Ancestor loss and genetic diversity

The concept of "coefficient of inbreeding" (COI) has never seemed very intuitive to me with regards to genetic diversity. Oh, I can recite the definition. But the fact that there seems to be different formulas for calculating COIs (giving slightly different results), disagreement on how many generations of a pedigree are necessary in order to get an accurate COI, and no clear agreement of what is a good COI versus a bad COI has always left me with a confused feeling.

With regards to genetic diversity, more intuitive to me is the concept of "ancestor loss". We are all aware that in looking at a pedigree, if we see all unique ancestors then we think "diversity"; whereas once we start seeing ancestors repeated in a pedigree we start to think "inbreeding" and loss of genetic diversity.

Now obviously if you go back far enough - even in human geneology - you start to get repeated ancestors. But the more unique ancestors there are, the more "mixed" are the genes. Mixing genes to get new combinations is the whole point of sexual reproduction.

So is there a way to "measure" ancestor loss? Yes there is ... and it is very simple. For a particular number of generations, just count all the different ancestors and divide by the number of possible ancestors. This is called the "Ancestor Loss Coefficient" (ALC). For example, in a three-generation pedigree (parent, grandparents, and great-grandparents) there are 14 (2+4+8) possible ancestors. If all the ancestors are all different, the ALC will be 1; if any ancestors are repeated, the ALC will be less than 1. The more repeated ancestors there are, the smaller the ALC.

Just like COIs, ALCs are dependent on the number of generations of the pedigree used in the calculation. So when talking about a particular ALC, one must also mention how many generations were used in the calculation of the ALC.

So what is a good ALC? The Finnish Kennel Club has put out a document "General Breeding Strategy" ([1]) where they make recommendations about breeding. They discuss genetics diversity, and on page 12 make the following recommendation - a dog should

1. have a three-generation ALC of 1 (this means that all the ancestors in the first three generations are unique), and

2. a four-generation ALC greater than 0.9 (this means that in a four-generation pedigree 90 percent of the ancestors should be different).

So is this recommendation realistic for our Norwich here in the United States?

I looked in my online pedigree database (version 1.85) at all the Norwich born in the United States and registered with the AKC in the last twenty years. I found a total of 2823 Norwich.

(Obviously there have been many more Norwich registered with the AKC in the last twenty years. But remember that the AKC stud books - my primary source for AKC pedigree information - only list dogs who have sired or whelp a litter).

Of these 2823 Norwich, for 290 of them I do not have a complete four-generation pedigree. This leaves 2533 Norwich.

Of these 2533, 1403 meet the Finnish criteria of having a three-generation ALC of 1 and a four-generation ALC greater than 0.9. So some US breeders have been (perhaps unconsciously, perhaps by accident) using this Finnish criteria.

As others may want to make use of the concept of Ancestor Loss Coefficient, I have added software to my online pedigree database to calculate the Ancestor Loss Coefficient for an individual dog, and for a "test breeding" of two dogs in my database. For duplicated dogs in a pedigree, my software also indicates their contribution to a dog. My software allows one to calculate the ALC for up to ten generations provided a complete pedigree is available.

Blair Kelly
AKC Breeder of Merit
3 Nov 2014