Black fur color in cats is determined by a specific gene called the melanistic gene, often referred to as the "B" gene. This gene controls the production of a pigment called eumelanin, which is responsible for the dark coloration in fur, skin, and eyes.

There are two possible variants of the melanistic gene: B (black) and b (non-black). The black variant (B) is dominant, meaning that if a cat inherits even one copy of the B allele, it will have black fur. On the other hand, the non-black variant (b) is recessive, so a cat needs to inherit two copies of the b allele to express a non-black color.

Let's consider an example to understand how black fur color is inherited. Suppose we have two cats, one with black fur (BB) and the other with non-black fur (bb). Since the black variant is dominant, the offspring will inherit one copy of the B allele from the black parent and one copy of the b allele from the non-black parent. As a result, all the offspring will have black fur because they possess at least one copy of the dominant B allele.

However, if both parents carry a copy of the non-black allele (Bb x Bb), there is a 25% chance that their offspring will inherit two copies of the recessive b allele (bb), resulting in non-black fur color. This is why black cats can sometimes have non-black kittens if both parents carry the recessive non-black allele.

It is important to note that the genetics of fur color in cats can be more complex, as there are other genes involved in determining patterns and shades of fur. For instance, the agouti gene (A) controls whether the eumelanin pigment is evenly distributed (solid black) or restricted to specific areas (tabby or tortoiseshell patterns).

References:

1. "Genetics of Coat Color in Cats." Veterinary Genetics Laboratory, UC Davis School of Veterinary Medicine, https://www.vgl.ucdavis.edu/services/cat/CoatColor.php
2. "The Genetics of Calico Cats." Cat Fanciers' Association, https://cfa.org/genetics-of-calico-cats/