Sara Does Science

Sporatically posting thoughts and amusements from a pretty rad (if I don't say so myself) lady physicist.
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Know the musical¬†Mamma Mia? It’s a delightful jukebox-musical based on Abba songs and some Maury Povich style paternity hijinks. It’s also one of my biggest guilty pleasures. Approximately 1 to 3 times a year I open a bottle of white wine, drink most of it, and sing along. Once while doing this, I got the brilliant idea that since all three actors playing potential baby-daddies had different hair and eye colors, I could use Punnett Squares and some basic probability to get to the bottom of this investigation. But because I was kind of drunk I got a bit lost along the way.¬†So after another entertaining viewing last night (where I realized that not only have I memorized all the songs by now but all the dialog, too!) I decided to revisit my quest.

As a disclaimer: I am well aware that this is not high quality genetics by any means. But hey, my Ph.D. is in condensed matter experiment and Mrs. Kenny’s eighth grad science class was the last time I studied anything about inheriting genetic traits. And now that my necessary “I am not a geneticist” statement is out of the way…let’s go!

First, some basic assumptions I took the liberty of making in order to fit my basic Punnett Squares model.

  • Blue eyes are recessive, brown eyes are dominant. People only have those two genes.
  • Blond hair is recessive, brown hair is dominant. People only have genes for those two hair colors.
  • Whatever eye/hair color people have in the movie is taken as their natural eye/hair color.
  • In the interest of keeping the mystery alive, all the dad-candidates who are expressing a dominant trait have a recessive gene floating around their gene pool.

Now that are initial assumptions are out of the way, let’s see what traits our mother, daughter, and the mother’s quick succession of lovers have:

  • Sophie, daughter (Amanda Seyfried): blue eyes, blond hair
  • Donna, mother (Meryl Streep): blue eyes, blond hair
  • Sam (Pierce Brosnan): blue eyes, brown hair
  • Harry (Colin Firth <3): brown eyes, brown hair
  • Bill (Stellan Skarsgard): blue eyes, blue hair

Next I whipped up some Punnett Squares. Basically I wanted to know that given the men’s eye and hair colors, what was the chance that a daughter they had with Meryl Streep would end up with blue eyes or blond hair.

And once we get that settled, let’s compute the probability for each man that their kid would have both blue eyes and blond hair.

  • Sam: 100% blue eyes * 50% blond hair = 50%
  • Harry: 50% blue eyes * 50% blond hair = 25%
  • Bill: 100% blue eyes * 100% blond hair = 100%

So Bill is 2 times more likely than Sam to make a kid that looks like Amanda Seyfried and 4 times more likely than Harry to produce that same kid. His odds go way up if Harry has fully dominant genes for his eye and hair color and Sam has fully dominant genes for his hair color.

Now in real-world genetics, there is a lot more at play. But this this movie takes place on a small Greek Island and Meryl Streep’s character barely knows what the internet is in it, I’m going to assume there is little access to more advanced paternity testing. So therefore, I will end by concluding: Bill Anderson (Stellan Skargard):