Disappearing Ancestors

Time and necessity have pruned your family tree.

You aren’t related to most of your ancestors.

It’s counter intuitive and shocking, but it’s true.  For the most part the human genome is finite and each parent only passes along half of their genetic material to their offspring.  While it’s theoretically possible for the exponentially increasing number of ancestors going backward to pass along an exponentially decreasing amount of genetic code going forward, the human genome does not double in size every generation, so the proportion of material any one ancestor passes along necessarily halves every generation without inbreeding.

Parents pass along whole chromosomes, half of them in fact.  Grandparents are represented by only parts of chromosomes, adding up to about 25% of all genes a piece. Great grandparents pass along 12.5% and their parents are down to 6.25%.  This contribution keeps decreasing by half, so pretty quickly non-repeated ancestors have very small contributions.

There are 3 billlion base pairs in the human genome, which means that maximally 3 billion ancestors could contribute to your DNA if it were possible for each of them to give you but a single base pair.  This is impossible because genetic material is not chopped so finely when it’s passed along, genes travel in paragraphs, and chapters — not in words and especially not a single letter at a time.  But even if it were possible, this would mean that you have just over 30 generations of ancestors worth of information.  This would place us at the High Middle Ages (1000-1300 AD) when the total global population wasn’t above 1 billion people, let alone 3 billion, so all human pedigrees experience pedigree collapse.

This question came up in a recent conversation with Dave from Prickeared, and I went searching for an answer on just how beefy the chunks of DNA are when they are passed along and what we could estimate using this information to assess when ancestors start dropping off as actual genetic contributors.  John Hawks posts an answer:

In practice, even though we have billions of nucleotides, our DNA cannot follow billions of genealogical lines. Recombination over 30 — 40 generations does not divide chromosomes down to individual nucleotides. In the medium term, most human DNA is separated by recombination hotspots into lengths of around 50 kilobases. Across very short spans of 30 generations, DNA is for the most part inherited in chunks of hundreds of kilobases or longer. So dividing six billion nucleotides by 50 kilobases yields a number of around 120,000 ancestral lines at most from which any individual inherits his or her DNA. Recombination will increase this number somewhat further and further back in time, but not nearly so fast as the doubling of possible ancestral lines in every generation. This means that the vast majority of your ancestral lines more than around 17 generations ago have left no DNA to you whatsoever.

Hawks uses 6 billion nucleotides instead of 3 billion base pairs (but because nucleotide pairing is deterministic,  G always pairs with A, T with C, there couldn’t be independent inheritance of both nucleotides). This difference in mental model doesn’t change the results as he is considering “kilobases” of information being the base unit and this measures individual bases, instead of base pairs; you’d get the same result if you said 3 billion nucleotide pairs divided by 25 kilo-pairs.

In humans, 17-30 generations takes us back much further than we can hope to document fully, but that’s not the case in dogs.  I can trace my dogs back this many generations and the very first Border Collies in the ISDS stud book can be reached coincidentally between 15 and 30 generations.  The pedigree collapse in dogs, though, is much more significant than humans and those foundational dogs don’t appear as only one line, the pedigrees actually go back to them thousands of times.

For example, Dublin goes back to Old Hemp between 14 and 64 generations, and 2.5% of his DNA is expected to be the same as Hemp.  This is because there are over 1.8 million paths from Dublin back to Old Hemp instead of just one.  All of this in just over 100 years.

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