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Entries in "Theory of evolution"
August 25, 2008
Why Darwin scares people
(The text of a talk given at CWRU's Share the Vision program on Friday, August 22, 2008 at 1:00 pm in Severance Hall. This annual program is to welcome all incoming first year students. My comments centered on this year's common reading book selection The Reluctant Mr. Darwin by David Quammen.)
Welcome to Case Western Reserve University!
You are fortunate that in your first year here you are going to part of a big year-long celebration, organized by this university, to mark the 200th anniversary of the birth of Charles Darwin and the 150th anniversary of his groundbreaking book On the Origin of Species.
In my opinion, Darwin is the greatest scientist of all time. You have no idea how hard it is for me to say that because I am a physicist and had long thought that the only competitors for that exalted title were Isaac Newton and Albert Einstein. But the more that I have learned about the theory of evolution over the last decade, the more I have to concede that Darwin has had the most impact on our thinking.
As you have heard today, the Share the Vision program at Case is part of the university's commitment to create a welcoming and unifying environment for people from all backgrounds. Darwin's ideas should be warmly welcomed by those who share those goals because one important implication of his work is that all of us are biologically linked because we all share common ancestors.
If any two of you in this auditorium could trace your ancestors back in time, it will not be long before you find that you share a common ancestor. In fact, we would find that everyone who lives in the world now shares at least one common ancestor who lived only as far back as around 1500 AD. So around the time of Copernicus and the Renaissance, some one was walking around who is the common ancestor of each and every one of us.
If that doesn't boggle your mind, then listen to this. If you go back to just around 3,000 BC, of all the people who lived then, about 20% have no living descendents. Their lines died out. But the remaining 80% are the shared, common ancestors of all of us. Think about that for a minute. This is quite amazing. We are all, literally, part of one big family. We are all cousins under the skin.
It gets even better. If we go back even further, we find that we are cousins with all the nonhuman animals as well, and going back further still, with all the plants and even bacteria, all of us tracing our ancestors back to possibly a single ancestral organism. All of life that presently exists and ever existed is connected by this tree of life.
No wonder that Darwin was moved by this stupendous insight to end his book On the Origin of Species, by saying, "There is grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved."
But, sadly, not everyone is as delighted as I am with the idea that worms are our cousins, and that we are both part of one big family with every organism that ever lived. Those who want to believe that humans possess some unique and special quality not possessed by other animals have found Darwin's idea deeply disturbing, and this is the source of much of the antagonism to him. Even the cautious Darwin himself, aware of this problem and the hostility it would arouse, only obliquely hinted at the linkage of humans to all other species in On the Origin of Species, leaving a full treatment to a subsequent book The Descent of Man published twelve years later.
Darwin's theory of natural selection and the tree of life is not only eminently plausible, but has been put on a rigorous mathematical footing and has abundant evidence in support of it. So why does the theory still arouse such strong opposition?
The superficial answer is that Darwin's theory goes against the religious belief that each species, and especially humans, were the result of a special act of creation by god. That idea seemed plausible at a time when it seemed obvious that every complex thing needed an even more complex designer to create it. But with Darwin, for the first time we had a scientific theory that showed how complex things could emerge from simpler things, without any outside intervention or agent or intelligence or design. Once the first primitive replicator, an early ancestor of DNA, had been created in the primeval soup, it multiplied and diverged, under the action of purely physical and algorithmic laws acting mindlessly, to eventually become the wide array of life we have now.
What is even more unnerving to some is that Darwin's theory reaches into every aspect of existence. As philosopher Daniel Dennett says, it is like an immensely powerful acid that once created cannot be contained by any boundaries because it can eat through any wall. People first tried to restrict it to nonhuman life but it broke through that barrier. They then tried to restrict it only to the human body but it broke through that too. Darwin's theory is now being applied to explain the origins of language and altruism and morality and other aspects of behavior, and to the workings of the brain and mind and consciousness.
Even intelligence, the feature that humanity prizes itself upon and which had been thought to be a precursor to creation, we now know occurred much later in life's evolution and came into being as a result of the same non-intelligent, undirected, natural selection mechanism that produced our arms and legs.
There seems to be no quality that we humans possess that could not have come into existence by the evolutionary processes described by Darwin and his successors.
Darwin's theory has extended even to what used to be considered purely philosophical questions. Paleontologist George Gaylord Simpson said that all attempts before the publication of On the Origin of Species to answer the question of what does it mean to be human were worthless and that we would be better off if we ignored them completely. Such is the significance of Darwin's work.
People who are wedded to the idea that human beings must possess some unique, non-material, and possibly divine quality, and that there must be some externally imposed purpose to their lives and the universe are highly uncomfortable by these developments. As cognitive scientist Steven Pinker says, "People desperately want Darwin to be wrong . . . because natural selection implies there is no plan to the universe, including human nature."
