Line-breeding and the coefficient of relationship

Often breeders choose to breed with dogs having common ancestors, with the aim of reproducing consistently a set of desirable morphological or behavioral characteristics.  In fact, all dog breeds have developed through a phase of in-breeding among members of a relatively small population. Once a breed is successfully established, still selected lines of dogs are used in the attempt of obtaining specific characters (line-breeding).  For a breed of relatively small size, such as FCRs, some level of line-breeding also appears due to a few dogs that have been used many times as stud.
Line-breeding has advantages and disadvantages. Having common ancestors in the parents' lines implies an increase in the probability of finding in the genotype areas of identical alleles (see figures). Organisms that reproduce sexually have their genome formed by pairs of alleles, with the case of of different alleles, heterozygosity, more frequent than that of equal ones, homozygosity. (The incidence of homozygosity in dogs is further discussed below.) In general, this is an advantage, since  undesired or pathological characters that may be present in a single allele are typically recessive, i.e. not active, in face of a complementary allele of different nature and generally healthy.
The presence of common ancestors in the lines of father and mother increases the probability of homozygosity. If the common ancestor is a carrier of a recessive genetic disorder (both alleles should be involved in order to be affected by the disease), the chance of the progeny being affected is increased compared to offsprings from unrelated lines.
Indeed, a number of hereditary disorders have been identified in dogs. Line-breeding or in-breeding increases the probability of recessive disorders, if the probability that the common ancestor carries the corresponding allele is larger than for an average individual. Several genetic disorders are understood as being poly-genic, that is involving several pairs of alleles. In affected individual they may appear with different degrees of severity (e.g.: hip dysplasia). These disorders are not easily eradicated with breeding selection programs. The probability of poly-genic disorders involving different chromosomes is scarcely affected by in-breeding, since combined homozigosity on different chromosomes would be required.

The coefficient of relationship (or in-breeding coefficient) describes the prospect for homozygosity, estimating the probability that any genome trait may be formed by identical alleles due to consanguinity. Limiting the analysis to two generations, a simple computation shows that the largest value of the coefficient is 0.25 (or 25%), achieved when breeding from any of the three closest cases of (a) brother and sister, (b) father and daughter or (c) mother and son. (The figure above, right side, shows the case in which the parents are half-brothers, and the in-breeding coefficient is 12.5%.) Higher values would be possible if the common ancestors had significant in-breeding coefficients of their own or if they were additionally linked to each other. The in-breeding coefficient is computed from the pedigree, with an accuracy that depends on the numbers of known generations.

In-breeding coefficients in our dogs and homozigosity in dogs                   (last update: 28/05/2011)