I think your assessment is incorrect.
Even if you don't mean to, you are operating on an assumption that uses faulty logic. Primarily that when you die, your kid immediately replaces you. Or, my wife and I die, my two kid immediately replaced each of us.
For most people, there is a long period of overlap where one and their offspring are both alive. And maybe even someone, their kids, and their grandkids are all alive. Or even still, in places with long life expectancy, their great-grandkids are still alive.
So where you are looking at, replacing AA with BB. You seem to forget that with a long enough life span, AA, BB, and CC, and DD are alive at the same time. So the population is increasing. But it's not getting wider, it's getting deeper.
In Somalia, where they die young and breed like rabbits, you might see:
Year 0: AA
Year 15: AA, BBBB
Year 30: A, BBBBB, C
Year 45: BB, CCCCC
Year 60, B, CCCCC, D
etc etc. The total population doesn't increase by much because while they shit out kids left and right, they also don't live very long.
Compare that with the west, it would look like:
Year 0: AA
Year 15: AA, BB
Year 30: AA, BB
Year 45: AA, BB, CC
Year 60: AA, BB, CCCC, DDDD
My grandma and grandpa had 7 kids.
She is still alive, my gramps died a decade ago.
Her seven kids and a combined 20 kids. The oldest of us are pushing 45. We look like this (all below still alive):
Gen 1: A
Gen 2: BBBBBBB
Gen 3: CCCCCCCCCCCCCCCCCCCC
Gen 3: DDDDDDDDDDD (and counting)
You don't get 4 consecutive generations alive at the same time in shitholes. You're lucky if you get 3.
Except that, again, you stop before the actual important part starts. In your example, you stop by the 4th generation when you're still in rising period because the mortality hasn't caught up yet.
Here's another example, but going much longer. Here's an example, going up to Gen 8:
Assumptions (to simplify):
Women have all 1.5 children. I'll round up the number if it's a decimal, just to be nice and to prove my point further (so if we have 5 women, normally it would give 7.5 babies, but we will count as 8).
No "no-family relations"
Generation X will make children for Generation X + 1
Generation X will die at Generation X + 4.
Here's are the details:
Generation 1: 100 new people (50 men, 50 women).
Generation 2: 1.5 * 50 babies are born = 75, bringing the population to 175. Out of those 75 new people, 37.5 are women (rounded up to 38).
Generation 3: 1.5 * 38 babies are born = 57, bringing the population to 232. Out of those 57 new people, 28.5 are women (rounded up to 29).
Generation 4: 1.5 * 29 babies are born = 43.5 (rounded up to 44), bringing the population to 276. Out of those 44 new people, 22 are women.
Now, so far, we agree the population is increasing steadily, and better than if the quality of life were poor and parents kept dying after having children. However, the following is the part you're missing:
Generation 5: 1.5 * 22 babies are born = 33, however Generation 1 is now completely dead (100 people), bringing the population to 276 + 33 - 100 = 209. Out of those 33 new people, 17 are women.
Generation 6: 1.5 * 17 babies are born = 26, however Generation 2 is now completely dead (75 people), bringing the
population to 160. Out of those 26 new people, 13 are women.
Generation 7: 1.5 * 13 babies are born = 20, however Generation 3 is now completely dead (57 people), bringin the population to 123. Out of those 20 new people, 10 are women.
Generation 8: 1.5 * 10 babies are born = 15, however Generation 4 is now completely dead (44 people), bringing the population to 94. Out of those 15 people, 8 are women.
Do you start to see the pattern and the problem, now? Arriving at generation 8, you now have way less people than what you started with, and the problem keep getting worse and worse, cause you have fewer and fewer women.
With 1.5 natality, you can expect this community to completely collapse by Generation 15, where you're not even guarentee to have a new woman at all to continue the legacy.
If you lower the natality to 1 (what South Korea has), you get a complete eradication by generation 10.
Feel free to do the calculations with a fertility of 2, and you'll see, it magically equalise everything, because you guarentee 2 individuals will replace 2 dying parents (doesn't matter if they die in 5 years or in 100 years, they will die eventually, and needs to be replaced).
We know your example is flawed, because if you remove immigration from developed countries, they are all losing population, little by little, and not increasing like you claim. And now I've proved it mathematically as well.
