By Carol Beuchat PhD
The coefficient of inbreeding was derived by Sewell Wright back in the 1920s to provide animal breeders a way to quantitatively assess relatedness of animals in lineages with complex pedigrees. It's easy to estimate relatedness of individuals from a few pedigree generations, but as the pedigree gets deeper, and inbreeding and crossings among lines get more complex, estimating relatedness of pairs of individuals becomes an overwhelming task.
Why was estimating relatedness important? Back in the day, breeders understood the general effects of parental relatedness on quality of offspring. They knew that a bit of inbreeding increased the uniformity, predictability, and quality of many traits in offspring. But they also found that too much inbreeding had negative effects, a phenomenon called "inbreeding depression." Starting with a population of outbred animals, Wright summarized the dual consequences of inbreeding here (Wright 1922):
Why was estimating relatedness important? Back in the day, breeders understood the general effects of parental relatedness on quality of offspring. They knew that a bit of inbreeding increased the uniformity, predictability, and quality of many traits in offspring. But they also found that too much inbreeding had negative effects, a phenomenon called "inbreeding depression." Starting with a population of outbred animals, Wright summarized the dual consequences of inbreeding here (Wright 1922):
| "First, [there is] a decline in all elements of vigor, as weight, fertility, vitality, etc., and second, an increase in uniformity within the inbred stock, correlated with which is an increase in prepotency in outside crosses... The best explanation of the decrease in vigor is dependent on the view that Mendelian factors unfavorable to vigor in any respect are more frequently recessive than dominant, a situation which is the logical consequence of the two propositions that mutations are more likely to injure than improve the complex adjustments within an organzism and that injurious dominant mutations will be relatively promptly weeded out, leaving the recessive ones to accumulate, especially if they happen to be linked with favorable dominant factors. On this view, it may be readily shown that the decrease in vigor in starting inbreeding in a previously random-bred stock should be directly proportional to the increase in the percentage of homozygosity... As for the other effects of inbreeding, fixation of characters and increased prepotency, these are of course in direct proportion to the percentage of homozygosis. Thus, if we can calculate the percentage of homozygosis which would follow on the average from a given system of mating, we can at once form the most natural coefficient of inbreeding.” |
| Wright is saying that deleterious mutations that are dominant will show their effects and can be weeded out, but recessive mutations that have no effect unless homozygous will tend to accumulate in the genome over time. Consequently, crossing related animals runs the risk of producing offspring that are homozygous for previously silent recessive mutations, with deleterious consequences that can range from an obvious functional defect to subtle changes in health, vitality, longevity, and so on. Therefore, breeders in Wright's time wanted to be able to figure out the level of inbreeding so they could balance the benefits with the risks when striving to producce the best quality animals. Wright realized that because both the positive and negative effects come from alleles on individual loci, changes in the fraction of loci that are homozygous would have a direct and proportional effect on the traits that are improved as well as those that are detrimental. This allowed breeders to identify the "sweet spot" in COI where their animals would have the highest value because of the best tradeoff between benefit and detriment. |  |
Wright's development of the coefficient of inbreeding revolutionized animal breeding because it provided a quantitative estimate of inbreeding based on an understanding of probability in inheritance of alleles. His expression of this has arguably been the most powerful tool in the box for breeders over the last century, and it remains just as important now as it was then because it is grounded on the fundamental processe of independent inheritance of alleles. In many populations of wild and captive animals (and plants, too!), the coefficient of inbreeding, and its related statistic, the kinship coefficient, remains the primary means of genetic management.
So why is it that I hear breeders declaring that "the inbreeding coefficient is "just a tool" or a "fad", or a crude, dusty relic of the olden days when breeders only used paper pedigrees for breeding? It is claimed to be "inaccurate", "pretty much worthless", and not useful now that we can estimate genomic inbreeding from DNA analysis. If this was true, why would today's foremost scientists in the fields of population genetics and animal breeding management still be using it?
