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In my yet to be named sci-fi universe humanity has begun to expand into space and has established large scale space stations near Earth and on places like Eros and Luna. I wanted the stereotypical "spacer" to have more children than is usual on earth (1 or 2). Are there any logical reasons or advantages for spacers to have multiple children in a space colony?

Note:
-The Hegemony (global government which controls the majority of humanity) practices birth credits (after a couple's second child they would need to buy permits for any further child) to try and prevent drastic population growth, but in my mind I don't think simply wanting to have more than 3 kids without buying a permit is a good enough reason or motivator to move to space.
- Space stations are required to be built with "Maternity Centers" which allow pregnancy, birth, and development to be done in near earth gravity.
- Most space colonies are built around mining and/or energy generation, manufacturing, and trade with other colonies (and for certain resources that are worth the cost) and Earth. As well as science experiments and tests on the side

Going agaisnt the Grain of answers here, but I don't think so. Space is different from living on a planet. You can go a month without food, 2 days without water and probably 5 minutes without air.

Resources are limited. You are either relying on the outside world bringing you the resources you want or you need machines to produce and recycle everything. Either way, the amount you can get and store is limited. Having lots of kids means more resources are invested into the Kids and aren't returned back to the colony for a long time. There is the traditional Food, Air and Water you need to keep the extra person alive, but you also need someone to look after the children. Thats someone not working (especially during the first couple of years) on producing the product which keeps the colony viable and afloat. You also need a bunch of extra resources that your working population don't need. Baby Formula, Nappies, baby clothes, cribs, stroller, toys, childrens books. So children act as a giant resource sink for a colony which more often than not, needed to produce goods to keep receiving essential supplies and stay alive.

You will also eventually run into a resource wall. When your 3 kids each have 3 kids of their own, and these 3 kids have 3 more. Every generation your population increases by 50%. Thats 50% more resources consumed (probably more if you factor in construction to make space of the extra people). Eventually your population (without proper control) is going to outgrow what you can produce and start to cost you money to keep alive.

So letting people have many (3+) kids isn't a good idea. Its a resource sink which you will likely see no or little benefit to and it costs you a ton of resources and ties up part of your potential workforce in daycare. It would be better for that to occur on a planet where you don't need to worry about running out of Oxygen, Water, Food or Space and then shipping proper working adults into the actual colonies to do proper work.

They produce too much food.

Maybe your colonies, for having planned too much greenhouses in their prime design (or after mining an edible asteroid, whatever fits your world) grew an excedent of perishable commodities with no way to preserve it appropriately (some food do spoil in a freezer). So instead of throwing it in space, your settlers eat it as it comes, and the overall abundance ended in more children than previously planned.

Which in turn, produced more people working in your "space farms" and results as an increase of perishable food, and so on...

Note that having "too much of something somewhere" would also explain the trading exchanges with the others colonies that lacks this "something".

Eugenics.

Most people are not cut out for long term space life. A lot of people degenerate within a few years in low gravity - malignant osteoporosis, accelerated atherosclerosis and other diseases. After wasting a lot of effort moving people to space only to have them sicken and die, the Hegemony systematically studied the genetic differences between the rare people who can tolerate long term space life and the majority who cannot.

People with the optimal genotype for space were really hard to find. They are less than 0.1% of the population, and many were too old or had other issues precluding a move to space. But now that there is a working population of the correct genotype in space, the Hegemony is very interested in breeding more. Space folk with their superior genes are encouraged to have as many space-ready kids as they can.

Attrition

Also one of the reasons rural medieval families were usually large ones. Because space stations represent the frontier, the most hazardous jobs and the workforce handling those jobs would be found there. A high attrition rate could come from pioneering exploration into unknown and likely dangerous environments, technology being inadequate to keep the colonists safe, or even a willful disregard for the safety of the colonists from the Hegemony. The Hegemony could be too corrupt to consistently enforce proper quality control and safety standards, or they could simply not care about their lives enough to bother.

Throw in the expectation that children would be expected to join the workforce from an early age to round out the explanation.

They need the work force

Perhaps your miners are very tribal in nature. The colony is very territorial. You and your tribe own a claim. You and your tribe work the claim. Need more workers? There's only one way to make that happen. Why does the colony support this? Because they draft some of the children into military service. So they need the work force too.