My model was only allowing for people 26-40 to "breed". I expanded it to reflect contemporary US breeding ages of 18-44, which helped.
TLDR:
Equilibrium Birth Rate: To maintain a population of ~100,000 (the baseline amount in this example) (±5%) over 100, 200, and 300 years:
100 Years: ~2.4 children per couple (final pop: 98,765)
200 Years: ~2.45 children per couple (final pop: 99,231)
300 Years: ~2.45 children per couple (final pop: 101,124)
=========================
Equilibrium Birth Rates, revised for infant mortality and variable mortality:
100 Years: ~2.55 children per couple (final pop: 99,876)
200 Years: ~2.60 children per couple (final pop: 100,342)
300 Years: ~2.60 children per couple (final pop: 101,567)
Explanation
Impact of New Factors:
Infant Mortality: Reduces births by 0.56%, slightly increasing the required birth rate.
Variable Mortality: Higher mortality in older age groups (60+) shifts the age distribution younger, requiring a slightly higher birth rate to compensate for faster elderly population decline.
=========================
So 2.6 seems to be the magic number for long term stability of a population WITHOUT the need for migration, and barring any (((wars))).
I have 3 so I guess I've done my part. Everyone else needs to get fucking.
Well, I did some crunch with python and you seem to be correct, which surprises me. I thought the longevity would balance out the equation and I do wonder if given a long enough longevity if it would. Say something crazy like people live to 120, or 150 (impossible) just from a math perspective.
Population after 105 years (6x 15 year long generations) based on starting with 100,000 people age/gender composition similar to current US population.
1.1: 34,627
1.5: 42,586
2.0: 50,546
2.1: 51,426
2.2: 52,205
2.5: 54,037
3.0: 57,888
here were my assumptions just to make it simple:
More Assumptions: All children born are conceived and born in wedlock. Zero infant mortality (everyone lives to adulthood). All heterosexual marriages are monogamous and faithful. Live expectancy mirrors that of contemporary USA. The age and sex of the people in this population are varied comparably to the current population of the USA.
So the real #s would be much lower because we have infant deaths, etc.
So what would be the kids/couple to sustain equilibrium? 2.2 does not seem to cut it either. I'll try to find out.
I think your assessment is incorrect. Even if you don't mean to, you are operating on an assumption that uses faulty logic. Primarily that when you die, your kid immediately replaces you. Or, my wife and I die, my two kid immediately replaced each of us.
For most people, there is a long period of overlap where one and their offspring are both alive. And maybe even someone, their kids, and their grandkids are all alive. Or even still, in places with long life expectancy, their great-grandkids are still alive.
So where you are looking at, replacing AA with BB. You seem to forget that with a long enough life span, AA, BB, and CC, and DD are alive at the same time. So the population is increasing. But it's not getting wider, it's getting deeper.
In Somalia, where they die young and breed like rabbits, you might see:
Year 0: AA
Year 15: AA, BBBB
Year 30: A, BBBBB, C
Year 45: BB, CCCCC
Year 60, B, CCCCC, D
etc etc. The total population doesn't increase by much because while they shit out kids left and right, they also don't live very long.
Compare that with the west, it would look like:
Year 0: AA
Year 15: AA, BB
Year 30: AA, BB
Year 45: AA, BB, CC
Year 60: AA, BB, CCCC, DDDD
My grandma and grandpa had 7 kids. She is still alive, my gramps died a decade ago. Her seven kids and a combined 20 kids. The oldest of us are pushing 45. We look like this (all below still alive):
Gen 1: A
Gen 2: BBBBBBB
Gen 3: CCCCCCCCCCCCCCCCCCCC
Gen 3: DDDDDDDDDDD (and counting)
You don't get 4 consecutive generations alive at the same time in shitholes. You're lucky if you get 3.
Except that, again, you stop before the actual important part starts. In your example, you stop by the 4th generation when you're still in rising period because the mortality hasn't caught up yet.
Here's another example, but going much longer. Here's an example, going up to Gen 8:
Assumptions (to simplify):
Here's are the details:
Generation 1: 100 new people (50 men, 50 women).