But the fact that the theory of evolution causes unease for some is hardly grounds for its rejection. The test of validity of a scientific theory is not whether it is perfect or whether it explains everything or whether it makes us feel happy or satisfies some deep emotional need, but whether it works better than any of its competitors. And there is nothing that comes even close to replacing the neo-Darwinian synthesis as the explanation of life's diversity.
As you will have read in the book, Darwin was nervous about where his ideas were taking him, even though he was increasingly convinced that he was right. He knew that in science just having a good idea isn’t enough, however beautiful the idea is. You had to have evidence to support it and to that end he doggedly spent most of his life, observing, experimenting, and collecting data from all over the world, despite ill health and recurring headaches and vomiting attacks and personal tragedy.
Since his death, the evidence in favor of his theory has increased with other revolutionary discoveries like genes and DNA and continental drift and fossils. The evidence in support of Darwin's theory of natural selection and the resulting interconnectedness of all life now exists in abundance.
This has not stopped the critics though. But they have been reduced to merely trying to find problems as yet unsolved by the theory of evolution because no alternative theory has been able to produce the kinds of evidence necessary to be taken seriously as a competitor. But as Herbert Spencer pointed out as long ago as 1891, "Those who cavalierly reject the Theory of Evolution as not being adequately supported by facts, seem to forget that their own theory is supported by no facts at all."
This year, you will all be able to be part of the Darwin celebration as eminent scientists, philosophers, and legal scholars from all over the world come to Case to discuss all the ramifications of his work. You have a unique opportunity to be part of that exciting year and I hope you take full advantage of it.
POST SCRIPT: Teaching evolution in high schools
Florida has just introduced evolution explicitly into its science standards. This story illustrates one teacher's efforts to teach it to his high school students.
August 10, 2007
Evolution-21: Why evolution speeds up with time
(Please see here for previous posts in this series.)
One of interesting things about evolution is that it seems to be speeding up with time. Earth was formed about 4.7 billion years ago and it took about a billion years for the first single-celled life to appear about 3.5 billion years ago. It then took another 2.5 billion years for the first multi-cellular life form (like sponges) to appear. So everything else, all the insects, animals, and birds, came into being within the last one billion years or so.
One reason that things seem to be speeding up is that once complex organisms appeared, selection advantages increased due to more sophisticated competition among them. For example, when you have a predator-prey relationship, the prey species will have a huge selection advantage for those qualities that enable it to elude the predator (such as the ability to run faster or climb quicker or hide better or hear and smell better) while the predator will also have a huge selection advantage for those features that make it better able to capture prey (run faster, jump higher, and more acute vision, hearing and smell.) It is like an arms race. Two nations that are locked in a battle for supremacy are more likely to rapidly develop sophisticated weaponry than a nation without enemies.
Such factors, along with things like sexual selection, speed up the evolutionary process considerably, by increasing the selection advantage.
But new discoveries keep coming in and just this year, researchers have found that bacteria and viruses are also speeding up the process of evolution. Scientists at Rice University report that "the speed of evolution has increased over time because bacteria and viruses constantly exchange transposable chunks of DNA between species, thus making it possible for life forms to evolve faster than they would if they relied only on sexual selection or random genetic mutations." Theories like this support suggestions that there is a selection advantage for those organisms that are more adaptable to change. In other words, evolution favors those organisms that evolve more readily, leading to ever-increasing rates of change.
In fact, the problem with the evolution of species is not (as some religious people would have you believe) whether it occurs at all but that it is impossible to stop it from occurring. Almost invariably, when some members of a species get isolated from the rest for whatever reason, they begin to diverge. This is why the isolation of islands makes them excellent breeding grounds for new species. All the islands smaller than New Guinea account for one-thirtieth of land surface but contain about one-sixth of the total number of known species (Almost Like a Whale, Steve Jones, p. 345). In the Caribbean, for example, different lizards have different kinds of legs suitable for the kinds of vegetation that they climb on. In 1977, when lizards from one island were moved to another that had no lizards and only plants with thin twigs, within ten years their legs had evolved to meet the needs of the new vegetation by becoming stubby (Jones, p. 96).
But Darwin also proposed that one did not need actual physical separation like islands for speciation to occur. Diversity could arise within the same geographical area as organisms adapted to fit different niches in the same environment. Just yesterday it was reported that new evidence suggests that the two species homo habilis and homo erectus lived side by side at the same time, challenging the earlier idea that there was a linear progression from homo habilis to homo erectus to us, homo sapiens. The news report of the findings says that "The fact that the two hominid species lived together in the same lake basin for so long and remained separate species, Meave Leakey said in a statement from Nairobi, “suggests that they had their own ecological niche, thus avoiding direct competition.” "
Zoos face this problem with trying to preserve rare species. Although the zoos are trying to preserve the animals that are being lost in the wild, the very fact that zoo animals breed within a small group paradoxically causes them to actually accelerate their evolution into new forms. (Jones, p. 47)
As a result of all these factors favoring evolution, "Over the past five hundred million years, through all its ecological alarms and excursions, new kinds appeared at an almost constant rate. A survey of tens of thousands of marine animals over that time gives a rate of four hundred and fifty new species a year." (Jones, p. 231)
This is the last post in this series on evolution. To be frank, I had not expected it to be this long when I started but the breadth and scope of the subject just kept drawing me in deeper. While I will definitely return to this topic many times (because it is inexhaustible and new and interesting discoveries keep popping up), the planned and sequential nature of these posts will cease. My goal was to move the discussion of the theory of evolution away from a high level of generality and show that evolution is not just a good idea but that, like quantum mechanics and relativity, it is a theory that has been developed in great detail and its ramifications explored using a wide array of scientific tools.
