How to calculate total number progressive...?

Question

Each clan now has 10 couples of man & woman (20 persons)

Assuming that there is :
10% of zero birth rate
due to infertility, premature death, cancer,
gay/lesbian issues, war/epidemic, etc,

Assuming that there is :
10% divorce/ remarriage
which will also bring babies of the same birth rate.

Clan A: average birth rate 2.5
Clan B: average birth rate 1
Clan C: average birth rate 0.9

After 10 generations,
the total number in clan A = ?
the total number in clan B = ?
the total number in clan C = ?

What method should I use and how to calculate?

And faster way to find out differences between the 3 totals?

Thanks

Assuming each generation do not marry each other but marry to someone else outside the clan.

fertility rate per couple/woman.

Answer 1

I'm a bit confused.

10% of zero is zero.

I don't see how divorce or infertility, etc come to play.

If you are given birth rates, they are usually a measure of births per person. It is usually calculated based on population changes over a standard number of years that represent a generation (IE pop was 30 million in 1970, 40 million in 1995 that is a 40/30 or 1.33 birth rate.)

If that is the definition you should be able to use the formula for compound growth:
A = P(rate)^n
You've said there are 20 people, so P is 20, rate is the birth rate and n is the number of generations.

For each, take the rate to the power of 10, then multiply by 20.

Answer 2

This is not a random number issue. However there is a weakness with your question. As you have an average birth rate, then that takes care of all aspects of the rate; including the 10% zero rate and lets say the 5% who have 10 babies. Now the next weakness is whether this rate is the number of babies per year for the 10 couples; if it is it is quite slow. The next issue is that after say 16 years then the females who have been born in the problem can also give birth; and yet again the ratio of girls to boys being born will affect the final answer. Or then again is the rate the number of children one couple has in a generation. If you could clarify some of these issues this could be an interesting problem. Sorry this doesn't solve it though.

Answer 3

1

Answer 4

well obviously this is a random process so you could do this with a random number generator to predict the number in each clan after 10 generations.

After you have determined which couples can have children you could use a poisson probability distribution to give the probability of a couple having 0,1,2,3, ... children.

You would then need to look at the boy girl ratio (if 1 generation only produced girls they would be in trouble) (perhaps 50-50 ratio)

Also you may want to discount the possibility of brothers and sisters becoming couples.

good luck with your model

Answer 5

2

Answer 6

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Cheers.