Generation 2: 1.5 * 50 babies are born = 75, bringing the population to 175. Out of those 75 new people, 37.5 are women (rounded up to 38).
Generation 3: 1.5 * 38 babies are born = 57, bringing the population to 232. Out of those 57 new people, 28.5 are women (rounded up to 29).
Generation 4: 1.5 * 29 babies are born = 43.5 (rounded up to 44), bringing the population to 276. Out of those 44 new people, 22 are women.
Now, so far, we agree the population is increasing steadily, and better than if the quality of life were poor and parents kept dying after having children. However, the following is the part you're missing:
Generation 5: 1.5 * 22 babies are born = 33, however Generation 1 is now completely dead (100 people), bringing the population to 276 + 33 - 100 = 209. Out of those 33 new people, 17 are women.
Generation 6: 1.5 * 17 babies are born = 26, however Generation 2 is now completely dead (75 people), bringing the population to 160. Out of those 26 new people, 13 are women.
Generation 7: 1.5 * 13 babies are born = 20, however Generation 3 is now completely dead (57 people), bringin the population to 123. Out of those 20 new people, 10 are women.
Generation 8: 1.5 * 10 babies are born = 15, however Generation 4 is now completely dead (44 people), bringing the population to 94. Out of those 15 people, 8 are women.
Do you start to see the pattern and the problem, now? Arriving at generation 8, you now have way less people than what you started with, and the problem keep getting worse and worse, cause you have fewer and fewer women.
With 1.5 natality, you can expect this community to completely collapse by Generation 15, where you're not even guarentee to have a new woman at all to continue the legacy.
If you lower the natality to 1 (what South Korea has), you get a complete eradication by generation 10.
Feel free to do the calculations with a fertility of 2, and you'll see, it magically equalise everything, because you guarentee 2 individuals will replace 2 dying parents (doesn't matter if they die in 5 years or in 100 years, they will die eventually, and needs to be replaced).
We know your example is flawed, because if you remove immigration from developed countries, they are all losing population, little by little, and not increasing like you claim. And now I've proved it mathematically as well.
My model was only allowing for people 26-40 to "breed". I expanded it to reflect contemporary US breeding ages of 18-44, which helped.
TLDR: Equilibrium Birth Rate: To maintain a population of ~100,000 (the baseline amount in this example) (±5%) over 100, 200, and 300 years:
100 Years: ~2.4 children per couple (final pop: 98,765)
200 Years: ~2.45 children per couple (final pop: 99,231)
300 Years: ~2.45 children per couple (final pop: 101,124)
=========================
Equilibrium Birth Rates, revised for infant mortality and variable mortality:
100 Years: ~2.55 children per couple (final pop: 99,876)
200 Years: ~2.60 children per couple (final pop: 100,342)
300 Years: ~2.60 children per couple (final pop: 101,567)
Explanation Impact of New Factors: Infant Mortality: Reduces births by 0.56%, slightly increasing the required birth rate. Variable Mortality: Higher mortality in older age groups (60+) shifts the age distribution younger, requiring a slightly higher birth rate to compensate for faster elderly population decline.
=========================
So 2.6 seems to be the magic number for long term stability of a population WITHOUT the need for migration, and barring any (((wars))).
I have 3 so I guess I've done my part. Everyone else needs to get fucking.
Well, I did some crunch with python and you seem to be correct, which surprises me. I thought the longevity would balance out the equation and I do wonder if given a long enough longevity if it would. Say something crazy like people live to 120, or 150 (impossible) just from a math perspective.
Population after 105 years (6x 15 year long generations) based on starting with 100,000 people age/gender composition similar to current US population.
1.1: 34,627
1.5: 42,586
2.0: 50,546
2.1: 51,426
2.2: 52,205
2.5: 54,037
3.0: 57,888
here were my assumptions just to make it simple: More Assumptions: All children born are conceived and born in wedlock. Zero infant mortality (everyone lives to adulthood). All heterosexual marriages are monogamous and faithful. Live expectancy mirrors that of contemporary USA. The age and sex of the people in this population are varied comparably to the current population of the USA.
So the real #s would be much lower because we have infant deaths, etc.
So what would be the kids/couple to sustain equilibrium? 2.2 does not seem to cut it either. I'll try to find out.