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Last updated:
17 Mar 2012

Teun v/d Dool
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© 2002-2017

STATISTICS FROM THE STUD BOOKS

Copyright © Teun C. van den Dool, Jan 2002
press here for a Dutch revision

4. INBREEDING

A small (effective) number of ancestors combined with line breeding or inbreeding can result in a highly inbred gene pool. A figure commonly used to indicate the amount of inbreeding is the Coefficient of Inbreeding (CI). CI is equal to the relationship or Kinship coefficient of its parents. CI is the probability that two genes chosen at random from distinct individuals are identical. An individual with equal genes is called homozygous (for this part of its chromosomes).

The following formula, commonly attributed to Sewel Wright (1922), is used to calculate the CI of dog X in a simple way:
    CI(X) = sum_over_all_common_ancestors_A[ {1+CI(A)}/2^N ]
where N is the number of dogs passed when tracing the non-crossing path from the sire to the dam through the common ancestor A, and 2^N means: 2 to the power N (2^3 = 2 x 2 x 2 = 8).

As an example take the (partial) pedigree depicted in figure 5. There are 6 paths via 3 common ancestors (31154, 82022 and 88472) of which the CI's are indicated. The formula is applied as follows:
0.356 = (1+0.422)/2^2 (path: 88472,154985)
0.178 = (1+0.422)/2^3 (path: 88472,114559,154985)
0.083 = (1+0.321)/2^4 (path: 88472,82022,114559,154985)
0.033 = (1+0.046)/2^5 (path: 88472,31154,82022,114559,154985)
0.016 = (1+0.046)/2^6 (path: 88472,31154,74933,82022,114559,154985)
0.002 = (1+0.046)/2^9 (path: 88472,31154,39602, etc.)

Summing gives a total CI=66.7%. Five Dogs have such a high CI. It actually is 66.9% due to some more common ancestors further back in time. These dogs were an attempt of Edward Smith to breed back to Wiston Cap 31154. None of these five dogs produced sustained progeny. David Rees and Roy Goutte wrote articles on these Dogs in WSN (see the references). These dogs had 87.7% of Wiston Cap's blood in the definition of figure 2. Even if these figures would be 100% it would not guarantee a copy of Wiston Cap as it would give a random mixture of its chromosomes. Often such breeding will result in illnesses, as it did in this case, although apparently it also produced excellent Wiston Cap-like copies.

pedigree example with high coefficients of inbreeding
Figure 5. Pedigree example with high inbreeding coefficients.


To calculate the CI's of all registered dogs including all generations in their pedigrees, I used the fast algorithm of Meuwissen and Luo (1992), which is based on a method proposed by Quaas and Henderson (1976) which in turn is also known as the tabular method. A fast algorithm is needed because most recent dogs have more than one million entries in their pedigree. Never more than 3000 different dogs though, but unfortunately that does not reduce the processing time. The foundation dogs are considered to be non-inbred (CI=0).

Figure 6 shows the resulting CI's as a function of the year in which the pups were born. Some CI's higher than 40% stand out:

  • One litter (30670..30672) was bred by J.H.Longmire in 1963 with a CI of 42.7%. It was an attempt to breed back to his Flo (10597). It produced no sustained ISDS registered progeny.
  • One litter with CI=54,5% (130179..130182) and some with CI=44% are due to several generations of brother-sister matings carried out by C.Winterton in an apparent attempt around 1970-1980 to breed back to Ridgeway Glen (49029) x Cherryholm Mist (103055). It also produced no sustained ISDS registered progeny.
  • The other dogs with a CI higher than 40% (38 in total) are due to E.Smith's attempt to breed back a Wiston Cap (31154). Some of these dog's genes are still present in the current population.
A thin line in figure 6 indicates the average CI for all pups born in a particular year. The dogs before 1949 have been registered in two summarising volumes (I and II) of the Studbooks. Their CI is low due to the small number of ancestors in their pedigrees. At an average of 5 year per generation, 25 years are needed to get complete 5 generation pedigrees. So the pedigrees can be considered complete since the seventies. This moment coincides with the moment of stabilisation of the increase in CI, which is a factor of 1.007 each year on average during the last 25 year or an absolute increase of 0.20-0.25% per generation (five year period).

Before 1950 a line can be seen at CI=25% (and less clear at 12.5% and 6.25%). A CI=25% is obtained by matings between parents and children or between siblings. After 1960 this line becomes vague and increasing due to influence of older generations in the pedigrees. This is also the reason why in recent years hardly any dog can be found with a CI lower than 4%. And even then most of them come from ROM (Registered On Merit) dogs.

Normally, people would look at pedigrees with 6 generations at most. Figure 7 shows the CI's when one would only use that information. This line shows a decreasing trend. The difference with a full pedigree is 7% maximum. So on a short term we may be more outcrossing than in the past, but in reality there is still an increased inbreeding. This is characteristic for closed populations with selective mating.

Over the last 10 year the CI was 7% on average. Is that high or low? I have the feeling that it is on the low side compared to many other breeds. More than 40% would be considered high by almost everybody, although not uncommon in many other breeds. Near 0% in 10 generations would be considered very low, and it is 4-5% on that time-scale. Probably the average CI is a little higher because the known founders were inbred themselves.

A CI of 7% is certainly low considering the small genetic diversity in the current population (effectively the genomes of 8 dogs). More inbreeding would:

  • accelerate the loss of genetic diversity,
  • make more dogs with the same appearance and behaviour,
  • reduce the possibilities to enhance the breed with ISDS dogs only.
Alltogether I think we may conclude that we still have a healthy population despite the low genetic diversity.


coefficient of inbreeding of all dogs
Figure 6.
Coefficients of Inbreeding (CI) for all ISDS registered Border Collies.
Each marker represents one litter.
Full pedigrees down to unregistered foundation dogs were used for this figure.
The thin line indicates the average CI for all pups born in a particular year.


coefficient of inbreeding of all dogs in 6 generations
Figure 7.
Same as figure 6 but CI calculated on the basis of 6 generation pedigrees.


COI change over the years of all dogs in 6 and all generations
Figure 8.
The thin lines from the 2 previous figures.


probability distribution of the coefficients of inbreeding
Figure 9.
Probability distribution of the CI's for all ISDS Border Collies born in the last 10 year.