That video does a very good job of explaining this. As child mortality decreases, family size goes down. I'm sure the data is manipulated to suit someone's purposes, but all seems reasonable to me...
http://www.ted.com/talks/lang/en/hans_rosling_shows_the_best...
http://www.ted.com/talks/lang/en/hans_rosling_reveals_new_in...
http://www.ted.com/talks/lang/en/hans_rosling_at_state.html
That video does a very good job of explaining this. As child mortality decreases, family size goes down. I'm sure the data is manipulated to suit someone's purposes, but all seems reasonable to me...