While some rather blunt models of population growth have been proposed (and been refuted) here, isn't the OTU implicitly assuming that birthrates can go up dramatically in the future?
I have made calculations several times of how the tens of billions of people might come about on some of the Hi-Pop planets. IIRC, I had to assume birthrates of 4+ per woman in many of the cases to get to the official numbers in the time since official discovery & colonization.
Now I see this as a great springboard for the imagination and see it as a feature. But if you really think that higher TLs (=standard of education & living) lead to lower birthrates all the time, then you will have big troubles explaining the settlement of known space.
I don't think the OTU assumes anything about populations. It just generates pops in a manner that is completely random without anything affecting the result. This causes totally non-sensical results in many cases. I use IMTU a slightly different method:
https://sites.google.com/site/moukotiger/sf-rpg/rules/uwp-1/population
Another alternative is to model growth which means estimating carrying capacity of a world.
On Earth, habitable land is about 33-38% of total landmass and consists of arable, pasture, and permanent crop land, so it is related to physiological density of population. I chose to use this single datapoint to figure that habitable land is related to land% * hydro%/2. For earth this makes habitable land to be ~10.5% of total surface area, which falls in the ballpark. This makes water act as a kind of limit of land usable for food/people; a world with no water will have no habitable land and thus need life support for food production. Non-habitable land are deserts, mountains, and land without top-soil.
Given all that, I looked at the 'net to see how many people 1 km^2 can support. Many sites agreed with a Cornell researcher that 1 acre could support a single person with a varied diet ( omnivorous ) and given that 1 km^2 has a bout 250 acres ( actually ~247 but I rounded to a neater number ), I figured a carrying capacity of 250 people per square km of habitable land. Using these numbers for earth's dimensions, I get a carrying capacity for earth of about 13.7 billion ( pop number of ~10.137 ), which falls in line with current estimates for max population of earth.
Currently, the earth uses approximately 50 workers per km^2 habitable land ( over varying tech levels ) to grow food. Tech level primarily affects this number of labor. Solar incidence, I would guess, effects growth and thus production, but shouldn't be a big deviation from '1' for worlds in the habitable zone. Again outside of this, a population would have to use some form of life support* to grow food.
so , for a world that doesn't use life support to grow plants,
total world area ~ diameter_km^2 * pi
total land area ~ world area * ( 1- hydro% )
habitable area ~ land area * ( hydro% / 2)
effect pop dens. ~ total pop / habitable land
12,800km diameter = ~514,718,105
land 30% = ~154,415,431
habitable area = ~54,045,401 ( earth pop ~7.5e9 )
eff. density = ~139 ( Earth's pop density ~145 pop/mile^2, or ~132 pop/mile^2 without counting Antarctica )
If the eff. density is less than 250, then the world is self sufficient and might even be able to export food.
If the eff. density is greater than 250, it must import food or else make up the difference with tech_life_support.
Not exactly related to the OP, but maybe useful in attempting to explain populations...
I'm also thinking that a world's population density is more important than total pop. A billion people on a tiny rock ball would be different socially than a billion people on a large world.
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