father is both my father and my mother's father. This case would suggest that it is possible for an individual to have more female ancestors than male ancestors.
You are correct, Matt. And in the situation where a man sires a child by both his daughter and his granddaughter, that offspring would have 2 fewer male ancestors than female. But that really isn't relevant to Heather's point. It's just something that precision nerds like you and me would point out.
For those that wonder about the word "grok". It is a Martian word meaning deep and complete understanding used by the first human baby raised on Mars by Martians, Valentine Michael Smith, who is the central character in Robert A. Heinlein's 1961 science fiction novel, "Stranger in a Strange Land." (With Google's obsession with political correctness and focus on wokeness resulting in its increasing inability to perform its core function, to find a specific answers to a specific question, it has made it impossible for find out how to underline text in Substack comments, I therefore had to resort to quoting the title to this book.)
I pondered for, oh, 5 seconds, on this topic when I heard someone claim that Alexander the Great is the most prolific ancestor on the planet. I don't remember exactly how that was stated, but the implication was he had himself quite a few females, and implied is that it isn't the worst obstacle in the world to be the son, grandson, great grand son of AtG. One may guess that its always been good to have a government job.
Ken’s comment below is close to the scenario you get with fertility doctors unethically using their own sperm to inseminate unsuspecting multiple women. Or just generally what can happen with pregnancy-by-male-donation with certain men as repeat donors.
Of course, as all roads lead to Covid these days, this practice is making Covid headlines because of an Israeli study on the “vaxx” impact on those little donated swimmers. To be expected, the published research attempted to obscure the actual findings lodged in the tables. And so one must root around in SubStacks to get an accurate analysis of the bad state of affairs.
Still, as Heather maintains, individuals have one genetic father and mother in the end. This is true as well for couples who use donated eggs — there’s a genetic donation and a biological mom that (hopefully) carries the baby to term.
The problem with this logic is that if one man has multiple children with multiple women, and those children or their progeny have children together, the offspring will have more female ancestors than male ancestors. That man will appear multiple times in the family tree next to multiple women.
Í'm pretty sure you are wrong about an individual having equal numbers of male/female ancestors, because you have not taken into account that the ancestor tree does not double every generation you go back. In fact, at certain points in history it will almost certainly get narrower. This represents multiple instances of one man or woman being an ancestor to many different ancestors of the individual concerned. Given your assumptions about populations - which are probably correct in general - I would expect if you go back say 100 generations, you will find fewer men who are ancestors of the "fuller" (nearer the expected power of 2) number of intermediate ancestors than women of that same generation.
I don't think that is correct, Iain. Each individual has 2 unique parents, 4 unique grandparents, 8 unique great grandparents, etc. The only situation where the individual could have fewer female ancestors than male is in the situation that Matt posited above: where one male ancestor has sired female offspring in more than one generation (i.e. your father is also your grandfather). Given the time required for a human female to reach the age of fertility and the life span of human males, an especially morally reprehensible man could sire, at most, offspring of his own daughter, granddaughter, etc. in about 5 generations. Looking back over those 5 generations, the individual descendant would have 5 female ancestors but only 1 male ancestor. However, looking back over 100 generations, the individual would have 100 female ancestors and 96 males ancestors. And over 1,000 generations, 1,000 female ancestors and 996 male ancestors. So the ratios approach the 1:1 female to male ratio that Heather is suggesting the further back you go.
No, the "unique" has to give way pretty quickly. After around 36 generations, the number of my ancestors would exceed the total number of humans who have ever lived (around 100 billion). There has to be considerable overlap, and I second Iain's conjecture that overlap is more pronounced for male ancestors.
The unique gives way very easily over generations. Start with someone say 20 generations back. His children probably knew they were siblings or half siblngs. Next generation - lower chance they knew they were all cousins. By the time you get 5 generations down, you are going start to have his descendents having childrent together. 10 generations down and it will be happening a lot because nobody will know they share that common ancestor. For Heather's theory to be correct, you need a mechanism to ensure that 'inbreeding' multi generations down is perfectly balanced. But she makes good arguments that it probably is not.
My simplest model: it starts with one m/f pair. A pair always produdes mmff offspring. Half of the m's do not reproduce, the other half get two f's each. Mating is only within a generation, and random.
The maximum number of male ancestors in the single generations is 1, 1, 2, 4, 8, 16, ...
The maximum number of female ancestors in the single generations is 1, 2, 4, 8, 16, 32, ...
