Today’s hyperfixation comes to you courtesy of the following tumblr post:

 

When the following image dropped itself into my head and wouldn’t leave me alone:

and it started to dawn on me that we’re working with more than one trait and as such, the Punnett Square would need to be bigger than four cells.

Now, look, I took genetics for my upper-division science requirement in college for my BA in Art nearly 20 years ago, which is to say that I am operating WAY out of my lane here. But I think I have enough background knowledge left to be able to figure this out. So, let’s go.

First, the premise is that a Centaur and a Mermaid are producing a viable offspring. And that there are real odds that you could get a Human, a Horse, a Fish, a Centaur, a Mermaid, a Seahorse, and Whatever the Hell This Is out of this coupling.

I also have to assume you can get these two monstrosities as well:

I spent hours trying to make this work and ended up in the weeds. At one point I was considering crossing up the notation with hexadecimal where each two digits represented a state of horse-ness, fish-ness, and human-ness, but I kept ending up with creatures with multiple heads, or worse, multiple bodies, and nobody wants that.

Fortunately, I have friends who are willing to follow me down these rabbit holes, with actual expertise in the subject matter.  My buddy Nicole started sending me punnet squares and gave me better ways to imagine the traits so that I get the expressions I want without driving myself nuts:

So in this scenario we end up with 48 human expressions, 9 Horses, 3 horse-body, fish-head abominations, 3 Seahorses, and 1 fish.

Which is pretty good, but it makes it impossible for Centaurs and Mermaids to exist, so what I need is for that third trait to swap the expression of the body and head. And so as not to make a third option, this is your basic Dominant/recessive situation, where the only way you get the swap is to have two recessive genes.

This Handy calculator let me work out the only scenario where we get our Fish-Headed, Horse-Bodied abomination, which is when you have a Mermaid and Centaur each with a heterozygous pair of Switch Genes:

and in this scenario, our precious son has a 1/8 chance of existing.