A DNA Primer for Dog Breeders. Genetic Diversity: Inbreeding (Fis)

By Carol Beuchat PhD
Sewell Wright, who first formulated the method for estimating inbreeding from pedigrees (hence, "Wright's Coefficient of Inbreeding"), also described another way of assessing inbreeding using something called a "fixation index", or Fis.

In a large, genetically diverse population in which mating is random, you would expect inbreeding to occur only rarely because the probability of two related individuals mating is low. If we were to find that there was a higher level of inbreeding in this population than what would be expected just by chance, that would be evidence of non-random mating of related individuals; i.e., preferential inbreeding.
If we know the allele frequencies of a particular marker in the population, we can estimate the genotypes to expect under random mating. These would be predicted by the "Hardy-Weinberg Equation" (p^2 + 2pq + q^2), where p and q are the frequencies of the two alleles for the marker of interest. Discussing the Hardy-Weinberg equation is beyond what we are going to cover here, but suffice it to say that we can use it to predict genotype frequencies under random mating. If we measure the actual genotype frequencies and find them to be different that expected based on H-W, then we know that mating has not been random.
We can use this tool to detect non-random mating using Wright's fixation index, Fis. Animals in a population with a level of inbreeding higher than expected based on H-W will have a positive Fis statistic. Animals that are outbred relative to what is expected under H-W will have a negative F statistic. An Fis of zero indicates a level of inbreeding equal to the expected value based on allele frequencies in the populaion.

In a nutshell, a positive Fis indicates inbreeding; a negative Fis indicates avoidance of inbreeding.
We can use our thousands of SNP markers to estimate Wright's Fis statistic for a population of individuals in a breed. The graphs below show the distribution of inbreeding coefficients (Fis) in Boxers and Irish Wolfhounds. For both breeds, there is "excess homozygosity" - a higher incidence of homozygosity on average than you would expect to see in a randomly breeding population. In both breeds, breeders are preferentially mating dogs that are more related than average in the population to produce higher levels of inbreeding.

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These data show that better choices when selecting breeding pairs could slow the rate of increase in inbreeding in both breeds and also lower the risk of genetic disorders caused by recessive mutations.

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