Well, I think a lot of breeders say these things because they heard somebody else say them. This is the "folklore" model of information development, where the loudest voices can produce "information" that is accepted by the masses because nobody does the fact check. People parrot these memes because it's what everybody else says, and they don't understand the biology enough to questions anything. The consequence is that you can't make the best breeding decisions working from bad information, and after all the work and expense that goes into breeding, nobody wants to do that!
In truth, we will continue to use the coefficient of inbreeding as long as we continue to breed animals and plants, which will be as long as we inhabit this earth. Here are a few reasons why, and these are also the ways you should be using it now.
First, the inbreeding coefficient can be used to reconstruct the genetic history of a population of animals. Dr Pieter Oliehoek used it in his analysis of the population genetics of the Icelandic Sheepdog to document the loss of genetic diversity over time, as reflected in the increase in average level of inbreeding in the population.
Oliehoek also used a related statistic, the kinship coefficient, to reveal how breeding strategy in the population had changed over time. The kinship coefficient measures the degree of relatedness (in terms of genetic similarity) between two individuals. The kinship coefficient is also equal to the inbreeding coefficient of offspring produced by a pair of animals. In other words, the inbreeding coefficient of an animal is the kinship coefficient of its parents. When Oliehoek plotted both the inbreeding coefficient (black symbols and line on the graph below) and kinship coefficient (red symbols and line) on the same graph as probabilities (i.e., values between 0 and 1.0), he showed that in the early history of the breed, there was preferential avoidance inbreeding that is revealed because average inbreeding was less than average kinship in the population (the black line is lower than the red line); that is, breeders chose to pair individuals that were less closely related than average in the population. This was the case until the early 1980s, when these lines flipped, with the average inbreeding increasing faster than average kinship, reflecting a preference by breeders for closer inbreeding, even when pairs were available that would produce lower levels of inbreeding.
Oliehoek also used a related statistic, the kinship coefficient, to reveal how breeding strategy in the population had changed over time. The kinship coefficient measures the degree of relatedness (in terms of genetic similarity) between two individuals. The kinship coefficient is also equal to the inbreeding coefficient of offspring produced by a pair of animals. In other words, the inbreeding coefficient of an animal is the kinship coefficient of its parents. When Oliehoek plotted both the inbreeding coefficient (black symbols and line on the graph below) and kinship coefficient (red symbols and line) on the same graph as probabilities (i.e., values between 0 and 1.0), he showed that in the early history of the breed, there was preferential avoidance inbreeding that is revealed because average inbreeding was less than average kinship in the population (the black line is lower than the red line); that is, breeders chose to pair individuals that were less closely related than average in the population. This was the case until the early 1980s, when these lines flipped, with the average inbreeding increasing faster than average kinship, reflecting a preference by breeders for closer inbreeding, even when pairs were available that would produce lower levels of inbreeding.
Oliehoek also used the kinship coefficient in a very clever way, to reveal the decline in the size of the gene pool over time. In the chart below, he used the relatedness of each animal in the population with every other animal in pairwise comparisons to compute "mean kinship" (Nmk), which is a measure of the size of the gene pool. This is expressed in terms of how many founder dogs would result in a gene pool of the same size, something called the "founder genome equivalents. This graph below shows that the population started with the equivalent of about 20 unrelated founder dogs in about 1955, but by 1975, only 15 years later, the size of the gene pool had dropped to the equivalent of only about three dogs, and it continued to decline in subsequent decades. By the end of the 1990s, breeders had the genetic diversity of only 2 dogs to work with. Again, this information is derived from calculation of the genetic relatedness among the dogs in the population from the kinship coefficients, which estimate the predicted COI that would result from a particular mating.