The mathematics of evolution has played an important role in substantiating its claims and advancing our understanding of how it works. Charles Darwin would have found this highly amusing because he had great difficulty with mathematics as a student, struggling with even elementary algebra. Because of the complexity of biological systems, the probabilistic nature of the processes, and the interplay of organisms with other organisms and the environment in general, modern biological calculations use advanced mathematics, computer simulations, and game theoretical techniques in addition to the more conventional differential equations. There is even a new game by the creators of the Sims series that enables you to manipulate the conditions of evolution and see what happens. You can "determine the evolution of a species, from an amoeba to an inter-stellar race."
This is how science works and how we build up knowledge. People with different skills and expertise bring them to bear on complex problems, publish so that it can be checked by others, and over time we create reliable knowledge. This does not mean that scientific knowledge is infallible by any means. It is not uncommon for people to find that new data or a different set of assumptions lead to quite different results, and so scientists continually probe for weaknesses.
But such revisions and critiques are of a very different class from those of people who reject scientific ideas as absurd simply because it conflicts with their intuitions or because they seem unimaginable, without looking into the details. Such people are doing the same thing as those who reject quantum mechanics and special relativity because the results seem so weird to them.
POST SCRIPT: Pampered elites
Jason Jones of The Daily Show has a very funny piece on how the very rich in this country don't want to allow even the slightest thing to disturb their lives. People like the Kennedys, who vociferously support environmental causes everywhere else, turn against eco-friendly projects when those might have an infinitesimal impact on their own neighborhoods.
August 08, 2007
Evolution-20: How selection advantage arises in evolution
(Please see here for previous posts in this series.)
In the mathematics of evolutionary change, the selection advantage is a key mathematical quantity that determines the rate at which a favorable mutation spreads through the population. The selection advantage is a quantification of the net result of advantages that a variety of a species gains by virtue of its fertility and fecundity and longevity. As we saw before, even a small selection advantage can lead to rapid spread of the mutation.
One of the interesting things that occurs is that since the entire organism is subjected to the same environment, a selection advantage for one feature can act simultaneously on many different features and can lead to a group of changes that might seem on the surface to be unrelated. Thus one can have many simultaneous changes in an organism, a process known as coherence.
Jerry Coyne (a professor in the Department of Ecology and Evolution at the University of Chicago) describes how this works.
Coherence is precisely the product of natural selection working with mutation. Yes, mutations are random in the sense I have described, but to say that an evolutionary step taken by an organism is unconnected to its predecessor completely ignores the fact that during evolution organisms are adapting to something in their environment, and that this adaptation can involve a coherent, coordinated response of many features. Consider the evolution of whales from terrestrial animals, now documented by a superb fossil record. The fossils show a wolf-like creature gradually becoming aquatic, with the hind limbs being reduced and finally lost, the forelimbs transformed into flippers, and the nostrils gradually moving atop the head to form the blowhole. How can anyone say that these changes (which of course look planned at the end) are unconnected or incoherent? They represent a case of natural selection eventually turning a land animal into a well-adapted aquatic one.
In Almost Like a Whale (p. 36), Steve Jones says that when some wolves were domesticated to become companions to humans and became the dogs we now have, its other features also changed, although these were not deliberately sought for.
Its ears, once pricked, are floppy, and the sounds of the world dulled. Its sharp eyes are blurred by a fringe of hair and can no longer stare an opponent into submission. The lupine tail, an expression of rage or delight, is in many breeds so curled as to bear no message at all. Most pets cannot even raise their hackles in anger as their hair is too long. All this comes from an unconscious preference by man for an animal that knows its place.
What was once done without thought has been echoed by science. In the 1950 Russia, silver foxes were farmed for fur. They were savage, suspicious and liable to die from anxiety. On a certain collective, in an attempt to improve matters, only those willing to accept human company were chosen as parents. Within twenty years and a mere ten thousand foxes, the farmers saw a great shift in their charges. The ranch was filled with well-behaved animals that looked more like dogs, with lowered tails and drooping ears. Many had piebald coats, quite unlike their unrestrained kin, and the females reproduced – like dogs – twice rather than once each year. To breed for tameness was enough to make the change. The other characteristics followed.
