Author Steven Lake

Looking for a little math help
Wednesday, June 23rd, 2021 5:55pm
Keywords: Population Growth, Births, Deaths, Colony, Story, Scifi

Okay, I've got a math problem I need help with, and it's not one I can just grab a calculator and figure out, as it's got a lot of variables in it.  Anyhow, here's the stipulations of the question.  And, sorry for the story problem, but this is how the whole thing plays out.  Anyhow, I'm starting with a colony of 100 people, 90% of which are what I call "breeding couples".  Namely, not everyone in the colony can, or wants to have kids.  So 90% is my happy maximum fertility rate, leaning towards the conservative side of things.  These 45 breeding couples, who are part of the 100 original colonists, have a period of 10 years before a second group of colonists arrives totally 500 people.  Again, keeping to the 90% fertility rate, produces 225 new breeding couples.

And sorry if this sounds like I'm talking about livestock.  It's the best way I can describe the people having kids.  Anywhere, this 225 is added to the original 45, making a total of 270 breeding couples.  Add ten years, and the last group comes in, totaling 2500 people.  This adds 1125 breeding couples, added to the previous 270 for a total of 1395.  Now, that being said, starting at about 16 years into the mission, since some young children, and tweens, will be coming along on the mission, you will start to gain new breeding couples out of the children who were either brought to, or born on the planet.  I'm figuring around a 5% growth rate of new couples to start with, going upwards of 10% as time goes along.  So, if you want a comfortable number to play with, let's say 7.5% growth of new couples as children age, and get married, while also taking into account a loss of about 1 in 10 children due to diseases, injuries, etc.

If you haven't figured this out, I'm trying to figure out a rough number or rate of population growth that would be believable, and yet get as close to 2 million people for total colony size, within 150 years.  Basically these colonists will be kinda doing the baby printing thing to build their colony as big as possible, as quickly as possible.  So kinda like "19 kids and counting", but colony wide. :)  And, if you look at the Duggers of 19 kids and counting, they churned out an average of 1 kid ever 1.25 years.  Sometimes for them they were spitting out a kid a year.  But 1.25 is a happy average for them.  And I'm not expecting the original colonists to keep churning out kids at this rate forever.  They'd probably get to between 30 and 45 kids and just call it quits. :)

Plus their rate of "production" would slow down over the years, so once they cleared about age 70, their birthrate, despite their ability to age much, much, much slower than everyone else (it's a side effect of how they got to the colony in the first place), would drop off quite a bit, and go from, say, yearly, or one child per 1.25 years, to maybe one every 3-6 years until completely stopping around age 70.  So after that only the younger couples under 50 would be having kids.  So again, do you see how complex this equation is?  The end goal is 2 million or so colonists.  Maybe a little above, and maybe a little below.  The reason for this number is they're going to absorb about 10 million refugees from another planet, and the 1:5 ratio was determined to be a good number that's not too low (ie, too easy, making for a boring story), or too high (making it too stressful on the colonists, causing societal and resource collapse).

Anyhow, that's the math question.  What I'm looking for out of all of this is a rough, approximate birth rate needed to achieve this number.  This would also allow for the locational arrival of twins, triplets, and quadruplets, even though they would only make up about 5% of the total number.  To give you some stats to go on, here's the average birth rates in the USA of Twins and Triplets:

  • Twin birth rate: 32.1 per 1,000 live births
  • Triplet or higher order birth rate: 87.7 per 100,000 live births

So, anyhow, if one of you could help me figure this out, and give me the estimated (I realize there's a ton of factors that can affect this, so I'm just after a rough number) births per xx years rate of growth, minus deaths (adults and children) via expected rates for a society with a level of knowledge equal to the early 21st century, but a lifestyle circa mid 1880's, that'd really help me a lot.  I'm thinking that one kid per 1.25 years might work when subtracting deaths from births (the death rate will increase as the children of the original colonists grow old and die) so that may not be fast enough to reach 2m people.  Anyhow, that's my question, and my thoughts.  Please let me know what you think would work, and maybe even chart it out for me to use as a reference.  Anyhow, have fun with the question. :)

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