Thursday, 22 November 2012

Stacking Up The Odds

How come Evolution can create such hugely unlikely things that it's hard for people who don't understand, wilfully or otherwise, how Darwinian Evolution works without being directed?

To understand this you need to understand a few simple ideas.

  1. How many ancestors have you got?
  2. This should be quite simple to calculate. You have two parents, four grand parents, eight great grand parents, etc, etc. So, for every generation you go back, the number of ancestors doubles. You can imagine this as a fan shape going back in time, starting with you, each line splitting in two at every generation. Suppose we want to know how many ancestors we had a thousand years ago, we need to know how many generations there have been in a thousand years - approximately forty, assuming the mean age of parents at child birth is about twenty-five years. Then, we start with two and double it, forty times. In other words, 240 (2 raised to the power of 40), which is 1,099,511,627,776 (a little over one trillion) ancestors who lived in the year 1000 CE.1

    To calculate how many ancestors you had who lived at the time of Pontius Pilate, (80 generations ago) it's 280, or 1,208,925,819,614,629,174,706,176 or a little over one quadrillion ancestors who live in the year 1 CE.

    But hold on! That's more humans than have ever lived! How can that be?

    Well, try researching your family tree. You can be sure that, before you get back very far, you will find a marriage between cousins, second cousins, third cousins and so on. My father's parents were cousins, as were his grandmother's parents. Before the invention of the bicycle, most marriages were between couples who lived within four miles of one another. There is no reason this would have been different in earlier times, so the chances of two people being first, second, third, fourth, cousins, etcetera would have been very high. Each of these marriages merges two of your expanding fan of lines into one. The further you go back the more certain it becomes that a couple were related in some way, so you're 'expanding' fan of ancestors tends to reach a maximum number of lines, and, if only you could go back far enough, it could never be larger than the total number of people alive.

    And this means you have a very high probability of being related to any one person who was then alive.

    Think about the enormity of that for a moment. There is a point in history at which you were very probably related to anyone then alive, apart from people who were extremely isolated from the rest of humanity, if there were any such people at the time in question! Your gene-line connects you to every human who ever lived before a certain point in history, so you can inherit any mutation that arose prior to that time.

    Geneticists have calculated that the earliest point in history when we all had at least one individual in common in our ancestry was a mere 350,000 years ago. Before that period the total human population of the world was probably numbered in the tens or hundreds of thousands, all concentrated in the plains of East Africa and the Great Rift Valley. It's not hard to see how we are almost certainly related to all of them. It has also been estimated that the number of humans who came out of Africa, and from whom all non-Africans are descended, was a mere few thousand.

    So, you have a good change of inheriting any of the genes anyone then carried. If there was exactly the same chance of any of them being passed on, there would be an equal chance that you would inherit any one gene.

    But, natural selection means there isn't an equal chance. Natural selection means that any gene which gives an advantage in terms of breeding success will increase it's chances of being inherited at every generation, while any gene which gives a disadvantage, or even just less of an advantage than another, will reduce it's chances of being inherited at every generation. In this sense, alleles of the same gene compete for success in the gene pool. One allele's success is another allele's failure.

  3. Mutation Probability
  4. Every time DNA is replicated there are mechanisms in place to correct the occasional error. However, even these fail sometimes. You only need to look at any group of individuals to see that we all differ from one another within limits. This is due (at least in part) to differences in our genes which arose in the past due to imperfect replication.

    So, what are the chances of a particular mutation happening at all and being passed on? The real answer is, it all depends on the particular gene and how it's arranged in the DNA. I won't go into the technical details here save to say that, if it's a seriously harmful mutation, it's unlikely to produce a new individual. Even if the egg or sperm carrying it are viable, the resulting embryo might well not be. Even if it passes that test, the resulting baby might not survive to produce its own offspring, so the harmful mutation won't be passed on.

    So we can be fairly sure that most mutations which get to compete for a place in the gene pool are not going to be seriously harmful. In other words, generally speaking only the potentially successful ones will actually be successful.

    So, let's assume a really low probability of a beneficial mutation happening - something in the order of one in a million. This means, on average, one person in every million will carry this mutation because it arose in the egg or sperm they developed from.

    We are talking about a beneficial mutation here, remember. That is, beneficial in terms of the number of descendants the carrier can produce, compared to the number he or she could produce with the non-mutant form of the gene. So, by the next generation, that average of one in a million will have been increased by natural selection. It doesn't matter whether the natural selection selected for the mutation or against the original allele; the result is the same. And this is so for every new generation.

    This means that the original one in a million chance of any individual carrying the mutation increases with every generation, even if no more mutations spontaneously arise. If there is a very clear advantage, the increase in the gene pool can be very rapid. In a small population, especially with strong selection pressure this can occur extremely quickly. See a few examples of this in Rapid Human Evolution, More Rapid Human Evolution and Rapid Evolution Makes Creationists Crabby.

    So, what we are seeing here is natural selection accumulating improbabilities and turning them into probabilities, even certainties, given time, as evolving organisms are pushed up an improbability gradient towards fitness peaks in their environment.

    This is the principle I tried to illustrate in my blog post Evolution for Creationists Who Can Recite Jack And Jill.

