Pedigree Collapse and the Law of Parsimony

So God created man in his own image, in the image of God he created him; male and female he created them. And God blessed them. And God said to them, "Be fruitful and multiply and fill the earth..." (Genesis 1:27-28a ESV)

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A Blog of random thoughts and ideas.
Caveat emptor.

When our oldest daughter was born in 1989 I became interested in genealogy and began doing extensive research, the culmination of which was a family history I compiled for our daughters and "published" for relatives in 1993. I wrote an introduction that contained the following paragraph:

Did you girls know that in the span of the last 600 years more than one million individuals have contributed directly to your existence and indirectly to your individuality? If my math is right, of the entire population of the world in the early 1400s (around 1420 or so), one million forty-eight thousand five hundred and seventy-six twentyorthirtysomethings were destined to become your great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-great-grandparents! In other words, you girls are by-products of the genes of more than two million people in the last 20 generations.

I actually took a Genealogy course from Brigham Young University in the early 90s. As I sifted through the layers of monogamy, polygamy, and levirate marriages, I encountered the phrase (and concept) pedigree collapse. I really didn't think much of it (nor about it) until I introduced it to a classroom of high school students a few years ago with the challenge to explain how the number of their ancestors would eventually exceed the population of Earth. I drew a diamond-shaped diagram on the board representing a single person at the bottom and a first pair of male-female progenitors (cautiously avoiding accusations of proselytizing by not calling them Adam and Eve) at the top. As they thought about it, I could almost hear their mental clutch cables snapping. It's quite the paradox... Or so I thought.

Even looking at this from a secular perspective, it seems simple enough that our world is ordered a certain way-- that living things exist as male or female for the express purpose of reproduction. So if every living is the issue of a mother and father, and it all had to start somewhere, then...well, okay...it's not so simple; however, I found a plausible explanation in a 2012 post to a blog maintained by an eclectic guy named Stephen Lewis called How many ancestors do you have?:

...the number of our ancestors can’t really have kept on doubling in an exponential manner as we go further and further back. Consider just one additional fact: it has been shown that the human race, homo sapiens, went through at least one population bottleneck during our history. At certain times it appears that humankind almost went extinct. Around 70,000 years ago scientists have suggested that the total world population dwindled to only a few thousand-- the so-called Toba catastrophe. So sooner or later the number of your ancestors must have stopped exploding and had to have started to shrink, and shrink fast.

Such a phenomenon is called "Pedigree Collapse," a phrase coined by Robert C. Gunderson... Essentially there are two interrelated reasons why the number of your direct ancestors does not keep on exploding and why their number will sooner or later start to contract. The first has to do with "cousin marriage." When you look back at your ancestry you will find that again and again your ancestors married, or better said, bred with their "cousins." This is not a conjecture, this is a fact. Although there will be much to say on the level of cousin marriage. Second, we need to understand the nature of the available "breeding pool" that our ancestors had; and this means considering issues of migration.

The first factor, cousin marriage, or inbreeding if you like, can help us explain why the number of your ancestors first grows and then will eventually shrink. The second factor, migration or "outbreeding," helps us to understand why the onset of this narrowing and shrinkage is sometimes pushed farther back in time.

As I was reading through the full explanation, my brain suffered its own Toba catastrophe. But it does make me wonder at the numbers...

If you've never visited answersingenesis.org, you ought to check it out. On this particular topic, the site reminds us that...

1) Evolutionary scientists reject the biblical history of humanity’s origin from just two people. Nevertheless, when a group of evolutionary geneticists in 2009 evaluated various models of human origins, they tacitly acknowledged the plausibility of human descent from the people dispersed from the Tower of Babel. What they called the “instantaneous divergence model” sounds pretty much like what happened at the Tower of Babel sometime after the global Flood. 

2) The need for the Cross of Christ is rooted in the facts of our Creation history. The origin of sin and suffering and death and our need for a Savior is rooted in the truth of human origins as described in Genesis. Therefore it is vital that Christians avoid the compromising positions adopted by theistic evolutionists who typically claim that Adam and Eve are mere allegorical characters. 

