How quickly can an interstellar human population grow after 200 years post-Apocalypse?

Question

Assume the earth gets destroyed in 2165 and the humans that would have survived move to a new planet.

Context: Humans mastered interstellar travel 80-90 years ago, after warp technology was developed, but before the planet's demise. They have founded a few colonies of a few thousand colonists (mining and agriculture), They had already established a new planet as their main colony planet with about 50,000 -70,000 colonists before the earth-death.

The humans and their alien allies start to evacuate earth with merely 2 weeks warning.

The population of the earth at the time was ~10 billion, which drove their colonization push. It is about to drop greatly, saving merely ~ 19 million humans. Full ships head out, drop off colonists, then come back for another load.

After the planet is gone, survivors are taken to the new homeworld and allied worlds. There they'd all be registered for a head-count of survivors and assigned supplies while they deal with the mess. Since humans are quite advanced and would rely heavily on their alien allies for aid, they'd have access to medical supplies, emergency homes and advanced technological equipment.

Abortions are illegal; embryonic transfer to an artificial womb is possible however, at a certain gestational development. Infant care is too costly, but people donate their DNA to a sort of gene bank for future diversity.

200 years later, the human population is back on their feet. What is their population now?

Math is not my strong suit, a little help please.

So, What would the approximate human population be in 2365?

Answer 1

Current average human population growth is about 1% per year, which doubling every 70 years.

By this condition your population would be around 20 000 000 * (1,01)^200 = 146 000 000 (almost like Russia)

If you put all efforts in ... breeding, you could get up to 5 grown up children per family. To many children per grownup leads to lack of control and care. And this greatly increases probability of different accidents. So even if family on average "produce" 10 children (this is a lot - it means that a lot of families has about 20 children) 2-3-5 of them would die before marriage (on average).

Since one "production cycle" is about 40 years (your need time born all them) it gives doubling population every 8 years. In 200 years there would be 25 doublings and total increase factor would be 33 554 432 times, thus given total population of 600*10^12 wich is like total humanity (or maybe Orcs?) from WH40K

So this is your "working interval" where you can take any number you want for your narration: from Russia (140 millions) to WH40k (600 trillion).

Anything in between is possible given the right conditions.

Answer 2

Human populations can easily double in 30 years in good conditions absent any new technology. 200 years is roughly 7 doublings, so you would expect to have 128 times as many as you started. Your 19 million would have grown to roughly two and a half billion.

Some individual countries are currently growing much faster, eg Southern Sudan with a growth rate of over 3.5%. Compounding this over 200 years = a factor of 972 so 19 million is now 18 billion.

However, given SF technology you might expect very much more rapid growth if there was a cultural/political will and the economy to support it -- make all children female and parthenogenic and with multiple births being the norm rather than exceptions. Population could easily be 180 billion or more...

Answer 3

I would start from @Cadence 's comment to the question:

With 20 million people crammed into colonies that were formerly supporting a few hundred thousand people, total, the question isn't how to have enough kids but how to feed, house, and clothe people - even just the people you have right now, let alone children.

So, unless the friendly aliens are willing to help without limitations and without strings attached (but why would they do that, especially considering how dangerous we, as a species, are ?), increasing population will not be the most important issue until the infrastructure to sustain a 20 million population is built and surpassed.

Second, what kind of people are those 20 million ? The rich, who can buy their way into the fleeing spaceships ? The yound and healthy, who can do physical work and reproduce (and fight their way into the ships if necessary) ? The old and wise, who know technology and skills ? Or, of course, a mix of those ? (Who gets do decide ? The already established colony, the aliens, the Earthbound establishment ?)

If this imported population is not young enough, it won't reproduce or build new facilities as fast, but it will probably help in planning the future and preserving important Earthan technology and general lore. If it is very young, it will reproduce and help building things more, but it can be a threat of itself, either due to ignorance, entitlement, or turbulence. If it is skewed to the upper classes, it might prompt conflict with the pre-apocaliptical colonial establishment. If not, it might become an underclass and pose another, more radical, threat to that establishment.

Plus: how is this selected ? Are they all Americans, or Anglospherans in general ? If not, how many different languages do they speak ? How comfortable are they with cultural meltpots ? What are their reproductive habits (I take in 2165, they will mostly be used to having few children, and to be sexually free, including from reproductive collateral effects of sex) ?

All of those issues might have a much bigger impact than mere mathematics... so chose any figure you wish, but be prepared to discuss how that figure was arrived at, including:

• The Rebellion Against Sexual Laws

• The Great Reproductive Strike

• The African Revolution

• The Alien Withdrawal

• The Advent of the Theocracy

• The Reintroduction of Slavery

• The War among the Languages

etc.