    The last component of this principle is the fact that exactly the same process can be happening to other mutations at the same time. Each mutation is, of course, a part of all the other genes' selective environment. It may be that, in some individuals, a mutation is more beneficial than in others because they also have another mutation. It could also be less beneficial, of course. However, where two or more, maybe several, mutations occurring together give a clear advantage, the individuals carrying them together will produce more descendants, so the chances of these mutations occurring together in an individual also increases with every new generation.

    Mutually beneficial combinations of genes are also pushed up the improbability gradient by the simple process of differential breeding success, or natural selection, as it's known.

    This simple principle gives the lie to creationist and Intelligent Design frauds who bamboozle their credulous and ignorant audiences by multiplying improbabilities together to produce a vanishingly small probability and then claim the maths just doesn't support evolution by natural selection. Of course, one mutation does not depend on another mutation happening first, so there is no basis for multiplying these probabilities together. It also ignores the power of natural selection to push an organism up the improbability gradient until it becomes highly probable, if not certain.

    And remember, you are connected through your gene line to everyone in whom these mutations could have arisen before some 350,000 years ago. Any beneficial mutation any time before then has a very high probability of being in you. You will also carry some which are on their way up the gradient and which, should the human species survive long enough, will have a high probability of being in everyone in another few hundred thousand years.

  5. Deep Time
  6. But all that is slow and takes a very long time! How come there is so much diversity to be seen on earth when all this evolution happens so slowly? The answer is because there has been so much time.

    I have used this quote from Richard Dawkins before but I don't know of a better metaphor for explaining the idea of how long life on earth has been evolving:

    Fling your arms wide in an expansive gesture to span all of evolution from its origins at your left fingertip to today at your right fingertip. All the way across your midline to well past your right shoulder, life consisted of nothing but bacteria. Multi-celled invertebrate life flowers somewhere around your right elbow. The dinosaurs originate in the middle of your right palm, and go extinct around your last finger joint. The whole story of Homo sapiens and our predecessor Homo erectus is contained in the thickness of one nail-clipping.

    As for recorded history; as for the Sumerians, the Babylonians, the Jewish patriarchs, the dynasties of the Pharaohs, the legions of Rome, the Christian Fathers, the Laws of the Medes and Persians which never change; as for Troy and the Greeks, Helen and Achilles and Agamemnon dead; as for Napoleon and Hitler, The Beatles and Bill Clinton, they and everyone that knew them are blown away in the dust from one light stroke of a nail file.

    Richard Dawkins, Unweaving The Rainbow

    We can see that evolution has had vast amounts of time. Life on earth is at a relatively mature stage of development. The major kingdoms and phyla were established by about 500 million years ago on basic body plans established a hundred million years or so earlier in the Cambrian era. About three hundred and fifty million years ago the major classes had been established apart from birds which evolved from the theropod dinosaurs, the rest of the dinosaurs having gone extinct, and mammals which evolved from earlier mammal-like reptiles starting some one hundred and seventy million years ago.

    But is that still enough time? About seven to ten million years ago, Hominids split off from Gorilla and Pan (chimpanzees). In that time we have changed just about 1.5% of our genes; 98.5% of them we still share with our closest ape cousins, and they with one another. We have just 24,000 genes in the human genome, so, assuming the same holds true for bonobos (Pan paniscus), and assuming they are responsible for half the difference between us, we have each only needed to change 180 of our genes to get as far as we now are from one another. Think how many generations have lived in those seven to ten million years. At present-day rates of human generation, that's somewhere between 280,000 and 400,000 generations in 'just' that short time (geologically speaking). Of course that's enough time to change a mere 180 genes.

Almost unbelievably, and yet unarguably, you are related to every one of those who lived through that process. Traces of their genetic evolution are to be found in you, and just about every winner in the competition for space in the hominid gene pool, up to about 350,000 years ago, can be found in almost every cell in your body. So there we can see that, with a little appreciation of a few basic principles, how easy evolution can be to understand, and how easy it is to understand how seemingly highly unlikely things can evolve against all probability because of the power of natural selection to concentrate and accumulate the improbable and drive a species up an improbability gradient until it becomes not only probable but highly likely, even certain. This was the ability to imagine this simple idea, and to appreciate it's power to explain, that made Charles Darwin one of the greatest scientific minds that have ever lived.

Of course, Creationists will tell you this is all nonsense, because they prefer you to believe it was all done by magic, because people who lived in the Bronze Age thought it must have been, and that makes it easier for them to sell you books without either of you needing to learn anything very much.

Further reading:
  1. Climbing Mount Improbable, Richard Dawkins.
  2. Wikipedia - Evolution.
  3. Wikipedia - Phylogenetic tree.
  4. Wikipedia - Timeline of human evolution.
  5. The Tree of Life.
  6. Evolution - Making A Monkey Of Creationists.
  7. Unintelligent Design And Vitamin C Deficiency.
  8. Why Species?

  1. Which makes one wonder how on earth the Joseph of the Bible knew he needed to go to Bethlehem for the census when one of his ancestors, David, allegedly lived there 1000 years earlier. Why David and not one of the other half a trillion male ancestors? And how did the Roman authorities know he had gone to the right town when practically any town or village in the area would have been where at least one of Joseph's ancestors had lived, including Nazareth, from where they allegedly travelled?

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