An individual in generation 6 (64 individuals) can have between 5 and 7 male ancestors (7 = 1+1+2+2+1; you multiply by 2 until you run into the maximum), but between 5 and 10 female ancestors (10 = 1+2+4+2+1). It is too late here now to work out the probabilities...
That makes sense. And I think you and Iain are correct that the overlap is more pronounced for male ancestors.
Are you saying you think there are examples of individuals who are the product of two eggs or two sperm? Because that is what it would take for any one individual to have an unequal number of male or female ancestors. Somewhere in their genetic lineage someone would have had to result from two fathers or two mothers—a biological impossibility as far as I'm aware.
No. all it takes is for people who are distant cousins (ie several generations down from a common ancestor) - who probably dont even know they are related, to have a child together. Rinse and repeat.
Hm, the rare incest situation is clear to me, but the fact of a common ancestor generations back is not. I think I’d have to see it mapped to see your point.
Let me try in words :-).
2 parents, 4 grandparents, 8 great grandparents, 16 g-g-grandparents, 32 the generation before (gggs). It is highly unlikely the parents have any idea who their gg grandparents were, let alone the gggs. If that's nto enough just add a few additional generations.
Now, imagine 1 of the G4 men has children by 2 different (G4) women. Both of those children are among the 32 GGGs. There may be knowledge or suspicions they are related, but go forward a few gens, perhaps all the way to the parents, and nobody will know. Now you have 32+16+8+4+2+1 women ancestors, and 31+16+8+4+2+1 men.
Now you know how it can skew without obvious inbreeding.
So - the question is: how often is that likely to happen? How likely that a man fathers children by different women compared to women bearing children to different men - over all of history? I would guess it is definitely not 50-50, so variants of the above scenario happen more often to reduce the number of men in the ancestor tree. If nothing else, we know of a number of cultures where polygamy was normal, we know that wars often result in male invaders raping women, and we know that it was not unusual for women to die in childbirth and for men to take a second wife. I imagine plenty of powerful men fathering children by servants, but far fewer women doing the same. There are probably loads of men who never fathered a child because of dying in wars, or hunting etc before they managed it, or never getting sufficient socio-economic status to balance things out in terms of couples.
Very helpful. Thanks for the explanation.
What about the case where the the same father is both my father and my mother's father. This case would suggest that it is possible for an individual to have more female ancestors than male ancestors.
You are correct, Matt. And in the situation where a man sires a child by both his daughter and his granddaughter, that offspring would have 2 fewer male ancestors than female. But that really isn't relevant to Heather's point. It's just something that precision nerds like you and me would point out.
For those that wonder about the word "grok". It is a Martian word meaning deep and complete understanding used by the first human baby raised on Mars by Martians, Valentine Michael Smith, who is the central character in Robert A. Heinlein's 1961 science fiction novel, "Stranger in a Strange Land." (With Google's obsession with political correctness and focus on wokeness resulting in its increasing inability to perform its core function, to find a specific answers to a specific question, it has made it impossible for find out how to underline text in Substack comments, I therefore had to resort to quoting the title to this book.)
I pondered for, oh, 5 seconds, on this topic when I heard someone claim that Alexander the Great is the most prolific ancestor on the planet. I don't remember exactly how that was stated, but the implication was he had himself quite a few females, and implied is that it isn't the worst obstacle in the world to be the son, grandson, great grand son of AtG. One may guess that its always been good to have a government job.
Ken’s comment below is close to the scenario you get with fertility doctors unethically using their own sperm to inseminate unsuspecting multiple women. Or just generally what can happen with pregnancy-by-male-donation with certain men as repeat donors.
Of course, as all roads lead to Covid these days, this practice is making Covid headlines because of an Israeli study on the “vaxx” impact on those little donated swimmers. To be expected, the published research attempted to obscure the actual findings lodged in the tables. And so one must root around in SubStacks to get an accurate analysis of the bad state of affairs.
Still, as Heather maintains, individuals have one genetic father and mother in the end. This is true as well for couples who use donated eggs — there’s a genetic donation and a biological mom that (hopefully) carries the baby to term.
It sounds as though Fathers should be more valued in our culture than they currently are.
Heather: thanks for throwing a bone to the nerds... :)
The problem with this logic is that if one man has multiple children with multiple women, and those children or their progeny have children together, the offspring will have more female ancestors than male ancestors. That man will appear multiple times in the family tree next to multiple women.