There are other factors that increase the selection advantage and thus speed up evolution considerably. The powerful driver that is sexual selection in the wild (usually females selecting males for mating based on certain qualities) prevents random mating and can result in generating significant selection advantages, and is believed to be the source of the exotic and elaborate plumage and songs of some male birds and the gaudiness of flowers (Jones p. 102). Animals tend to prefer to mate with others that either look like themselves or with those animals that look like the ones that raised them, if they had foster mothers (Jones p. 49). Darwin himself first emphasized the importance of sexual selection (On the Origin of Species, 1859, p. 87).
All kinds of factors can come into play that result in one variety of a species separating from the rest, and evolving into a new species as a result. As Jones says (p. 231):
Species are divided from each other in many ways – by space, by time, by mating preference, by the inability to fertilize an egg or produce healthy young, or by the sterility of offspring. The hurdles at which the sexual athletes fail are as varied as life itself. Those involved may never meet, or may mate at their own special time or season. Males and females of different kinds may choose not to pair, or may – with more or less enthusiasm – mate but fail to make a fertile egg. The geographical checks can be as narrow as the few inches between different orchids upon which certain bees feed or as wide as the ocean that separates American and European species of gull. When it comes to time, some flies mate in the morning and some in the evening and some crickets in the spring and others in the autumn; but two kinds of cicadas in North America emerge and mate every thirteen or seventeen years. The difference ensures that they almost never get together (in spite of a certain confusion every couple of centuries).
Colour, song, scent and more all play a part in settling who is, and who is not acceptable.
As soon as one group within a species separates out from the rest and breeds within itself in a new environment, differences get accentuated leading to the eventual formation of new species with new characteristics. But some aspects of the environment (like gravity) are the same everywhere on the Earth and have remained unchanged for a long time. For example, the radiation from the Sun has not changed, and the visible spectrum of light that reaches the surface of the Earth is pretty much the same everywhere on the Earth and has been stable for a long time. Hence it should not surprise us that the ability to see has a huge selection advantage and has evolved independently over 40 times in evolutionary history, although the resulting eyes differ in detail.
Thus if we could run the evolutionary clock all over again, while some things will be quite different, certain features like the eye are likely to recur in some form simply because the environment that makes them advantageous is stable and unchanged by the life forms that happen to come into being. Such a process is called convergent evolution.
All these things constitute evidence that evolution, far from being purely random, is a strongly constrained and law-like process.
POST SCRIPT: Religion as divider
In the film Deconstructing Harry Woody Allen discusses the role that religion plays in creating us-them distinctions.
August 06, 2007
Evolution-19: The Boeing 747 in the junkyard
(Please see here for previous posts in this series.)
As I have emphasized repeatedly in this series, the hardest thing to appreciate about evolution is how a cumulative sequence of very tiny changes can lead to big changes. The problem is that our senses can only detect gross differences between organisms and our minds can only comprehend short time scales and to appreciate evolution requires us to overcome those limitations. This is why skeptics need to actually study the details and convince themselves that it works.
I have the same problems when it comes to teaching modern physics topics like quantum mechanics or special relativity. Our senses and intuition have evolved to enable us to deal with objects that are on a human (or 'classical') size scale and traveling at speeds that are not too great. But the effects of quantum mechanics only become manifest when describing the very small, subatomic level of particles that we cannot see, and there our intuition completely breaks down. Similarly, the effects of special relativity become manifest only for objects traveling close to the speed of light, which we do not encounter in everyday life and again our intuition is incapable of dealing with it. So when physicists talk about a single electron simultaneously traveling by many different paths from a single initial starting point to a final point, or twins aging at different rates depending on their speed of travel, these ideas initially seem preposterous.
When teaching these subjects, I warn my students that their intuition is quite likely to lead them astray, that what their gut feelings tell them is reasonable or unreasonable is undependable, and that they have to constantly check those intuitive reactions by doing calculations to convince themselves that these counter-intuitive results drop out naturally from a coherent theory
The same thing is true for evolution. Mutations are too small to be visible and time scales are too long to comprehend, so one should not depend upon what seems reasonable to make judgments. Steven Pinker (How the Mind Works 1997, p. 163) points out that: "A hypothetical mouse subjected to a selection pressure so weak that it cannot be measured could nonetheless evolve to the size of an elephant in only twelve thousand generations." This is quite an amazing result. It is not at all intuitive and is hard to convince oneself that this could be possible unless one does the calculations, or trusts those who do the calculations.
But people who want to throw doubt on evolution exploit this breakdown of intuition by making statements of broad generality. For example, one often hears that the evolution of life as described by natural selection is as likely as a tornado sweeping through a junkyard and spontaneously assembling a Boeing 747 airplane. This analogy was initially proposed by astrophysicist Fred Hoyle in his 1983 book The Intelligent Universe. Hoyle and his co-worker Chandra Wickremasinghe used this example to support their alternative theory of panspermia, that life originated elsewhere in the universe and arrived on Earth from outer space via meteors.
Neither Hoyle nor Wickremasinghe are creationists and have their own reasons to want to discredit natural selection, but intelligent design creationists seized on this vivid image of the 747 in the junkyard and exploit it heavily in their anti-Darwin crusade, and Wickremasinghe has even appeared as a witness for them at some court trials.
