Rebuilding humanity from forty-ish people in the middle of an alien world within 400 years

Question

Near the beginning of my fictional worlds history (that is, when things start getting bad)the small population of around 10,000 humans is mercilessly slaughtered by the recently formed population of 10,000 goblins that can turn invisible, and they did it while everyone was sleeping. Luckily, an angelic messenger warned one of the humans about this afew months before this happened and the aptly named "council of swords" turned bloody, but this dude was only able to convince a group of forty-odd people to go to him in the middle of nowhere away from the only site of civilization (on land in the northern hemisphere of this planet) on the night the goblins were planning to kill all the humans. Trust me, they kinda had a good reason to do it, but it was pretty bad, ngl. Nonetheless, the Goblins thought their plan would work pretty well since nobody knew about it, and they could turn invisible, so they had absolutely nobody on the lookout making sure a random group of humans didn't escape. Because of this, the forty people warned by the angel got away perfectly unscathed and unnoticed. The same cannot be said about the goblins, but that is a question for another time.

Nonetheless, about 428 years after this event (the 427th year of the forest, each year is 360 days split into ten months of 36 days and there are no seasons) three evil dark lords come to town and destroy the human homeland they fled to during the "council of swords". Well, between these two points, that homeland developed into an empire (by ancient standards. Certainly not as big as Britains). How do I explain the empire? Note, it didn't take 427 years for the empire developed, the empire fell 427 years after the 40 odd humans that escaped the slaughter of humanity arrived in safety to their new homeland as the only people left in that solar system. How do I explain the existence of that empire given the short amount of time I have to work with?

427 years. Now, I guess I will need to provide some more details, cause my question requires an empire alot earlier than 427 YF (1 YF is when this people group would have started rebuilding). at 367 YF, I need humanity to be large enough and stable enough to have founded a singular kingdom, about the size of Morroco, that is then able to fight a war, almost entirely alone, against magical orcs with a dark spirit who has ludicrous unknown powers so great they might just be able to tear the page in half if they make you angry enough or something. Oh come on, with how long this has to be, I'm trying to entertain you! don't get annoyed. Nonetheless, after a near hopeless conflict, humanity nearly doubles the size of their empire to two Morrocos, and they're both very green, jungly kind of thing, but not as hard to get around as the Amazon. (I think the second Morroco is a little browner) After this war, humanity is still so bold, and populated enough, to send out colonies to random places led by a magic superperson, and all those colonies together would add up to yet another Morrocco, so by the year 410, the empire has to be about three Morrocco's large, and the population is dominated by humans.

Now, not only that, we need to account for the existence of two other populations of humans: the dwarvish farmers and the freemen. The dwarvish farmers are not dwarves; instead they are the humans who get payed by the dwarves to farm their fertile fields so the dwarves don't have to do any of that work, and they get payed in exquisite jewels from the mountainlords they serve that are worth alot of money in their home country of Agoroth (that is the human nation btw). However, this population of farmers in dwarven lands is obviously much smaller then even the population of the colonies, and many of them will only live temporarily in Dwarven lands anyways. The other population of humans outside of Agoroth that I have to account for is the free men (not fremen) who decided (after 367) that they would like to just leave Agoroth and make their way out in the rugged frontier, living under nobody and no-one telling them what to do. They inhabit another area about the size of Morocco; so humans live in four Morocco's, and three of them are in one empire. That fourth Morocco inhabited by the free men is also populated by orcs and stuff, so it also probably doesn't factor into the overall human population too much.

The final thing I need to explain is the existence of an earlier conquering king (pre-367) named Kazentha, whose violent conquest of most human cities led to the guardian of humanity (kinda like a guardian angel, but not really, and he dies in 427)to depose him and establish the kingdom of Agoroth. Kazenthas reign was short lived, maybe five or six years, and there was no functioning empire before that, but I still need to explain how he conquered multiple cities before 367 when humanity literally was reduced to forty-ish people in year 1.

So here's the quicklist of what I need to explain:

367 years after humanity was reduced to forty members, it needs to be able to fight off a civilization of orcs that had ~10000 members 367 years ago (though it had gone through more wars in the mean time).

Sometime before this, I need to know when humanity would have been able to have a large number of independent walled cities (like ten or something) so that I can know the earliest date for the reign of Kazentha and the founding of Agoroth.

Finally, somehow, the population of Agoroth needs to be able to grow fast enough after 367 that humanity is able to colonize, claim, and protect a collection of spread out islands and continental colonies that amount to roughly the area of Morocco before the year 410.

