Cat inbreeding for cat breeders must by force of necessity be part of the process of developing purebred cats that are sufficiently of the right type (appearance). It happens a lot and cats become ill sometimes because of it. That is part of the breeding process. Close breeding creates the situation where it is possible for defective mutated recessive genes to come to the fore and produce disease.
A case in point might be the Bengal cat. Does this breed suffer from cat inbreeding? Such a fine looking cat but they have a predisposition towards contracting HCM, a heart disease. And importantly, the Bengal cat breed started off with a relatively small number of cats, such as as Tory of Delhi, Millwood Finally Found, Centerwall ALC, etc. Apparently lots of Bengal cats have high inbreeding coefficients (20%). Even if a breeder uses 0% inbreeding over 4-5 generations the process will result in cats with 20% inbreeding coefficients over the entire pedigree of the cat. Does this mean that the Bengal cat is relatively inbred? In other words outcrossing at this stage in the development of the breed fails to lower the coefficient it seems. (see a critique of Jean Mill, the much lauded founder of the Bengal Cat breed).
Some cats have a higher number of foundation cats. An example is the Norwegian Forest Cat, apparently. In contrast, the Burmese has been developed from one cat it seems, Wong Mau. It would seem that the important thing to prevent cat inbreeding is to ensure that at the beginning there is good number of foundation cats.
Turning to wildcats, an interesting question is whether inbreeding happens in the wild (i.e. is it natural to inbreed). If so cat breeders could argue that all they are doing is what happens naturally. What happens naturally, if one agrees with the evolutionary theories of Charles Darwin, must be done in the interests of survival of the individual and if the survival of the individual depends on the survival of a group you would have thought that cats would take action to protect the group as well.
As genetic diversity breeds better health and health aids survival it would seem plausible that cats in the wild do not naturally mate with close relatives. It does happen though when the population is very low. This happened with the Cheetah population. There are only about 12,500 Cheetahs left in the world and at one time it would seem the population was lower to a point where cat inbreeding took place leaving the current population having a very similar genetic makeup to laboratory bred animals that approximate cloned animals.
A similar problem exists currently when low populations of wild cat species are isolated in small pockets of remaining habitat. Although the overall population may seem sustainable the forced inbreeding occurring in the low population zones results in poor survival due to inbreeding.
Some say that cats can distinguish related cats through scent and on that basis are able to preserve health by not mating with close relations. Others disagree. We know that cats use their sense of smell to recognize territory. Even the age of a cat's spray (marking out territory) can tell another cat whether the cat is still around by the deterioration in the smell due to its age.
We also know that cats mate freely and the sheer numbers help preserve the species. My gut feel is that cat inbreeding does happen in the wild but not as a first choice but only out of necessity.
Update: A post about inbreeding depression and genetic frequency - click here.
Update 18th October 200: In an interesting article in the Times newspaper on 18th October we can see parallels with inbreeding in humans in the UK. Yes, this sounds surprising but it is happening. The current Immigration Minister is concerned he says about the number of marriages between first cousins in some families. In these communities there is a higher than average proportion of physical disability amongst children. The risk of disability amongst these communities is 4.7% he says. This is double the average. This reinforces on a very simplistic level the reasons behind the marriage laws in the Western world and why I think similar rules should be in place in relation to cat breeding. I know that this flies in the face of current practice but why should we apply different rules to cats or other animals? Cat keepers have a duty towards and a responsibility for the welfare of our cat companions. A cat breeder's responsibility is higher still because she/he brings the cat into the world.
Update 17-3-09: See some more on this subject in relation to a recent story from the Daily Mail: Inbreeding Makes Pedigree Cats Diseased.
See Purebred Pedigree Cat Breeding
Cat Inbreeding to Abyssinian cat
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