Originally posted by iamatiger
Husband and Wife A and B have three daughters C D and E
C D and E marry, and have 6 children between them
A and B say "3 children and 6 grandchildren have descended from us, we have increased the world population"
Are they correct?
As far as I know, the long-term birth rate needed to keep the population steady is slightly over 2 children per couple (somewhere around 2.3?). If every couple had 2 kids that lived, it would be perfect. However, we need the extra little bit to make up for accidental deaths, disease, etc...
So over the first generation, parents A and B have slightly over-contributed to the population. Over the second generation, kids C, D and E (really couples C, D and E) have slightly under-contributed to the population. In a perfect world, A and B would give birth to C and D, who would later marry C2 and D2 and give birth to E, F, G and H (2 kids per couple, total of 6 "offspring" of A and B and 2 spouses, 10 people total). In a slightly more realistic world, A and B would give birth to 2.3 kids, who in turn would marry 2.3 spouses and give birth to 2.3 kids each, for a total of 11.5 people.
In this example, the total number of people is 14 (A, B, C, C2, D, D2, E, E2, F, G, H, I, J and K), so they have slightly increased the world's population (if everyone else had 2 kids per couple).
Assuming no one died, then there would be a net increase. However, if you take the qestion to mean "what if everyone carried on the way this family did" then it depends on the death rate and the sampling/averaging rate. For example, if there were a nuclear holocaust and everyone died except for this family, then the family could theorectically (a) increase the population (addition of C, D and E counting before the deaths); (b) decrease the population (everyone else dies, add 14 people to the mix, net decrease in population); or (c) keep it the same (sample taken after 14 people died, net equilibrium in population).
Pedantic, I know, but still important if you were ever to carry out a pratical census, ain't it?!? Practical being taking a census in the middle of a nuclear holocaust.
Whatever!!! It's still up in the air.