# QotW: How does a surname multiply?

## Question

If 300 years ago one person had a certain surname, how many people could have that surname today?

## Answer

**What's in a name? Eva H****igginbotham’s been crunching the numbers to figure out an answer to this question from Beata...**

Eva - I am the proud participant in a Facebook group called ‘The Family Higginbotham’ which boasts 1.8 thousand members with the tagline ‘We’re all cousins somehow’. People are always posting their latest detective work, tracing Higginbothams back through the ages, but could we do the reverse as Beata suggests, and instead project forwards to see how many people could have our name in the future? I put the question to maths whiz James Grime

James- This was a question of great interest to the Victorian nobility, who were very keen to know whether their grand noble names would live on or die out. So, let’s start with a quick calculation. And to do this, we will treat surnames in the traditional sense, as something passed from father to son. Of course, this is not necessarily true, but allows us to perform a calculation based on the average number of male children.

Eva - Now, in the 1800s, the average number of children per family was 5. Unfortunately, 2 or 3 children typically did not reach adulthood. Later, as the infant mortality rate decreased, so did the fertility rate.

James - For the sake of the maths, we have to use an average - so let’s say the average number of children has been a steady 3 children per family. Or about 1.5 male children. That means, for each generation, the number of males increases by 50%. And over 300 years, say 10 generations, the male population would grow from 1 individual to 58. Of course, I used an average here. If instead, each generation had three boys, then the number of descendants sharing that surname could be as large as 59000. On the other hand, a couple of generations with no male children could lead to the surname dying completely.

Eva - And it was the potential dying out of their surname that the Victorian nobility were concerned about. So, two great Victorian statisticians, Francis Galton and Henry Watson, decided to investigate the problem.

James - And they determined that a surname would ultimately die out if the average number of male children was less than or equal to 1. That might sound obvious, because that means the average number of males would be decreasing with each generation. But now they could show that this was a mathematical guarantee. Now, family names are actually more complicated than that. But these ideas can be used in tracing something that is passed from father to son, which is the Y-chromosome. Or equally, something inherited from our mothers, such as mitrochondrial DNA.

Eva - That means that by my calculation, in 10 generations, we could have 106,288,200 Higginbothams… yes, yes, plenty to start the master plan...oh! What? Oh yes, thanks James. And next week we’ll be looking into this question from Robyn:

Robyn - I often wonder when I listen to music in the car when my dog is with me: since they hear higher frequencies than humans, do they also perceive for example loud music louder than us?

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