## Is This Kitten Homogeneous?

When you see a KittyCatS cat with the trait that you want and then you view its family tree; it’s very easy to assume that it may be pure in the trait that you want, if you see **ONLY** this trait being held by all its parents and grandparents.

Suppose you see a cat with azure eyes and you look at the family tree and notice that both the parents and all four of the grandparents have azure eyes, what do you think the chances are that the cat in front of you has azure as both the dominant and recessive traits? (What are the chances that the cat is homogeneous with this particular trait?)

It would be very easy to assume that the chances were particularly high. In fact, I confess, before I did the mathematics, I thought that the mathematical chance that the cat was homogeneous laid at roughly 90 or 95%. However, I was shocked when I took a scrap of paper and calculated it in full.

Assuming the worst case scenario that all four of the grandparents are heterogeneous (they have a recessive hidden gene that is not azure but some other more recessive colour), the chance that the final offspring is homogeneous is actually just 50%. Yes, that is right, there is only just a 50/50 chance that both the dominant and recessive genes are the same. Unbelievable, isn’t it! If you still need some verification, here are my rough scribbles:

**Explanation for above scribbles:**

Each of the four grandparents are heterogeneous (Aa) and so there is a one in three chance that their offspring are homogeneous. (We can discount the “aa” offspring from the maths for we know that the recessive fur is not showing.) When combining these three different combinations for the two parents, 16 homogeneous offspring are produced. Again, we can again discount the four “aa” results because we can see from the pedigree page that no cat has a recessive fur type. This means that there are (9×4)-4 different combinations.

I was surprised to see that, despite having a whole page of identical traits, the final cat only has mathematically a 50-50 chance of being pure in the given trait.

What this means, when we view a page full of identical cats, the chances of the final cat being homogeneous in one specified trait is simply 50% (if the grandparents were heterogeneous.) So, don’t let a family tree, full of identical kittens, deceive you into thinking that the final cat is pure.