To counter this analogy, one needs to look at exactly what natural selection says and compare it with what its opponents portray it as. Jerry Coyne (a professor in the Department of Ecology and Evolution at the University of Chicago) in a devastating review of intelligent design creationist Michael Behe's new book gives a nice example using the familiar example of throwing dice.
Take for example, some adaptation of a gene that, starting from the original organism, requires twenty mutations at twenty different locations for the desirable new feature of the organism to appear, with the mutations occurring in a specific order so that each mutation confers a slight selection advantage to the organism. Suppose that the random mutations are represented by the throw of a die and the required mutation at a particular site occurs when you throw a six. This means that it will take an average of six throws for the first mutation to occur. Recall that evolution is a step-by-step process that builds on past successes and I have already described how even a slight selection advantage is sufficient for a single mutation to become universal in the population, so this mutation will be stable. It will then take another six throws for the second advantageous mutation to occur, and so on, so that it will take an average of 120 throws for all twenty mutations to occur. If the dice is thrown at the rate of one a second, that means it will take about two minutes for all twenty mutation to have gone into effect.
What the Boeing 747 analogy does is to assume that you have twenty dice and throw them all at once and that all twenty must come up six simultaneously for the new feature to appear. The odds against this are astronomically high. At the same rate of one toss per second, this would take more than one hundred million years. As Coyne says, "This sequential way of getting twenty sixes is infinitely faster than Behe's method. And this is the way natural selection and mutation really work, not by the ludicrous scenario presented by Behe."
Arguing by analogy and example is often necessary when trying to explain esoteric points, but is also tricky and has to be done with care. No analogy is a perfect replica of the actual process and you have to make sure that the analogy you select corresponds accurately to the phenomenon being analogized as far as the crucial elements are concerned. In the case of evolution, the key point to bear in mind is that a sequential series of changes, each of which is beneficial and stable, takes much less time (i.e. is far more likely) to occur than for them to occur simultaneously. This is why intelligent design creationists try to desperately find examples of systems that (they argue) could not have occurred by sequential changes. But they have failed.
POST SCRIPT: If FDR had been like George Bush. . .
Jacob Sager Weinstein says that he "got tired of right-wingers saying, "If the media had been as hard on FDR as they are on Bush, we'd have lost World War II." So I started wondering. . . What if FDR had run his war like GWB?"
Here is the video that resulted from his musings.
August 03, 2007
Evolution-18: Missing links
(Please see here for previous posts in this series.)
About ten years ago, a group of engineering students came into my office. They were taking part in a scavenger hunt during Engineers Week and the one item that was very hard for them to find was a 'slide rule'. They had little idea of what it was and no idea how it worked or what one even looked like but they knew it was old technology and they figured that I was old enough to possibly own one.
They were partly right. I had once owned a slide rule as a physics undergraduate in Sri Lanka but unfortunately did not have mine anymore.
For those not familiar with slide rules, the standard type looks like a ruler with another sliding ruler attached, and you use it to do complicated calculations. It was the precursor to the handheld calculator but with the arrival of cheap electronic versions of the latter, the slide rule went extinct. I actually owned a more unusual type of slide rule that was cylindrical rather than linear and was like a collapsible telescope. It had the advantage that it was small enough to carry around in your pocket, and being able to whip out a slide rule when the occasion demanded defined the nerds of that time.
The difficulty that the engineering students had in getting hold of a slide rule is due to the fact that when a new technology comes along, the old technology is superceded and devices built using it become extinct because no more units get produced and the old units get thrown away and end up in landfills. As another example of this phenomenon, at Case we have a state of the art Freedman Center where you can take information stored in any form (say phonograph records of any vintage, old 8mm home movies, etc.) and convert to digital formats. The one old format they cannot currently convert is videotapes made using the Betamax format and this is because they simply cannot get hold of any working Betamax players anywhere anymore. It has gone extinct. (If anyone has an unused but working Betamax player they would like to donate to the Freedman Center, they would be happy to take it off your hands.)
Like slide rules and Betamaxes, you would be hard pressed now to find many things that were mass-produced even just a decade or two ago. Apart from those in the collections of museums and idiosyncratic collectors, most other artifacts have disappeared forever.
Imagine an extraterrestrial archeologist visiting the Earth and seeing an electronic calculator. Even if he looks around fairly carefully, he would likely not find slide rules or indeed any earlier versions of such devices and conclude, erroneously, that Earthlings are brilliant designers who went straight from nothing to a fairly sophisticated calculator in one jump.
The analogy with missing links in evolution is obvious. This difficulty of finding well-preserved specimens of old things is even worse with the fossil record in evolution. As an organism evolves to a newer form, the old versions rapidly disappear and become extinct. As Steve Jones points out (Almost Like a Whale, 1999, p. 161), "When we see any structure highly perfected for any particular habit, as the wings and birds for flight, we should bear in mind that animals displaying early transitional grades of the structure will seldom continue to exist to the present day, for they will have been supplanted by the very process of natural selection."
