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Economics/demographics question: If a child unexpectedly dies, how much does this shrink the next generation?
The answer seems obvious - the next generation will have one fewer person (in expectation) - but it's not that simple, and it's been bugging me for about a day now.
Suppose you are an average 15-year-old, and your parents are too old to have any more children (they won't have more children to "replace" you). The ~2 children you would have had obviously won't be born. Naïvely that means the next generation will be smaller by 2, but this disagrees with the obvious answer (smaller by 1).
Where this reasoning goes wrong is in assuming that everyone else will still have the same number of children. The sex ratio will shift so that the surviving members of your sex have n more children, and the size of the next generation will decrease by 2 minus n. If n is 1, we get the intuitive answer that there'll be 1 less person.
But there's no reason why n has to be 1 for both sexes! If both a boy and a girl die, the sex ratio is unaffected and the next generation will be 1 smaller, so n has to average to 1, but n may or may not be the same between sexes. Have there been any studies estimating the value of "n" for each sex?
(I posted this because it's relevant to population ethics, but I'm not entirely sure whether it belongs here, so I also posted it to Reddit. Should questions like this go in Discussion or in an open thread?)
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Comments (12)
It is equivalent of turning the clock a little back in the population size time series. Assuming a constant capacity, these curves are idealized as logistic functions (although delays in the feedback mechanisms can induce overshooting).
If the population is in the stationary region of the logistic function, then there is no significant effect: the person who dies is replaced by somebody else using the freed up resources.
If the population is in the exponential region of the logistic function, the loss of a single person will reduce population size by 1 in the current generation, k in the next generation, k^2 in the second next generation and so on, where k is the (unisex) growth rate. In order to take into account gender differences, replace the first k in each of these products by a gender-specific rate.
Certainly in an idealized world the reproductive capacity of a tribe of humans is only limited by the number of women. C.f. Randy the guinea pig, father of 400.
But on the other hand, neither modern humans nor ancestral humans lived in that kind of idealized world. In the modern world we have limited monogamy and reduced pressure to have kids. Somewhere around 18% of women in the U.S. don't end up having kids - I'd expect that a woman surviving would lead to more kids, but not actually 2 more, and similarly a missing man wouldn't just be replaced by the nearest available sperm-producer. I dunno how to put a number to it.
In an ancestral environment close to equilibrium (what you imply by saying that each person has 1 kid on average), the situation is even more egalitarian. That equilibrium is maintained by something other than birth rate. If the issue is limited resources, and if an additional person can gather additional resources, then a man and a woman will both be able to increase the long-term number of children about the same. If the population is growing exponentially but is occasionally devastated by war, a man will lead to a larger population the war is in five years but a woman will lead to a larger population if the war is thirty years. If by disease or famine, there might be very little dependence on gender.
One way to start estimating it would be to correlate local sex ratios with local birth rates and try to control for as many things as possible. Unfortunately, this is probably very hard to do...
I'm actually most interested in the answer for modern poor countries, which are neither stable in population nor Malthusian. Basically, I'm wondering how interventions that save lives of one gender (but not the other) today will affect the population size 20 to 30 years in the future. Non-replacement fertility doesn't qualitatively change things: the question just becomes whether a life saved increases the population by more or less than "next generation's size / current generation's size". Replacement fertility is just the special case where the ratio is 1; I used that number in my question only for simplicity.
Long term, it depends upon what the constraints are upon population size.
For example, if it happens in an isolated village where the food supply varies from year to year due to drought, and the next year the food supply will be so short that some children will starve to death, then the premature death of one child the year before the famine will have no effect upon the number of villagers alive 20 years later.
The same dynamic applies, if a large factor in deciding whether to have a third child is whether the parents can afford to educate that child, and the cost of education depends upon the number of children competing for a limited number of school places.
Suppose generation 0 is the parents, generation 1 is the generation that includes the unexpectedly dead child, and generation 2 is the generation after that (the children of generation 1).
If you are asking about the effect upon the size of generation 2, then it depends upon the people in generation 1 who didn't marry and have children.
Take, for example, a society where generation 1 would have contained 100 people, 50 men and 50 women, and the normal pattern would have been:
And the reason for this pattern is that each man who passes his warrior trial can pick and marry 2 women, and the only way for a woman to marry to be picked by a warrior.
In that situation, having only 49 women in generation 1 would make no difference to the number of children in generation 2. The only effect would be having 40 women marry, and 9 not marry.