Counting the Inhibitions

Calla is bored by counting, even counting kittens…

I got an interesting genetics question this morning from Sheddy Murphy, who has a litter of six kittens (Maine Coons) some of whom are showing signs of the Inhibitor gene from the dad cat.  One of the kittens, though, can’t show Inhibitor because it has the Dominant White gene masking any color at all.  Is there any way we can give a probability that his kitten too has the Inhibitor gene masked away?

I came up with the chances in a response but I thought I’d go through it again, just in case I messed it up.  And I think I have an easier way to show how you can figure it for some other situation.

The easy way to start is to list all possible options for the father (I/I), (i/I), (I, i), (i,i).  The kitten can inherit each of these 8 with the same chance.

  1. i  from i/i
  2. /i from same
  3. I from I/I
  4. /I  from I/I
  5. i from i/I
  6. I from i/I
  7. I from I/i
  8. i from I/i

So, it is 50/50.  But knowing that the dad must have a single I means that #1 and #2 can be eliminated right now, leaving 6 options – and 4 of them the kitten masks an I.  Not bad!

Next we add on the second kitten in the litter.  In the first two cases, where the dad is an I/I, the new Inhibitor kitten doubles the options in each case because it could inherit either one from dad.  The other 4 cases, though, there is only one I to inherit so the number is unchanged – a single possibility that matches the known facts

  1. I from I/I (x2)
  2. /I from I/I (x2)
  3. i from i/I
  4. I from i/I
  5. I from I/i
  6. i from I/i

So with 2 kittens we have 8 options, and only 2 cases does the white kitten not carry I.  The third kitten with I doubles case 1 and 2 again leaving us with 10/12 chance of an I in our kitten.  Kitten 4 gives (16+2)/(16+4) or 18/20.  Kitten 5 gives 34/36.  Kitten 6 gives us  66/68 or about 97 percent chance of our white kitten masking Inhibitor.

I had made a little mistake this morning, in that I did not count i/I and I/i as two independent cases and got a slightly different result.  But basically seeing five out of five kittens with I  showing makes it pretty likely that the dad cat has two I genes.  The chances of a 50/50 shot coming up the same way is pretty low.

Without going into a lot of theory, most probability questions are all about figuring out the number of options you have and discarding those that are ruled out.  You could just write them all down and cross them off and eventually come up with the same results.  The rules that math uses are just shortcuts to the same answer.  

Calla was told there would be no math in this post…

Gus has another vet checkup tomorrow morning.  Here’s hoping he is less scared this time that the last few rounds.

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About Oldcat

Engineer with Cats
This entry was posted in Calpurnia, Cats, Genetics, Julius Caesar and tagged , , , , , . Bookmark the permalink.

3 Responses to Counting the Inhibitions

  1. I love the genetic information, it always makes me look at my kitties, and past kitties, with new eyes. Is it true, or just a wives tale, that a cat can have more than one father per litter? Let me tell you, my old momma cat could have some pretty varied litters!
    Purrs for Gus and his appointment tomorrow!
    That first picture of Calla, she looks like a bored queen lazily reaching for a bonbon just for something to do.. MOL

    Like

    • Oldcat says:

      Yes, this is true. Female cats don’t even ovulate until after sex, and the sperm has to hang about waiting for the eggs to show up. There are little places to rest for them. Presumably it is a way to increase genetic diversity in an animal that is usually fairly solitary. But even one pair can have a lot of variety in a set of kittens.

      Here’s an interesting documentary: http://topdocumentaryfilms.com/in-the-womb-cats/

      Like

  2. kimkiminy says:

    I know noth-inks about genez, inhibitors or ozervise.
    I do know i vant to stroke Calla’s aerm in de first pic, und ze last vone, my goodnezz… de tongs, de shin, de furs, de viskeers, de feets… I em verklempt. 🙂

    Like

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