Even when it comes to fossils, since fossilization occurs only under very special conditions of organism and soil and climate, most of these dead organisms disappear forever and thus it is hard to find a continuous record of evolution. Even if a fossil is formed, the Earth itself is a dynamic system, with its crusts moving over each other, erosion, sedimentation, glacier movement, and even the rise and fall of mountains and oceans, all of which can destroy or bury or hide any fossils unfortunate enough to be in the way. As a result, "We continually overrate the perfection of the geological record and falsely infer, because certain genera or families have not been found beneath a certain stage, that they did not exist before that stage." (Jones, p. 269) "The Cambrian Explosion [beginning about 545 million years ago], so called, is a failure of the geological record rather than of the Darwinian machine. Its radical new groups reflect not a set of exceptional events but something more banal: the first appearance of animals with parts capable of preservation. Before then, there were soft creatures that decayed as soon as they died. Why shells appeared all of a sudden is not certain." (Jones, p. 274)
The rarity of fossilization can be seen by the fate of the passenger pigeon. Estimates put the number of them at over nine billion alive during the time of the Mayflower, more than the total of all the birds in the US today. They were still flourishing in the US as late as the times of the Civil War but the species went extinct in 1914 and not a single fossilized specimen has ever been found. If not for the existence of written records about this bird, we would not have known it even existed. (Jones, p. 266)
What gets preserved as fossils tend to be big and hard things like dinosaurs and mammoths, just like it is easier to find earlier versions of cars and ships than of slide rules. But thanks to the new techniques of DNA mapping, we do not have to depend exclusively on fossils to learn about how our ancestors evolved and diverged. DNA can interpolate the gaps in the record much better than even fossils can.
POST SCRIPT: Family Guy's Stewie and Brian go to Iraq
August 01, 2007
Evolution-17: How species diverge
(Please see here for previous posts in this series.)
When my daughter was quite young, about five or so, the question of where people came from came up in a mealtime conversation. Naturally we told her that human beings had evolved from ancestors who were monkey-like and then became human-like. She sat there for a while silently digesting this interesting bit of new information and mulling it over in her mind. It seemed clear that she was not at all disgusted or even bothered by the thought that we were related to the monkey family. That kind of revulsion seems to be something that has to be acquired, often nurtured by religions.
But something was bothering her and she finally articulated it, asking "But when that happened, wouldn't the mother monkey notice that her child looked different?"
She had hit upon an issue that many skeptics of evolution raise. They argue that there is a contradiction if we assume that we had evolved from an ancestor species that was so different from us that we could not interbreed with that species. Surely, the argument goes, doesn't evolution imply that if species A slowly evolves into species B, then there must be a time when the parent is of species A while the child is of species B? Isn't it a ridiculous notion for parent and child to belong to different species?
The answer is that it is perfectly possible that as we go from generation to generation, for each child to be the same species as the parent, while of a different species from a distant ancestor. In fact, we have living examples of such a phenomena,
In The Ancestor's Take (p. 302), Richard Dawkins uses the example of the ring speciation of the herring gull and lesser black-backed gull to illustrate how this happens. In Britain, these two kinds of birds don't hybridize even though they meet and even breed alongside one another in mixed colonies. Thus they are considered different species. But he goes on to say:
If you follow the population of herring gulls westward to North America, then on around the world across Siberia and back to Europe again, you notice a curious fact. The 'herring gulls', as you move around the pole, gradually become less and less like herring gulls and more and more like lesser black-backed gulls, until it turns out that our Western European lesser black-backed gulls actually are the other end of a ring-shaped continuum which started with herring gulls. At every stage around the ring, the birds are sufficiently similar to their immediate neighbors in the ring to interbreed with them. Until, that is, the ends of the continuum are reached, and the ring bites itself in the tail. The herring gull and the lesser black-backed gull in Europe never interbreed, although they are linked by a continuous series of interbreeding colleagues all the way around the other side of the world.
Dawkins gives a similar example of this kind of ring speciation with salamanders in the Central Valley of California, which is ringed by mountains. If you start with salamanders at one end of the valley and proceed clockwise around the mountain range to the opposite side of the valley, the salamanders change slowly, at each stage being able to interbreed with the neighbors. The same thing is true when you go counterclockwise from the same starting point. But when you arrive at the opposite point of the valley where the two chains of evolution arrived at by going in different senses meet, you find they are now two different species.
The herring gulls and salamanders are the examples separated in space (which we can directly see now) of the same argument separated in time (which we can only infer) that says that as descendants are produced, they form a continuum. Each generation, while differing slightly, can interbreed with its previous generation, but over a long enough period of time, the two end points of the continuum need not be able to interbreed.
Thus it is possible for one species to evolve into another and for an organism to be intermediate between two species.
POST SCRIPT: Family Guy on why Congress voted for the Iraq war
July 30, 2007
Evolution-16: The evolution of the eye
(Please see here for previous posts in this series.)
The eye is one organ almost invariably brought out by creationists to argue against evolution. How could something so complex have possibly evolved incrementally, they ask?
