It’s common to visualize one’s ancestry as a pyramid with the current individual at the apex descending back across time and generations in an expanding wedge. Every generation has twice the number of ancestors so the pyramid theoretically grows very quickly: 1 child = 2 parents = 4 grandparents = 8 great grandparents = 16 GGGP = 32 GGGGP, etc.
“The greatest shortcoming of the human race is our inability to understand the exponential function.”
- Professor Albert Bartlett, CU Boulder
This is called exponential growth, and very few natural systems which exhibit this growth model can sustain it for very long given just how explosive the resource requirements are to maintain it. Overpopulation alarmists use this model to project human populations looking forward in time, and it is often referred to as “The Malthusian Law” after Reverend Thomas Malthus who wrote an early and very influential doom tract on human population growth.
In pedigree analysis we use this model to look backward in time to analyze past generations instead of future ones. As each older ancestor generation is double the size of their children’s generation, there is one more ancestor in that next oldest generation than all the previous younger generations combined. When our knowledge of the pedigree runs out we call that last generation the foundation, and much like a real pyramid, it’s theoretically a large base upon which all further generations are built.
Although this tree grows backwards in time, we live life going forward so we can not manufacture twice the ancestors every new generation to accommodate our theoretical tree. We quickly discover that as we go back in time the number of theoretical ancestors keeps growing as the number of actual new ancestors falls. At 32 generations we’ve accounted for 8.5 Trillion ancestors, and this is more ancestors than total people alive today. While it might be hard for you to think of your 32nd Great Grandfather, this actually isn’t such a great genealogical distance for dogs.
The distance between my Mercury and Old Hemp who was born in 1893 varies between 15 and 71 generations. The dogs that show up between 25 and 35 generations ago are almost all clustered in the mid 1950s. So one human lifetime is enough to witness a great many generations of dogs. An equivalent number of human generations might take you back to the mid 14th century when the Black Death wiped out huge swaths of Europe’s population.
There weren’t even 4.3 trillion people on the planet in the 1350s, the number was much closer to 430 million, only one tenth the number of people we’d need to fill spaces in our 32nd generation of our pedigree. So even if the entire population of the world at that time was one “generation” and an equal ancestor, they’d each have to appear 10 times. This is a pedigree collapse of 90%.
If we choose to not repeat ancestors and give each unique ancestor only one space in our tree, but still draw branches connecting them to all their offspring and their parents, we could visualize how our actual ancestor tree differs from the theoretical. You’ll notice in the above pedigree of my Border Collie Mercury that after expanding out in the predicted pyramid shape the pedigree eventually starts to shrink. The resulting diamond shape is a visual representation of pedigree collapse.
Pedigree collapse is caused by inbreeding; both recent close breeding and more distant founder effects. When a breeder inbreeds they are cutting the pedigree pyramid of their stock down dramatically. When two cousins mate, creating a COI of only 6.25%, they have actually permanently cut out 25% of the possible ancestors for their offspring.
Normal Norma is not inbred and she has the expected 4 grand parents and 8 great grandparents. Inbred Ted’s parents are first cousins, meaning that one of their parents are siblings. This means that Ted has only 6 great-grandparents because two of them are doing double duty in his pedigree. This represents a pedigree collapse of 25% and that continues back forever into his history.
Pedigree collapse and the resulting loss of genetic diversity doesn’t require recent inbreeding to have a devastating effect. When breeds are formed from a small founding generation and/or go through population bottlenecks, there simply aren’t enough ancestors to go around and there aren’t enough mating combinations to sustain genetic diversity. This causes inbreeding to rise even though breeders avoid close pairings.
For example, let’s look at Claire Wade’s Nova Scotia Duck Tolling Retriever: Am, NSDTRC-US CH Edlyn Seastar Dodge N Burn WC CGC CCD JD 3/8/2007 a.k.a. ”Burn.” I’ve rotated his pedigree pyramid so that it fits nicely on a computer screen and matches the standard presentation on written pedigrees: sires over dams, older generations to the right.
Burn’s breeding is not very close in recent generations; his first repeated ancestors are three great grandparents. Two of them show up again once in the next generation and one shows up twice. But you can see from his complete pedigree chart above that Burn’s pedigree quickly collapses into only a handful of dogs. You can even see the popular sires and dams as they have a fan of connections coming into them; each one of those lines represents ancestor loss as that connection could have been made with a unique dog, but the Toller’s foundation is so small that swift pedigree collapse was guaranteed from the founding of the studbooks combined with early and often popular sires and an aversion to outcross to new blood.
When we look at only two more generations of Burn’s pedigree you can see that the vast majority of ancestors in those later generations is highlighted in a variety of colors indicating repeat ancestors that show up elsewhere on the pedigree. This is inevitable in all Tollers as there are only so many ancestors they have to work with and many of those ancestors were not widely bred.
Remember that in my earlier post I showed how a founder would have to have over 10 children that each survived to pass along their genes for the gene pool as a whole to retain over 99.9% of that founder’s genome. As you can see in the fish shaped pedigree chart above, several of those “founder” dogs on the far right had only one recorded child in the Toller studbook. At most 50% of their genes would be conserved in that child and we can see that often their children had very few children as well. This indicates that Tollers had a very small founding population and that a big chunk of the extant genetic diversity in that small founder pool was lost almost immediately.
In my next Toller post, I’ll examine how looking at a limited number of generations for a Toller COI can attempt to hide the real situation that breed is in.
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