Population Growth of an Extraterrestrial Colony
Okay, i need help here. I'm sure this question has been asked before and if it has, please refer me to it. But a story I have been working on for a while now revolves around the adventures of a colony on a alien earth-like planet many thousands of light years from earth. In the course of the story, which is set in the early 22nd century, the colony loses contact with earth (as the wormhole they have been using to transport new colonist and supplementary supplies to the colony collapses unexpectantly). The colony, at the time of the collapse, is decently developed and reasonably autonomous and self-sustaining, as in it has farms, water treatment facilities, government, etc., with a population around 8,000-10,000. My question is, how do I calculate how the population will grow in say a hundred years, assuming they have the means to live self-sufficiently? Please provide formula or some mathmatical process that can help me.
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Ok, lets start with a population of 10,000 colonists.
I will assume that the population consists entirely of adults that have been selected to be of reproductive age, and that half the population is female.
Each woman will produce between 0 and 5 offspring. Assuming that they're voluntary colonists, it is likely that all available females are willing to produce children, so lets say that each female colonist produces at minimum 1 child. The average number of offspring in the first generation is 3.
So, generation 1 produces 15,000 children. I don't have a value for the rate of childhood mortality for this colony, but assuming 22nd century medical technology, it will likely be low.
Generation time for a 22nd century colony could reasonably be similar to that of late 20th/early 21st century developed nations, so: roughly 25 years.
Generation 2 (25 years): ~22,500 children.
Generation 3 (50 years): ~33,750 children.
Generation 4 (75 years): ~50,625 children.
Generation 5 (100 years): ~75,938 children.
So, the total number of births in 100 years is going to be around 197,813.
Death rates are a bit trickier, given that "22nd century technology" could have a massive effect on that. Have your colonists cracked the longevity problem? Is colonial life particularly dangerous? Are there alien pathogens around that kill off colonists?
Even without knowing these things, I think that ~200,000 colonists after 100 years is a good ballpark estimate.
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