Darwin himself suggested the way that the eye could come into being. Due to the fact that eyes don't fossilize and thus leave a permanent record, it is hard to trace back in time and see the various stages in the evolution of the eye as linear developments. So he looked instead at the eyes of currently existing different organisms at intermediate stages of development, and concluded (On the Origin of Species, 1859, p. 188):
With these facts, here, far too briefly and imperfectly given, which show that there is much graduated diversity in the eyes of living crustaceans, and bearing in mind how small the number of living animals is in proportion to those which have become instinct, I can see no very great difficulty (not more than that in the case of many other creatures) in believing that natural selection has converted the simple apparatus of an optic nerve merely coated with pigment and invested with transparent membrane, into an optical instrument as perfect as is possessed by any member of the great Articulate class.
Steven Pinker (How The Mind Works, 1997, p. 159) describes how Darwin established how the eye could have evolved, according to the step-by-step process that I have described earlier, each step having a low probability for an individual but becoming likely when large numbers of organisms are involved over long times.
By looking at organisms with simpler eyes, Darwin reconstructed how that could have happened. A few mutations made a patch of skin cells light sensitive, a few more made the underlying tissue opaque, others deepened it into a cup and then spherical hollow. Subsequent mutations added a thin translucent cover, which subsequently was thickened into a lens, and so on. Each step offered a small improvement in vision. Each mutation was improbable, but not astronomically so. The entire sequence was not astronomically impossible because the mutations were not dealt all at once like a big gin rummy hand; each beneficial mutation was added to a set of prior ones that had been selected over the eons.
Still think it is implausible? Once again, using mathematics and computer simulations based on strict natural selection principles and starting, as Darwin himself suggested, with a light-sensitive nerve, it is possible to estimate how long the process of eye evolution took (Pinker, p.164):
The computer scientists Dan Nilsson and Susanne Pelger simulated a three-layer slab of virtual skin resembling a light-sensitive spot on a primitive organism. It was a simple sandwich made up of a layer of pigmented cells on the bottom, a layer of light sensitive cells above it, and a layer of translucent cells forming a protective cover. The translucent cells could undergo random mutations of their refractive index: their ability to bend light, which is real life often corresponds to density. All the cells could undergo small mutations affecting their size and thickness. In the simulation, the cells in the slab were allowed to mutate randomly, and after each round of mutation the program calculated the spatial resolution of an image projected onto the slab by a nearby object. If a bout of mutations improved the resolution, the mutations were retained as the starting point for the next bout, as if the slab belonged to a lineage of organisms whose survival depended on reacting to looming predators. As in real evolution, there was no master plan or project scheduling. The organism could not put up with a less effective detector in the short run even if its patience would have been rewarded by the best conceivable detector in the long run. Every change had to be an improvement.
Satisfyingly, the model evolved into a complex eye right on the computer screen. The slab indented and then deepened into a cup; the transparent layer thickened to fill the cup and bulged out to form a cornea. Inside the clear filling, a spherical lens with a higher refractive index emerged in just the right place, resembling in many subtle details the excellent optical design of a fish's eye. To estimate how long it would take in real time, rather than compute time, for an eye to unfold, Nilsson and Pelger built in pessimistic assumptions about heritability, variation in the population, and the size of the selective advantage, and even forced the mutations to take place in only one part of the "eye" each generation. Nonetheless, the entire sequence in which flat skin became a complex eye took only four hundred thousand generations, a geological instant.
In his book The Ancestor's Tale, Richard Dawkins points out (p. 388) that after the evolution of light-sensitive cells in worms about 600 million years ago, the kinds of image-forming optics that we now call the eye is estimated to have independently evolved more than 40 different times in various parts of the animal kingdom. Vastly different eye forms like the human eye and the compound eye of the crustaceans evolved differently and independently from a primitive common light sensitive cell that formed a proto-eye.
So far from being an event of unimaginably breathtaking improbability, the evolution of the eye is relatively mundane, although the organ itself is quite remarakable.
That is exactly the point that those opposed to natural selection refuse to acknowledge when they act as if all the parts of the eye must have come together almost at once. What is highly improbable to happen in one fell swoop becomes possible when it happens gradually.
Richard Dawkins in his book Climbing Mount Improbable looks at case after case of things that seem to be very complex and how they could have come about by natural selection. But Darwin did not need Dawkins to be convinced. In his own day, he had enough evidence to satisfy him. "If it could be demonstrated that any complex organ existed, which could not possibly have formed by numerous, successive, slight modifications, my theory would absolutely break down. But I can find no such case." (Darwin, p. 189)
He further added (Darwin, p. 109): "Slow though the process of selection may be, if feeble man can do so much by his powers of artificial selection, I can see no limit to the amount of change, to the beauty and infinite complexity of the coadaptations between all organic beings, one with another and with their physical conditions of life, which may be effected in the long course of time by nature's power of selection."
POST SCRIPT: Great moments in the evolution of technology
Have you seen the the sideways bike?
