To answer the question, I believe that it is sensible to divide the domestic cat world into two categories: purebred and non-purebred cats (moggies). That’s because there is a distinct difference when answering the question between these two categories.
Purebred cats
Thanks to selective breeding i.e. artificial selection within the cat fancy, the normally “hidden” genes (recessive genes) that create the brown coat are brought forward and so this genotype is manifested in this unusual phenotype to use fancy language. In other words, the genes which normally don’t take effect do take effect under selective breeding.
And I can think of two cat breeds which are chocolate brown namely, in the UK, the Suffolk Chocolate and in the USA, the Havana Brown. These are mainstream cat breeds and therefore they cannot be considered to be rare.
RELATED: Rare Cat Breeds
Non-purebred (random-bred) cats
“Brown” is an old term for “chocolate”.
Brown cats a.k.a. chocolate-coloured cats are very rare among the random-bred population. In fact, despite looking at tens of thousands of photographs of cats over the past 15 years, I can’t recall seeing a random-bred or feral cat that was chocolate brown. The reason is that random-bred cats are just that: they breed (when allowed) randomly and not selectively. Although there is some selection going on when they mate it is not based on the objective of creating cats of a certain colour! Under natural selection the recessive genes creating the chocolate coat are inactive. Now to the genetics.
Genetics
The reason why we don’t see chocolate brown moggies is because the gene which creates the brown coat is either recessive or dominated by other genes which affect the colour of the coat. Update: it is recessive.
Sarah Hartwell, a cat genetic expert, tells us that there are two recessive genes at play in creating the chocolate-coloured coat or cinnamon coat which is a more dilute version of chocolate and these are b and b1.
She tells us that the black/brown gene signified by the symbol B is dominant and the above-mentioned genes are recessive to this dominant gene. The gene that creates cinnamon is the most recessive.
The best book available to us on cat genetics is Robertson’s Genetics for Cat Breeders and Veterinarians Fourth Edition. It is a difficult book to read!
The authors state: “The two mutant brown alleles (two copies of each gene) change the normal black appearance created by normal granules [melanin and phaeomelanin pigment granules in the hair strands] into different intensities of chocolate or brown. Wild type allele B is dominant to both b and b1 and b is dominant to b1. Therefore, both the heterozygote bb1 and the homozygote bb1 have the phenotype of chocolate brown.”
They state that these mutant, recessive genes alter the shape of the pigment granules. They change the normal round almost spherical shape to either oval in the case of the chocolate-coated cats and to a rod shaped in cinnamon-coated cats. This has the effect of diluting the color.
Conclusion
The conclusion is that chocolate-coloured cats are rare because the genes which create this coat colour are recessive and are therefore inactive until breeders employ selective breeding which is a form of inbreeding which allows these inactive genes to become active. Consequently chocolate-coloured cats are rare amongst the random-bred population but not rare in the cat fancy.
Below are some articles on the genetics.