ISDS Border Collie Database

STATISTICS FROM THE STUD BOOKS

3. FOUNDERS

It seems that the current Border Collie population is dominated by a small number of dogs. Another way of looking at the gene base of a population is to define the foundation dogs (founders). These are the registered dogs with one or two unregistered parents. The unregistered parents could also be considered the founders but because they have no ISDS numbers it is not easy to find out which unregistered parents are equal for different registered pups. In that case the number of founders would be higher than in reality.

There are 3143 registered founders of which 1481 produced registered children. Only 643 of them have had influence on the pups born in the last five year. An even smaller number of founders already have a major influence, see table 2.

Boichard (1997) compares three methods to measure the effective number of dogs that have (had) influence on a particular population. These methods appear to be used for estimating genetic variability in rare (wild) animal species.

The first method gives the effective number of founders. The contribution to the current gene pool of the 643 founders given above is very different. The two most influential ones contribute 9% together. Others have an almost negligible influence. To account for this difference in contribution, the effective number of founders is defined as:
    EF = 1/sum_over_all_foundation_dogs(contribution^2)
where ^2 means: square

The effective number of founders appears to be EF=71.3 in this case. This is the number of founders that would give the same gene diversity if they all contributed equally to the current population. So from the original number of founders, effectively only 71.3 have an influence on the current ISDS population.

Note that effective dogs have little to do with real dogs. One effective dog is a measure for the number of genes in a single dog but these genes might be (and in practice always are) spread over many real dogs.

Boichard gives a second (approximate) algorithm that takes into account 'bottlenecks' due to the reduction in gene diversity caused by often used stud dogs. The resulting number is called the effective number of ancestors (EA). He gives the example in figure 3 to explain the difference with founders. The current population in this example has 6 founders (1,2,3,4,15,16) but only 4 ancestors (5,6,17,18). The effective number of founders is 5.6 because the second family has a smaller number of representatives in the current population so the genes of 15 and 16 have effectively lesser influence. In this case the effective number of ancestors appears to be EA=2.94.

The EA algorithm finds the ancestors by recursively looking for the dogs with the largest genetic influence on the current population. The effective number of ancestors is calculated from the real number of ancestors with the same formula as used for the effective number of founders. EA is always lower than EF because bottlenecks will reduce gene diversity.

Figure 3. Pedigree example showing the difference between founders and ancestors.

For the current ISDS population EA=18.5. Like the list with number of founders given above, an equivalent list can be made for the number of ancestors needed to explain a particular amount of the genes in the current generation of ISDS dogs. This is considerably less then the number of founders, see table 2.

The third, most accurate but time consuming algorithm, accounts for all causes of loss in genetic diversity. In a population of unlimited size with random mating the genetic diversity will remain constant. However, in populations of limited size with selective mating like ours, the diversity will decrease due to a process called 'random drift'.

Random drift can be explained with the following example. Suppose a dog and a bitch mate and both have genotype B/b at some locus of one of their chromosomes. Their children will inherit one chromosome from the father and one from the mother to form a new genotype at that locus. If by chance they produce two children both with genotype BB, than the properties that go with gene b will be lost forever if these parents were the only living dogs with allele b. Note that this mating not necessarily reduces the effective number of founders or ancestors.

This third algorithm gives EG, the effective number of different genomes from founders that are still present in the current population. It does so by simulating the random selection of a particular gene during the fathering of all dogs ever registered. After this simulation the genes in the current generation of Border Collies are counted. This simulation of the total Border Collie population is repeated many times (1000 in this case) and the average occurrences of the genes are calculated from the results. For the current ISDS population the effective number of founder genomes is EG=8.3. So effectively the genes of only 8.3 founder dogs are present in the current generation of approximately 25000 ISDS registered Border Collies. Amazing isn't it?

Figure 4 shows how the different (effective) numbers of dogs have evolved over generations since the fifties. Before 1950 the pedigrees are incomplete and show a wild behavior starting at zero around 1900. Since 1980 the effective numbers are almost constant. Sometimes even a bit increasing due to ROM (Registered On Merit) dogs or dogs with otherwise unknown parents. So the main selection took place before 1980. Maybe not accidentally the last big reduction in genetic diversity (1965-1975) coincided with the rising star of Wiston Cap 31154.

A little extra explanation for those puzzled which those 8 'effective' dogs are. They do not exist in reality, we cannot point at these 8 individual dogs. You should think of it as an amount of genes spread over all dogs. Many dogs have the same genes and only very few different genes are present in our dogs, only an equivalent of 8 dogs. That is what 'effectively' 8 dogs means.

Another way of looking at it is, suppose that we would have 8 founder dogs with differences in their chromosomes. We let them mate with each other randomly to produce a new generation of 25000 pups. This new generation will have the same genetic diversity as the current ISDS population. In this example we can point at the 8 effective dogs but in reality we cannot, the chromosomes have been selected over many generations from many dogs.

You might think 'but Wiston Cap must be one of them'. Well, he surely caused a considerable reduction in the effective number of genomes but he did not add anything. He just caused a particular selection of chromosomes from its ancestors to become more dominant.

Figure 4: Evolution of the (effective) number of founders, ancestors and genomes as a function of time. Each time a five-year period (one generation) is considered. Note the logarithmic vertical scale.

Next: 4. INBREEDING