Originally posted by curufinwe
Actually I believe you're mistaken. I child per family is perfectly plausibe and still growth is possible. If you havea long enough life expectancy than when one child grows up, you get another one. So saying 16 years you could have quite a few children.
Wow, I wrote that post a long time ago - never thought anyone would find it and respond.
Anyhow, I think you are mistaken - it takes two parents to create a child. So the replacement rate, regardless of mortality, cannot possibly be fewer than 2 children per couple (and must be more if some individuals do not produce offspring). If the individuals in your population have a finite life span, then in the long term (for times long compared to an individual lifetime) a population producing fewer than two children per couple will dwindle, even if in the short term (times short compared to an individual lifetime) there is growth.
Look at it with a concrete example. Suppose you have an initial population of 8, with a lifetime of 100 years per individual. Further suppose that every person has one child, at the age of twenty-five.
year 0: population = 8 (A,B,C,D,E,F,G,H)
year 25: population = 12 (A,B, and their child a; C,D, and their
child c; E, F, e; and G, H, g)
year 50: population = 14 (your original A-H, plus a, c, and their child x, and e, g and their child y)
year 75: population = 15 (A-H, a,c,e,g, and x and y and their child z)
year 100: now you start to see the dwindling. z has no one of her generation to mate with, and A-H all die. your population is down to 7 and will only shrink further.
year 125: a, c, e, and g die - only x, y, and z are left. You get the point.
Now consider the same idealized population, only suppose they have children at replacement rate - 2 per couple, if we assume every individual produces offspring. Now you will see that the population can sustain.
year 0: A-H are born.
year 25: A-H produce 8 more children (two per couple), a-h; population = 16
year 50: a-h produce 8 more children, a'-h'; population = 24
year 75: a'-h' produce 8 more children, a"-h"; population = 32
year 100: A-H die, but a"-h" produce 8 more children, a'''-h''' to replace them, so population holds steady at 32
year 1225: a'-h' die, but a'''-h''' produce 8 more children to replace them, so population holds steady at 32 again ... you get the picture.
These are idealized populations, obviously, but hopefully it makes clear why you need at least two children per family in order to sustain a population (absent immigration), and more than that for growth.