The Math of Human Overpopulation

People seem to think that the two children have replaced the couple, but indeed they have not, the couple is still alive. In fact, in many parts of the developed world children will have parents, grandparents, and sometimes even great grandparents.

The birth of a child cannot be counted as a replacement for the death of a great grandparent, simply because that great grandparent probably has other descendants, and where theoretically replaced with the birth of their own child, so in fact were replaced many times over. We are living longer today, and have fewer infant fatalities than ever before. These are two contributing factors to human over population.

Now let us do the fun part: Math!

We want to take 4 couples, we will have 2 couples have children at an early age, and 2 couples who will have children at a later age. Every couple will have no more than 2 children, as such we are discounting the possibility of multiple births. We also assume that the couples have no living relatives.

The first 2 couples, for the sake of keeping the math easy, will have 2 children by the time they are 20 years old, and their children will repeat this pattern. The second 2 couples will have their two children later in life, let us say by the time they are 35. In both cases we will assume everyone dies at age 70 (lower than the average death rate in most developed nations but this will account for other earlier deaths). We will cover both sets of couples for 100 years.

Study 1

• Year 0.   Start with 4 people (2 couples)
• Year 20.   The population has doubled into 8.
• Year 40.   The 4 original people are still alive as are their kids who now have kids 4+4+4=12.
• Year 60.   The 4 original people are alive, their kids, and grandkids, who now have kids, 4+4+4+4 =16.
• Year 70.   The 4 original people die, 16 – 4 = 12.
• Year 80.   The last 4 now have kids, 4+4+4+4 =16.
• Year 90.   The first kids born now die, 16 – 4 = 12.
• Year 100.   Add another 4 births, 12 + 4 = 16.

Study 2

• Year 0.   Start with 4 people (2 couples)
• Year 35.   The population has doubled into 8.
• Year 70.   The first 4 people die, but indeed their children have had kids 8-4+4=8.
• Year 105.   The first children die but their kids have had kids 8-4+4=8.

When we look at these 2 studies we see that BOTH have shown population increases even by only having 2 children. In the first example, by having kids at a young age, the population soon skyrocketed before reaching a plateau, in the second it climbed slower but still showed growth. The theoretical replacement factor took place in different generations, and only happened because nobody had more than 2 children. Had anyone had more than 2 children a plateau and replacement factor never would have occurred. PLUS with advancement in the medical field our average lifespan is exceeding 70 years, especially in developed nations. Remember, it was not that long ago (the early 1900’s) when the average human lifespan was 45.