3) Christians should also be confidently able to share the Gospel of salvation by beginning with the truth that the Bible is not anti-science.

Another website, creation.com, poses the unanswerable question "What if people had been around for one million years?" Then answers it:

Evolutionists claim that mankind evolved from apes about a million years ago. If the population had grown at just 0.01% per year since then (doubling only every 7,000 years), there could be 10⁴³ people today-- that’s a number with 43 zeros after it. This number is so big that not even the Texans have a word for it! To try to put this number of people in context, say each individual is given "standing room only" of about one square meter per person.

And still another website (World Population Since Creation) poses the next question: Where were they buried and what happened to their bones? An even more disturbing question is: What happened to their souls?

...using the most conservative figures for which we have even the remotest justification, if the theory of human evolution is true, there have been at least 300 billion people who have lived and died on the earth--almost all of them a long time before Christ came into the world and before any other revelation was given to man about God!...

It may be claimed that none of these calculations really prove anything, since no one really has any way of knowing exactly what birth and death rates and what population figures existed in prehistoric times. This is quite true, of course, but the known facts of population growth do fit the Biblical chronology very well and they do not fit the assumed evolutionary chronology at all. 

Scientists work in terms of "models" and try to evaluate each proposed model of a particular process in terms of the "degree of fit" of the known data into that model. On this basis, we are abundantly justified in concluding that the creationist model with its brief chronology fits the actual known data of population statistics far better than does the million-year evolutionary model. 

If you've made it this far, you (and your brain) are ready for the much-easier-to-grasp explanation of "pedigree collapse" from the amorphous Cecil Adams of The Straight Dope website:

Consider an extreme case. Mr. and Mrs. Nosepicker have two children, a girl and a boy. These two develop an unnatural yen for one another and marry. Six months later the girl gives birth to an eight-pound horseradish with a lisp. In theory, the horseradish has four grandparents. In reality, its maternal and paternal grandparents are identical. Two of the four grandparent slots are thus filled by duplicates-- pedigree collapse with a vengeance. Only slightly less extreme is the case of Alfonso XIII of Spain (1886-1941). Because of inbreeding in the royal family, he had only ten great-great-grandparents instead of the expected 16.

If you go back far enough, however, pedigree collapse happens to everybody. Think of your personal family tree as a diamond-shaped array imposed on the ever-spreading fan of human generations. (I told you this was cosmic.) As you trace your pedigree back, the number of ancestors in each generation increases steadily up to a point, then slows, stops, and finally collapses. Go back far enough and no doubt you would find that you and all your ancestors were descended from the first human tribe in some remote Mesopotamian village. Or, if you like, from Adam and Eve in the Garden of Eden.

These simple facts have given rise to some remarkable displays of statistical pyrotechnics. Demographer Kenneth Wachtel estimates that the typical English child born in 1947 would have had around 60,000 theoretical ancestors at the time of the discovery of America. Of this number, 95 percent would have been different individuals and 5 percent duplicates. (Sounds like Invasion of the Body Snatchers, but you know what I mean.) Twenty generations back the kid would have 600,000 ancestors, one-third of which would be duplicates. At the time of the Black Death, he'd have had 3.5 million-- 30 percent real, 70 percent duplicates. The maximum number of "real" ancestors occurs around 1200 AD-- 2 million, some 80 percent of the population of England.

Pedigree collapse explains why it's so easy for professional genealogists to trace your lineage back to royalty-- go far enough back and you're related to everybody. For that matter, you're probably related to everybody alive today. Some geneticists believe that everybody on earth is at least 50th cousin to everybody else.

The bottom line? No one has been able to point out a time when God was wrong. And it seems to me that 14th-century William of Occam, for whom the principle Occam's Razor is named, was spot on. Among competing hypotheses, the one with the fewest assumptions should be selected. Genesis 1. At the risk of sounding parsimonious, lex parsimoniae.