If we want to talk polygamy, we want to talk about African and Islamic cultures. But even where it is most accepted, actual polygamy rates are fairly low, though this is exaggerated by recent declines in Africa.
If there is something like a 80% to 40% difference—that would surprise me—I doubt that saying `polygamy’ would cover it. If there is a big difference, it should be bigger, and I think a better and more familiar explanation would suit: men have relativity few time and resource constraints on reproduction. Looking at it historically, the costs of reproduction come overwhelmingly from pregnancy, birth, and risk of child mortality. Reproducing under (historically) typical conditions involves keeping women pregnant. So we should expect women to have a reproduction greater than or equal to that of males.
Start with 100 men and 100 women (generation 0). Now suppose that in each generation, 80% of adult men are successfully monogamous, a dominant 10% reproduce with two women, and 10% do not reproduce. To keep things simple, suppose each human pair produces an average of two successful children—one a man and one a woman—in that they live to be sorted into this 10/80/10 split. Each generation is assumed to die off to make math simpler for the kids, and I’m going to make a lot of stupid independence assumptions.
At generation 1, we have descendants for all 100 generation 1 women and for 90 of the generation 1 men.
At generation 2, we have descendants for all 100 generation 1 women and 81 of the generation 1 men have descendants.
At generation 3, we have descendants for all 100 generation 1 women and ~72 generation 1 men.
I think we can see where this is going. At generation n, we have 100*(9/10)^n men with descendants and 100 women, giving us a ratio of (9/10)^n men to women with descendants at generation n. I’ve also been assuming that children of dominant parents are as likely to be sorted into the dominant/monogamous/unsuccessful groups as any other child. I doubt that this assumption holds in reality, and think its failure would tend to reduce the ratio. [Edit: I neglected female-line descendants. This only holds for strictly male-line descendants. I’ll work on something better.]
As for determining via experiment the actual reproduction rates for men and women throughout history, I am not optimistic. All the evidence we have points to relatively recent population bottlenecks. On a more obvious note, human populations over the last few centuries—and then millennia—are huge historical outliers. And within these outliers, there are catastrophic fluctuations due to plague and conflict, e.g. the black death or the Congo Free State. In the last few centuries especially, we’ve seen dramatic cultural shifts concerning marriage norms. Particularly relevant to polygamy would be the movement of people from mixed polygamous/monogamous/polygynous cultures to nominally monogamous ones.
You forgot to take into account female-line descendants of the generation 1 men. With your approximations, every generation 1 man who reproduces the first time ends up having descendants going straight down the female line after the first generation.
I derped that one up, didn’t I? With the other assumptions, the 90 generation 1 men would always have descendants, since each pairing produces one woman. I guess the only conclusion I can salvage from that scenario is that strictly male-line descendants of generation 1 collapse exponentially while female-line descendants remain constant. I’ll work out something better.
Actually, because the paper Wilder 2004 relied on mitochondria from women and y-chromosomes from men, which can only be passed down through same-sex kids, your model might reproduce the data they use!
That brings some tweaks and ideas to mind, but I obviously need to take a long break and do some serious reading before retrying my hand at amateur population genetics. Any resemblance to useful data in that mess is entirely coincidental.
It would be interesting to make some plausible adjustments to see what happens to strictly male-line inheritance. One could substitute probabilities for the strictly 10/80/10 divide I used and make plausible assumptions e.g. probability(male is dominant|male is descended from dominant male)>probability(male is dominant|male is descendant from monogamous male). But I’m betting this sort of thing has been done elsewhere and that the job was better than that.
If we want to talk polygamy, we want to talk about African and Islamic cultures. But even where it is most accepted, actual polygamy rates are fairly low, though this is exaggerated by recent declines in Africa.
If there is something like a 80% to 40% difference—that would surprise me—I doubt that saying `polygamy’ would cover it. If there is a big difference, it should be bigger, and I think a better and more familiar explanation would suit: men have relativity few time and resource constraints on reproduction. Looking at it historically, the costs of reproduction come overwhelmingly from pregnancy, birth, and risk of child mortality. Reproducing under (historically) typical conditions involves keeping women pregnant. So we should expect women to have a reproduction greater than or equal to that of males.
Start with 100 men and 100 women (generation 0). Now suppose that in each generation, 80% of adult men are successfully monogamous, a dominant 10% reproduce with two women, and 10% do not reproduce. To keep things simple, suppose each human pair produces an average of two successful children—one a man and one a woman—in that they live to be sorted into this 10/80/10 split. Each generation is assumed to die off to make math simpler for the kids, and I’m going to make a lot of stupid independence assumptions.
At generation 1, we have descendants for all 100 generation 1 women and for 90 of the generation 1 men.
At generation 2, we have descendants for all 100 generation 1 women and 81 of the generation 1 men have descendants.
At generation 3, we have descendants for all 100 generation 1 women and ~72 generation 1 men.
I think we can see where this is going. At generation n, we have 100*(9/10)^n men with descendants and 100 women, giving us a ratio of (9/10)^n men to women with descendants at generation n. I’ve also been assuming that children of dominant parents are as likely to be sorted into the dominant/monogamous/unsuccessful groups as any other child. I doubt that this assumption holds in reality, and think its failure would tend to reduce the ratio. [Edit: I neglected female-line descendants. This only holds for strictly male-line descendants. I’ll work on something better.]
As for determining via experiment the actual reproduction rates for men and women throughout history, I am not optimistic. All the evidence we have points to relatively recent population bottlenecks. On a more obvious note, human populations over the last few centuries—and then millennia—are huge historical outliers. And within these outliers, there are catastrophic fluctuations due to plague and conflict, e.g. the black death or the Congo Free State. In the last few centuries especially, we’ve seen dramatic cultural shifts concerning marriage norms. Particularly relevant to polygamy would be the movement of people from mixed polygamous/monogamous/polygynous cultures to nominally monogamous ones.
You forgot to take into account female-line descendants of the generation 1 men. With your approximations, every generation 1 man who reproduces the first time ends up having descendants going straight down the female line after the first generation.
I derped that one up, didn’t I? With the other assumptions, the 90 generation 1 men would always have descendants, since each pairing produces one woman. I guess the only conclusion I can salvage from that scenario is that strictly male-line descendants of generation 1 collapse exponentially while female-line descendants remain constant. I’ll work out something better.
Actually, because the paper Wilder 2004 relied on mitochondria from women and y-chromosomes from men, which can only be passed down through same-sex kids, your model might reproduce the data they use!
This is rather far from my expertise though.
That brings some tweaks and ideas to mind, but I obviously need to take a long break and do some serious reading before retrying my hand at amateur population genetics. Any resemblance to useful data in that mess is entirely coincidental.
It would be interesting to make some plausible adjustments to see what happens to strictly male-line inheritance. One could substitute probabilities for the strictly 10/80/10 divide I used and make plausible assumptions e.g. probability(male is dominant|male is descended from dominant male)>probability(male is dominant|male is descendant from monogamous male). But I’m betting this sort of thing has been done elsewhere and that the job was better than that.
Given some knowledge of the distribution of the number of children, both for women and for men, we could treat this as a Galton-Watson Process.