What has a chance of passing into an animal is what you can get from the animal it self and its Stats Button or its Parents Stats Button. This is also equal to that of the bottom row of each animal on the ancestry page. As seen here.

Taking a closer look at the pages – and recent change to the Collection Edition specifically the ones with Exclusive furs and the added Exclusive furs of the parents.  We have always stated that the Ancestry page shows you what went into the animal that your looking at.  This way you can see what parents of the parents to be were mixed together and created the animal all in one place.
When the baby grows up it will move to either the right or the left side depending on its sex of course when you look at its babies.

As the animals move to the top row they are no longer going to be considered when the animal your looking at goes to make a baby.  The animal in the light green area only take its traits and the animals to either side of it in the bottom row.

The parent exclusive furs will only come out from the Resulting Baby. By restricting this it makes the trait very rare and more valuable as it will stay rare for some time.  It can not come out from the Random pull it can only come from the animal with them as the parents.

A few questions that have come to us since this post.

If the trait is in the bottom row will it pass?  Yes

If the trait is in the top row and has passed in to the resulting baby can it pass? Yes

When the RootBeer Fur was introduced it has a parent of Cream Soda and Licorice will all RootBeer Furs be able to pass Cream Soda and Licorice Furs?  No – the RootBeer is a Exclusive Fur but it will only produce something similar to it self.

If my animal is a Cream Soda Fur will it have a chance of passing? Yes, If the resulting Cub is not a Cream Soda can it pass a Cream Soda? Yes, as it is in the Bottom Row.