3
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i've heard that if in a population each pair has 4 children, then after 4 generations it's a 1600% increase..

I suppose after 1 generation it is 200%, and each successive generation is 200%, and they multiply 200%^4 But, if I try it out with figures like this, I never get 1600%

suppose a population of 10

g  g1 g2 g3  g4 10 20 40 80  160 

So each generation is double the previous, and from the start of g, population of 10, each of 4 generations g1-g4 have 4 children.

10+20+40+80+160=310
(310-10)/10 = 3000%

Not 1600%

Howcome i'm not getting 1600%?

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    The value $g_n$ in your notation denotes _the entire population_ at generation $n$. It is not necessary to add in previous generations (at least not very many) since a generation is assumed to have survived their parents. In your figures it is easy to see that $\frac{160}{10}\cdot 100$ is $1600$%.2011-03-31
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    @Joshua Shane Liberman gn in my notation is not the entire population at generation n. 'cos each generation has 4 children.. so by the time of g1, the entire population is g1+g=30.2011-03-31
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    I suppose 1600% is how many times bigger the last generation is than the first. Not % increase. And not comparing population sizes.2011-03-31
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    Maybe I am not making myself clear. If $g_n$ were your notation for the entire population during time period $n$ (and we know that no members of generation $n-1$ are still alive and no members of the next generation have been born) then we do see the kind of progression you were asking about, which would explain why your answer is different. It is to a different question! An example of this kind of population is the cicada of genus Magicicada, the periodical cicada with the 13- or 17-year life cycle, although a female cicada often lays hundreds of eggs instead of four.2011-03-31
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    Thanks Joshua. Well, the 2 posted answers are both excellent. Arturo's and Douglas's with his all important follow ups. When I consider follow-ups and I do and must, then i'm stumped!2011-04-01

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