The Coefficient of inbreeding

Unquestionably inbreeding can lead to a loss of biological fitness. The animals in the inbred lineage are less likely to survive and less likely to reproduce than animals in more outbred lineages. This has been demonstrated many times in well-studied, naturally outbreeding species. Inbreeding can result in reduced fertility both in litter size and sperm viability, developmental disruption, lower birth rate, higher infant mortality, shorter life span, increased expression of inherited disorders and reduction of immune system function. The immune system is closely linked to the removal of cancer cells from a healthy body (Smyth et al., 2006), so reduction of immune system function increases the risk of full-blown tumours. (Professor Bateson, the Bateson enquiry into dog breeding 2009)

The inbreeding coefficient is defined as the probability that both genes (alleles) of a pair (one inherited from each of the parents) are identical by common descent. In other words they both originate from a single allele, from a single ancestor within the pedigree. It occurs when particular ancestors appear on both the sire and dam sides of a pedigree. The degree of inbreeding depends on how many common ancestors there are and how close they are to the dog itself. For example, a common grandparent has a very much larger impact on the degree of inbreeding than does a common great great grandparent. The degree of inbreeding is computed using a formula known as Wright’s Coefficient of inbreeding, first published in 1922 by the great American geneticist, Sewall Wright.

The value provided here is calculated using 10 generations (2046 ancestors) but to understand what the values mean consider this: If we just look at a single generation mating and ignore any previous inbreeding the following matings produce inbreeding coefficients of:

Brother x Sister                       25.00%
Parent x offspring                   18.75%
Grand parent to grandchild      12.50%
First Cousin                              6.25%

From the published data provided by the Kennel Club, 137 IWS litters have been registered from January 2002 to September 2009.
The distribution of the COIs is shown in the table below and are calculated to 10 generations (2046 ancestors)

Why is minimising inbreeding so important?

Most canine genetic diseases (75% +) require two copies of a faulty gene (one from each parent) to be inherited in order to cause the disease in the individual. A carrier, where only one copy is inherited won't show the disease but could pass the gene on causing disease in subsequent litters. Inbreeding increases the chances of this happening and continued inbreeding greatly amplifies this possibility. The same applies to polygenic diseases, such as hip dysplasia, where more than one gene is responsible for the disease. In the natural world, Darwin's theory of evolution by natural selection would come into play meaning that any gene mutations which cause an individual to have a disadvantage would either disappear completely or be present in the population in very small numbers (survival of the fittest).
Unfortunately, in pedigree dogs this natural control mechanism is not allowed to exist because man selects the matings and he is not as discerning as nature.

Consequently, although low COIs are important for minimising inbreeding depression, they do not guarantee that any given genetic disease will not occur in dogs. Indeed, it is possible that for a given disease, matings with low COIs could be just as harmful as line breeding for spreading the deleterious genes around.
However, as there are no genetic tests for any of the genetic diseases known to exist in the IWS and breeders in particular are not forthcoming about divulging which of their dogs have developed which disease, it is currently very difficult to eradicate genetic disease.
In this situation, the best that can be done is to try to mimic nature and have litters with low COIs.