Significant Genetic Relationships

Breeding article by Dr. J. Armstrong

How would you determine the impact of a famous Champion on his breed?

A famous champion who has won many shows and earned many titles may be (or have been), quite popular as a stud and may have sired more winning progeney than other contemporary males, but that does not guarantee that he will have more impact five or ten generations down the line than another dog who was bred only two or three times. So in order to answer this question we will need to do some genetic calculations.

Percent Contribution

If sufficient data is available, one way of determining the significance of an ancestor is to calculate his genetic contribution to his descendants. The percentage of contribution (aka percentage of blood) is determined by the way genes are passed from the parents to the progeny. An individual inherits one set of chromosomes, and the genes they carry, from its sire and a second, homologous (equivalent) set from its dam. Thus each parent always passes on (contributes) 50% of its genes to each of its offspring and it therefore seems reasonable to expect that 25% of an individual's genes will come from each grandparent, 12.5% from each great-grandparent, and so on.

Each generation of ancestors in a pedigree contributes 100% of the genes for the target animal (proband). So the percentage of contribution from each ancestor at a given generational level is 100 divided by the number of ancestors in that generation. Since the number of ancestors doubles in each preceding generation, the contribution from each ancestor in each preceding generation is halved.

However, this is not like mixing paint! Percentage of blood for ancestors beyond the parents are probabilities, not certainties. When a male passes on one set of his chromosomes, they will include a random selection of the genes he inherited from both of his parents, but there is no guarantee that the genes he passes on will contain an equal amount from each of his parents and in fact it rarely is. There is even a small chance (very small) that he will pass on those genes from only one of his parents. On the other hand, the more times that an ancestor appears in a pedigree behind different offspring, the more likely it will be that the percentage of genes passed down from each of its parents will be closer to 50%.

By the time we get back 10 generations, the contribution from each of the 1024 ancestors would, in theory, amount to slightly less than 0.1%. However, in the pedigree of the average purebred dog, there are seldom more than 100-200 different (unique) ancestors and some may appear 50 times or more. These are the significant ancestors that make the major genetic contributions.

If you have a pedigree, you can calculate % contribution of any repeats simply by multiplying the number of times each ancestor appears in any generation by the appropriate percentage for that generation and then add together all of the calculated percentage of contributions from each generation. The table listed below shows the percentage of blood inherited from each ancestor at the given generation levels. Generation "1" is the parents.

Databases exist for many breeds that will contain the data enabling you to extend a pedigree to 10 generations or more. Manual computation, though tedious, is still possible, but hardly convenient. However, the CompuPed pedigree program will quickly calculate % contribution for selected ancestors or all ancestors for a specified number of generations, providing you with information on which dogs have been most influential.

Is there a quick way of determining how genetically similar two dogs are?

Suppose a breeder has two bitches (A and B) she wants to mate to different males. After careful research the breeder identifies three potentially suitable males (C, D and E), all of which look equally good. The breeder hopes to get a male puppy from one litter and a female from the other, and would like to eventually breed these puppies to each other. The objective could be to pick the combination that will minimize the potential inbreeding. Alternatively, the breeder may be looking for two dogs that are not close relatives yet have similar heritage.

One approach would be to produce hypothetical litters for all combinations: AC, AD, AE, BC, BD and BE, and then look at the possibilities for the second generation. There will be six if shared grandparents are not permited, and 36 if there are no restrictions. These potential litters could then be evaluated for inbreeding or the % contribution of significant ancestors. This will certainly provide the data, but is unnecessarily tedious.

The Coefficient of Relationship

The relationship coefficient (RC) provides a way of objectively assessing the similarity of two pedigrees by giving a number that is a direct measure of shared ancestry. In most human populations, two individuals picked at random would likely have a RC of 0, a brother and sister 50% and identical twins 100%. Other relationships would fall somewhere between 0 and 50%.

The number generated may be viewed as analogous to the % composition, except that you are comparing two dogs instead of looking at one. A brother and sister will have an RC value of 50% as long as they have no ancestors that are repeated. Once ancestors start to repeat, the individuals no longer have an inbreeding coefficient of zero. Two sibs from a highly inbred line may have an RC of 80% or more, and two dogs that are not sibs may have an RC above 50%.

The formula for the RC is:

where f_AB is the inbreeding coefficient of a hypothetical litter between A and B, and F_A and F_B are the inbreeding coefficients for the two individuals, A and B.

A simpler approach to the breeder's problem would be to compute the RCs for C vs D and E, and D vs E. This is not an easy pencil and paper calculation. However, presented with just such a problem, it took me about 2 minutes to obtain the three RCs with the latest version of CompuPed. My results were RC_CD = 10.4%, RC_CE = 13.4%, RC_DE = 17.2%.

D and E share the most common ancestry, while C and D share the least, and respectively so would the progeny from their two prospective litters. To minimize inbreeding and maximize diversity, all else being equal, C and D would be the best choice. (These values actually all fall below the average for the breed, which is about 23%.)

The Kinship Coefficient

The f_AB term in the RC equation is sometimes called the "kinship coefficient" and may also be used as a measure of the relationship between two individuals. It's computation is the same as that of an inbreeding coefficient for a hypothetical litter between the two dogs. (It doesn't matter if they are the same sex.)

The mean kinship (mk_i) for individual i is is the average of the kinship coefficients (f_ij) between i and all the other breedable individuals in the population:

A conservation biologist would consider the individual with the lowest mean kinship to be the most genetically valuable in terms of maintaining diversity in the population, and would try to favor that individual in a breeding program.

Acknowledgement. . .

We warmly thank Dr. Armstrong for giving us permission to post this informative information on our web site. We would also like to encourage you to vist Dr. Armstrong's very comprehensive Genetic Diversity web site at the University of Ottawa for more information on many related subjects.