Human Population and My Ancestors

Human Population and My Ancestors

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My mother and grandmother - image taken a few years before the start of Facebook. Rhett Allain

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My mother and grandmother - image taken a few years before the start of Facebook. Rhett Allain

Here is a fun plotting game (suggested by my colleague David Norwood).

We all know that in the past there were not as many humans on Earth as there are now. Right now we are around 7 billion humans on this planet but just 200 years ago the population was around 1 billion (or less). So, the further back in time you go the fewer humans are on Earth.

Ok, now what about your ancestors? Personally, I have two parents. Both of my parents had parents so that I had 4 grandparents. My grandparents had parents which gives me 8 great-grandparents and so on. The further back in time I go, the more ancestors I have.

Now let’s merge these two sets of data. How far back in time do I have to go such that the number of my ancestors is the same as the human population? To answer this, I need two things. First, I need a plot of the Earth’s population. This isn’t too difficult. Just check out this page on Wikipedia regarding World Population. There are plenty of graphs from which you can get population data. I used one of those along with plotly’s web digitizer to get the data.

What about a plot of the number of ancestors? If I call myself the zeroth generation and my parents the 1st generation, then I can write the number of humans in a generation as:

Where N_g is the number of humans (just in that generation) and n is the generation number. But what is the time frame for a generation? If my ancestors have children at the age of 20 instead of 30, there will be a different number of ancestors 300 years from now. Of course the actual time between generations varies. For this calculation I will use 25 years for all generations.

Now for the plot.

According to this estimation, in the year 1280 I had 351 million ancestors and there were 351 million humans on Earth. But what does this really mean? Nothing.

Homework

When life gives you meaningless problems, make homework. I think that is an old saying. Well, here is some homework.

• What happens if you change the time span of a generation? What year does your ancestor size equal the population for a time span of 20 years? What about 30 years?


• Suppose the generation span (time between generations) is not constant. Maybe it is a random distribution (you can pick the kind of distribution) with times between 20 and 30 years. How does this change the crossing date?


• Make the generation span a random function that also depends on time such that the further back in time, the more likely the generation span is shorter.


• Of course, this model assumes no mixing. It assumes that all of your ancestors were unrelated. Is there any way to make a model with ancestor crossover (not sure what to call that).


• What if you were born in 1950? How much would that change your cross over date?


• Final homework question: write a story to explain why all of your ancestors are the only people on Earth.