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If a high death rate is the reason for large families, then surely any new child would be to replace one that died which would mean that although there may be a large number of births the total children alive at any point in time is not large.
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Erm, no. People are dependent on their children to take care of them when they are old. Since you don't know who and how many will survive, the safe option is to have many children, which results in a net population growth. How many children would you have if you were dependent on them and you knew the chances of them living to adulthood are slim?
I posted this earlier in another thread:
Infant mortality by country
In the top ten of that list, one in five children do not live to the age of 5. By comparison, the figure for the UK is 6 in every 1000. And that's just the stats on infant mortality. Couple that with the fact that many/most people in these countries live on less than 1 US dollar per day, and you can start to imagine just how big the drama is. High birth and death rates are an enormous financial strain for the people involved.