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260,000 embryos

Remember, women are born with all the eggs they are ever going to have, and they don't make any new eggs during their lifetime. Women are born with approximately two million eggs in their ovaries, but about eleven thousand of them die every month prior to puberty.

If you were to extract all those eggs at a young age, and had some kind of artificial womb to grow the babies, then you could have a lot of babies.

Now, if you waited till she was 25 to harvest the eggs, then it's going to be a lot less.

11,000 a month till age 12 = 1,584,000.

Then 1000 a month from 12 to 25 = 156,000.

So you are looking at around 260,000, give or take a few.

Recent research has suggested that the conventional wisdom is wrong and that people can generate new eggs within their bodies that were not in there when they were born.

On the other hand, some other smart people have looked at the research and the evidence and remain quite dubious.

On the gripping hand, I don't see any data on the rate of egg creation, which is sort of what your specific question requires, so you're still kind of on your own.

While I don't have actual numbers for you, the method will be to induce maturation of multiple eggs in a given ovulation cycle, then harvest them. Harvesting whole ovaries doesn't work. The eggs have to ripen. We don't know how to do that.

Not all women will be able to produce eggs at all, others will react badly to the medications and surgeries, and number of eggs as well as endurance in number or frequency of harvesting cycles will vary woman to woman too.

For the purpose of obtaining a decent average, you need the following information:

Number of usable eggs obtained X number of harvesting cycles in any given time period

Don't assume one cycle per month. It may take longer to get things going hormonally. And bodies need to rest. The few citizens of your world who are able to provide eggs aren't resources to exploit. Don't assume that if it's safe to do a harvesting cycle, say, every 3 months, that this means 4 times a year times the number of years the woman remains at peak fertility. It doesn't work like that. There may be a maximum number of cycles someone can endure.

A lot of people are saying things like, well at least you can get one egg per month. But you can't. Remember, the eggs don't just come out like a chicken's. You want a viable human egg, you have to perform surgery. Don't need a lot of cutting, but it's still invasive. You really want to do that every month?

For your research, focus not on women undergoing fertility treatments but on women who donate (or sell) their eggs. Not all women using fertility treatments to increase egg production will have their eggs harvested for IVF or the like. So in those cases, you don't want maximum egg production. Also, women undergoing fertility treatments are more likely to be older and they will usually have diagnosed fertility issues. So, even with the same treatments, their egg production might be lower than that of a young healthy woman donating her eggs.

I found this site that describes the process (and side effects... Yikes! Tons!). Perhaps you can call them and saying you're researching for a novel (or whatever it is) and would they mind telling you the range and average number of eggs harvested, how long between harvests, and how many times someone can safely donate. http://web.stanford.edu/class/siw198q/websites/eggdonor/home.html

https://www.rogelcancercenter.org/fertility-preservation/for-female-patients/normal-ovarian-function

You start with about 1 million eggs at birth but these decline per month. At puberty you have about 300.000 eggs left. In the 30 to 40 years after puberty these are also depleted. This means at a "worst case" you lose about 10.000 eggs per year, assuming puberty for women starts around 12 years (again keeping it low for a worst case scenario) you would have 170.000 eggs remaining.

So given enough artificial wombs, you harvest the entire ovaries and use techniques to have a 100% success rate if maturing and infecti... I mean fertilising the eggs with male DNA, you would have a pretty awesome growth.

Edit: Willk in the comments noted this source: fertstert.org/article/S0015-0282(17)32178-7/fulltext. Which mentions a current-day method of harvesting eggs. Such a method, if not a more advanced due to the technology seemingly available, could be used for the harvesting.

Assuming a woman is fertile from age 13 to age 48, producing one egg per month, she can produce about $12 cdot 35 = 420$ eggs.

If you take her from age 25, this means about 276 eggs.

I wasn't sure if you could just take them all at once, but someone said in comment elsewhere that you cannot. I leave the route where you can below in case OP wants to go that way, especially since there is some advanced technology. But going the route where you cannot...

For each woman who wants to contribute to this, I will assume the slowest normal production of approximately 1 per month. In 10 years, that should lead to greater than 100 children. Approximately half of them are themselves female, and at approximately that time those new females can contribute as well. For each one of them who does, the same pattern continues.

So worst case scenario is that every decade the population multiplies by approximately 100. In 2 decades, that is a factor of 10000, 3 decades is 1 million, 4 decades is 100 million, 5 decades is 10 billion which is more than are on Earth today. And there will be no problem whatsoever with fertilization from males at this rate of population growth.

So a planet can be completely repopulated, at least by the numbers, in 1 person's lifetime.

But remember, that is from 1 starting woman who wants to contribute. For 100 starting, subtract 1 decade from the repopulation. Further, some people suggest that you should have tens of thousands of people minimum for a repopulation due to genetic diversity, so if you have that then subtract 2 decades. The planet has plenty of population in 2 decades, is fully repopulated (to today's level) in 3 decades. In 4+ decades it has a huge number.

Previous Answer (the fast track to full repopulation in 2 years)

My initial reaction was the same as in Andy's answer (though I did comment there about how I was not sure if you could just take them all at any time), but since your purpose is planetary repopulation you can go a step further.

1. That is per woman, but only the women who contribute. Some might not.




2. That is just the first generation of repopulation...

So you do your first generation of repopulation, and you have approximately (number_of_women * 100000) new people now, but approximately half of them will be female as well, so if this is the route you are going, in just 1 year you can do this again with females which possess even more eggs, on the order of a million.

I will assume for a moment that "a very limited number of human females remaining" is 10. Let us ignore genetic diversity for a moment, as this calculation is just to make a statement about population growth rate. So we have 10 females.

10 * 100000 = 1 million babies next year

Then you collect the eggs from the new females, approximately 500000 females at approximately 1 million eggs each...

500000 * 1 million = 500 billion new babies that year

So in only 2 years you have gone from a few humans to 500 billion; that is already 100 times more people than are on our planet today. And if you did the same thing again the next year, there would be... what's after a trillion again? Whatever, a huge number of people.

However!...

Those eggs need to be fertilized, so now you have to ask the same kind of question about males. They generate a lot of sperm all the time, and each 1 could fertilize a very lot of eggs, but not a million of them all at once. So you would need to fertilize them in large batches which would slow this all down a bit. However, this slower rate is still exponential crazy-super-high rate of population growth, and once again total repopulation would not take long at all.