The brown squares along the x-axis of the graph above represent the importation of new dogs into the population. Breeders assumed from scrutinizing pedigrees that these dogs were relatively unrelated to their breeding population and would therefore restore some lost genetic diversity and reduce the level of inbreeding. But Oliehoek once again used the kinship data to reveal that the population of the breed had clusters of related dogs, and that unfortunately, the imported animals were genetically part of the main cluster so did nothing to improve genetic diversity. The chart Oliehoek produced below showed where relatively less-related dogs could be found in other clusters, and it also showed that some of these other clusters were perilously small in size and at risk of extinction. Breeders could use this information to make better selections of dogs to import, and to also make sure that lines with small numbers of dogs were not accidently lost.
| We can see that the coefficient of inbreeding and the related statistic, the kinship coefficient, can be valuable tools in providing breeders with information that can be used for breeding decisions as well as population management. But the inbreeding coefficient has another, extremely useful role to play, this one in the prevention of genetic disorders and inbreeding depression. The inbreeding coefficient quantifies the probability of an animal inheriting two copies of the same allele from a shared ancestor. This is also the fraction of all loci that are expected to be homozygous. We can put this information to use to reduce the risk of genetic disorders in offspring. We know that most genetic disorders in dogs are caused by autosomal recessive mutations, with estimates ranging from about 60% to 80%. So, for these health issues, the risk of producing a problem in a puppy is equal to the probability of that puppy inheriting two copies of the same mutation, which is exactly what the coefficient of inbreeding tells us. So, if the inbreeding coefficient is 25%, the equivalent of a pairing of littermates, the risk of producing a genetic disorder caused by a recessive mutation is also 25%. Similarly, if the COI is 40%, there is a 40% chance of a puppy inheriting two copies of the same mutation. Likewise, a COI of 10% puts the risk of producing a genetic disorder from a recessive mutation at 10%. When recessive mutations account for such a large fraction of all genetic disorders in dogs, the benefits of being able to reduce or even prevent them is very significant. Note that this also means that if the inbreeding coefficient predicted is much below 25%, there would be little benefit from doing DNA tests. |  |
 | Remember that there is another deleterious effect of inbreeding apart from causing genetic disease from recessive mutations, and that is inbreeding depression, which is a general decline in the traits for "fitness" - things like lifespan, fertility, and what breeders used to call "vigor" or "vitality". These are not caused by a mutation per se, but by the loss of advantageous alleles or combinations of alleles at particular loci. For instance, there is something called "heterozygote advantage", in which the heterozygous genotype is more beneficial than either homozygous state (i.e., Aa is better than either AA or aa). You lose these beneficial allele combinations when inbreeding, and even though the effects can be are subtle, they can impact the quality of life of the animal in important ways. |
These properties and uses of the coefficient of inbreeding are why it remains an essential tool in the savvy breeder's kit today. Even in the face of new molecular technologies, it will still be around for the long term because it can provide information we can't get any other way. Inbreeding can now be estimated from DNA genotyping data, avoiding the limitations of using incomplete or potentially erroneous pedigree data. But for genomic inbreeding, you must have a DNA sample from the dog of interest, which might not be possible if the dog lives far away or no longer alive. But a well-tended pedigree database will provide information for any dog in the breed's history, limited only by the care taken when curating the pedigree database.
The Coefficient of Inbreeding has been around for a long time, and it is no less useful today than when it was first described by Wright a century ago. Genomics can now provide us with lots of information that was just a dream only a few years ago, and it's fair to say that we are in the midst of a new era of what can fairly be called "precision breeding" . But as long as breeders continue to use pedigrees when making their breeding plans, the inbreeding and kinship coefficients will continue to be used to estimate relatedness, predict litter inbreeding, and balance the benefits of prepotency and consistency with the risk of genetic disease and inbreeding depression.
REFERENCES
Oliehoek, PA, P Bijma, & A van der Meijden. 2009. History and structure of the closed pedigreed population of Icelandic Sheepdogs. (pdf)
Wright S, 1922. Coefficients of inbreeding and relationship. Am Nat 56: 330-338. (pdf)
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