Analysing an interstellar colony

#1
Hi,

This is really easy stuff for all the stats wizards here, but I'd really appreciate some help please. :yup:

Suppose there's a colony of 3,000 people (men, women and children) sailing on this starship in the middle of nowhere in space. Suppose it's been 2,000 years since they left Earth and that they have birth control onboard such that the population is always kept around this figure of 3,000 people. (The voyage is multi-generational, meaning as one generation dies off, the next one takes over, etc.) The average family profile in this community, is 2 children per couple.

Now, at the end of this 2,000 years of voyaging since leaving Earth, I want to analyse the averages.

1) I take it, the generation now sailing the starship is the 80th generation? Is that right if I assume 25 years per generation, so 2,000/25 = 80?

2) If a preseident ruled the starship from the start, using a succession planning dynasty structure, so that as he grew old and retired, his son took over, etc. If the average rule per president was for 30 years, then would I be right to assume the 66th president is now ruling? (2,000/30 = 66)?

3) How many children can I assume there are in this 3,000 pupulation? Would there be anything radically wrong if I said there's 1,000 men, 1,000 women and 1,000 children?

Thanks very much for any thoughts...:)
 

JohnM

TS Contributor
#2
Points (1) and (2) seem reasonable, but (3) runs counter to your original statement about an average of 2 children per family.

If there are 1000 man and 1000 women, that implies 1000 "families" or couples. Then, if there are 1000 children, that gives you:

1000 children / 1000 families = 1 child/family
 

heD

New Member
#3
Well.. Your guesses are not really conflicting with the problem as you gave it..
It's just that the very problem conflicts with a known result. Isolated population's generations follow Galton-Watson branching process.
There is a theorem that says that the probability of ultimate extinction of the population is equal to one if every individual has one or fewer offsprings (or each family 2 or fewer).
The population approaches the extincion exponentially in this case.
So, in 2,000 years, I think, everyone would be pretty much dead. It's possible to calculate the E(X_t), where X_t is the size of the population after 2000 years.

However, I don't think you really need all this, it just came to my mind.

Cheerz
 
#4
Hi,

Thanks very much for confirming. I stand corrected on point 3, as there'd have to be 1,500 children, 750 men and 750 women (750 couples) in total, to fit the assumptions.

Thinking on a different level, if I wanted to have every one death replaced by one new birth, would I be right in saying the average family needs to have two plus children per couple? And would they need to be a boy and a girl?

I like to think so... but does it fit from a maths perspective...
 

JohnM

TS Contributor
#5
I'm not well-versed on population models, but it makes intuitive sense that each set of parents needs to at least "replace" themselves, on average. So, at least 2 children per family, on average - probably more to account for things such as premature death, learning disabilities, or anything else that would hamper the continuation of the colony.

...and each set of two children would need to be boy-girl...or every family with two boys needs to be offset by a family with two girls.
 
#6
Thanks heaps for confirming. It will be a very delicate process, operating an interstellar colony with a population size only running in the few thousands at most, because of the restricted amount of space available on the generation ship. And the voyage will last.... 50,000 years! ;)

(I went into it in some detail in a novel here: http://www.publishedauthors.net/aa_spaceagent/ but I will need to address it again in the follow up sequel that I'm currently writing... hence the need to sense check it again.)

Thanks very much for all the help.

S
 
#7
i think the guy should consult a geneticist on this as this is a very limited gene pool to survive 2000 generations or more.

one additional common sense observation is that not all adults will marry and reproduce. this makes the family arrangement even more tenuous.

cheers
jerry