My question is just how big can the human population get in these four centuries and, if I want all the events I have listed, should I extend the timeline?

Answer 1

40 is not enough to preserve genetic diversity; this experiment will probably fail. But we'll give it a shot, that's what we've got.

A woman's ideal reproductive career is from 15 to 33; she can bear about 12 children while staying healthy (one every 18 months). Earlier than 15 is not biologically sexually mature enough, it risks complications and still birth. Later than 33, risks genetic damage and unhealthy children (Ideally we'd like to stop at 27 or so).

Too frequent pregnancy and constantly nursing is physically stressful and too risky for the mother's health; 18 months is about the shortest safe time span between children. Again, ideally, 2+ years is preferable; two year olds are beginning independence.

For the sake of genetic diversity, each child should have a different father (physically and mentally healthy), young but 3-5 years older than the mother, and chosen at random from that pool. So build that requirement into your culture, no expectations of a woman pairing off for life with one husband, and no males dominating the mating; unless physically or mentally disabled, they all mate with about the same number of women. No harems! We need the greatest possible mixing of genes we can get, if we are to do our best to avoid inbreeding.

The men bear shared responsibility to the support and care of mother and child for every child they father; we expect the males that have fathered children for a given mother to cooperate in the support of that family.

I'd focus the work and danger on Men, the job of women here is to stay healthy, reproduce, nurse and care for children.

That is a shitload of work, but not dangerous work; reserve that for men. We can lose penises, we want to minimize the loss of wombs.

This is just math and biology: A dozen men can impregnate a hundred women and have a hundred children in a year. But a hundred men cannot impregnate a dozen women and have a hundred children in a year; no matter how many men mate with a dozen women, they will only have about a dozen children.

Thus biology dictates men are more expendable than women, especially so when our priority is population growth.

Older women (over 33) can aid in child care and domestic care, or become professionals of some sort.

None of this requires any dominance of men over women; the genders can be equal or even a matriarchy with women in charge. That would make sense, since the "family unit" is a woman raising a herd of kids with all different fathers; there is no "marriage" or two-party partnership here. In fact if some fathers are lost, other fathers pick up the slack or their society does.

Presuming of the dozen children we can raise (all things considered, including child mortality) an average of 5 females to reproductive age, then the generational multiplication factor is 5 per woman. We can count just women, since they birth equal numbers of boys and girls.

The "generation" is roughly 17 years: From birth of a female until she gives birth to another female (considering she may birth one or more males first).

So what does it take to get us from 20 females to, say, 2 million females? (and of course 2 million males).

That is a factor of 100,000. We multiple by 5 each generation. So I'll say a little over 7 generations; 5x5x5 x 5x5x5 x 5 = 78125, multiplied by the original 20 women, the number of females is 1.562 million. The 7 generations (at 17 years) is 119 years. The population with both genders is about 3 million.

So actually we are being are too hard on our women. We have 367 years to get to two million women, not 119!

Let's say our generation is still 17 (youthful reproduction, around 16 for females, is still ideal for infant health); but what growth factor do we need to take 367 years to get to two million? Turns out that is 21 generations. So we need the women to have, on average, 1.73 females raised to reproductive age, each generation. at 50% female birth, and say 15% female mortality or infertility, that is four children per woman in her reproductive career, which should span 8 years (children two years apart); say 17 to 25; which is even better for infant health. A childcare career is still to the age of 35-40 for women, but this will be far less stressful with four kids instead of 12, and may leave her time to be educated for a subsequent career at 35. Doctor, engineer, chemist, biologist, etc.

Nor does her sexual career have to end; but she should be prohibited from bearing more children after meeting her quota of 4.

Starting with such a narrow gene pool these children should still be by random choice of healthy fathers without repeats; for the sake of genetic diversity.

Your biggest problem is going to be ramping up food, water and shelter production that doubles every 17 years, pretty much the entire male population, along with the mothers retired from child bearing and raising, must be devoted to this doubling effort.

It requires a relentless growth rate of about 4% a year in supplies, including territory. Clearing and breaking new farmland, and/or hunting and fishing territory, or ranch land for herding. At first we can rely on hunting, but that does not scale to thousands or millions. We need huge food factories, huge farms and ranches of goats. (Goats are ideal, they eat just about anything, including the stems, leaves and roots of food plants, weeds and brush. They breed fast and produce great milk. They are docile and can work as light labor animals. And the excess rams and retired ewes provide meat.)

We need food, clean water, safety, and protection from the elements. And of course good medical care.

We need to build shelters that last, perhaps irrigation ditches. and we need a focus on expansion, both in population and the territory to support it.