As the population of the world is increasing, overall the birth rate is exceeding the death rate, but one does not affect the other as a “rate”. Yet, I have repeatedly observed in my family’s deaths and births examples that births occur within a year or less of each family member’s death. From my longstanding genealogical research, I am not aware of any theological or sociological basis, or scientific or mathematical studies, about the death of one family member correlating with the birth of another. So, only from my familial perspective, do I see a balanced rate of births and deaths.
Our Unbounded Heritage: 12th Century & Beyond 
I never really considered this. Although I must say that after being unable to conceive, I became pregnant after the death of my father in law. My spouse noted the connection right away. My tree does have months with many births/ deaths in the same month.
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