July 27, 2007
Evolution-15: How species evolve
(Please see here for previous posts in this series.)
The final feature that needs to be addressed is the probability of mutations cumulating to produce new organs and species.
This question lies at the heart of many people's objections to evolutionary ideas. They cannot envisage how infinitesimal changes, each invisible to the eye, can add up to major changes. That is because they tend to think that the two foundations for this to occur (the occurrence of successful mutations and the mutations then spreading throughout the population) are both highly unlikely, and so that the chance of a whole sequence of such processes occurring must be infinitesimally small.
What this series of posts has shown is that given large population sizes and the long geological times available, not only are those two things not unlikely, they are almost inevitable. The mathematical results discussed in the previous posts have shown two very important results. The first is that when the large sizes of populations and the long times involved are taken into account, the probability of favorable mutations occurring is quite high. The second is that the probability of a single favorable mutation spreading to every organism in the population is also high. These two results undercut the arguments of those who simply throw their hands up in the air and declare that evolution is extremely unlikely to have occurred.
Once that is understood, it is not hard to see how successive mutations that each have a selection advantage can pile one on top of another to produce new species leading to the diverse and complex biological system that we see today. The history of twentieth century biology is the discovery of case after case of the evolutionary history of organisms. Richard Dawkins's book Climbing Mount Improbable describes many such cases.
In order to understand how speciation comes about, we need to understand better what constitutes different species. As pointed out by biologist Steve Jones, "Species are divided from each other in many different ways – by space, by time, by mating preference, by the inability to fertilize an egg or produce healthy young, or by the sterility of the offspring." (Almost Like a Whale, p. 231)
The most famous historical example is that of the finches of the Galapagos Islands. During his five year trip on the Beagle Darwin had periodically shipped various specimens back to England to specialists to study them, and a respected ornithologist John Gould had agreed to study the birds. Soon after his return to England in 1836, Darwin met with Gould who gave him the surprising news that birds that Darwin had thought were different species like wrens and finches and orioles were actually all different kinds of finches. Furthermore, Gould had also found among Darwin's specimens three mockingbird species, each set of which came from a different island in the Galapagos. (The Reluctant Mr. Darwin, David Quammen, (2006), p. 24)
This fueled Darwin's suspicions that these birds had evolved from a single species that had somehow made the difficult journey to the Galapagos from the South American mainland, and after spreading out to each island had then become isolated from the others and evolved into separate species under the different selection pressures they experienced on the different islands.
Darwin decided to devote himself to the study of speciation and in order to do so, started with the breeding of animals in captivity. He extensively studied another bird (the pigeon) that was highly popular among breeders in England at that time and for which there existed a huge number of breeds. By studying pigeons (the first chapter of On the Origin of Species deals exhaustively with them), Darwin satisfied himself that all the species of pigeons were descended from a single type, the rock pigeon. "Great as the differences are between the breeds of pigeons, I am fully convinced that the common opinion of naturalists is correct, namely, that all have descended from the rock-pigeon (Columba livia)." (On the Origin of Species, Charles Darwin, (1859), p. 23)
In an interesting follow up to the Darwin finch story, Rosemary and Peter Grant spent twenty years in the Galapagos studying the finches and they actually observed the evolution that Darwin could only speculate about. For example, Darwin had noticed that the finches' beaks "resembled different kinds of pliers: heavy duty lineman's pliers, high-leverage diagonal pliers, straight needle-nose pliers, curved needle-nose pliers, and so on. Darwin eventually reasoned that one kind of bird was blown to the islands and then differentiated into thirteen species because of the demands of different ways of life on different parts of the island, such as stripping bark from trees to get at insects, probing cactus flowers, or cracking tough seeds." (How the Mind Works, Steven Pinker (1997), p. 163)
Darwin felt that such changes would occur too slowly to be observed. But what the Grants did 150 years later was to show that such changes could in fact be observed in real time. They "painstakingly measured the size and toughness of the seeds in different parts of the Galapagos at different times of the year, the length of the finches' beaks, the time they took to crack the seeds, the numbers and ages of the finches in different parts of the islands, and so on – every variable relevant to natural selection. Their measurements showed the beaks evolving to track changes in the availability of different kinds of seeds, a frame-by-frame analysis of a movie that Darwin could only imagine." (Pinker, p. 163)
Evolution is a fact. Natural selection is far and away the only theory that comes even close to explaining in detail how it happened, although will always be many things as yet unexplained. As biologist Steve Jones writes, "Although biologists still argue about how the process works, fossils make it impossible for anyone, biologist or not, to deny that it happened." (Almost like a Whale, 1999, p. 306)
Next in the series: The evolution of the eye
POST SCRIPT: The Darwin Year 2008-2009
This series of posts was inspired by the fact that 2009 will be the 200th birth anniversary of Charles Darwin and the 150th anniversary of the publication of On the Origin of Species. Case is planning a year long celebration of this event for the 2008-2009 academic year.
As part of this, the Common Book Reading committee has selected David Quammen's The Reluctant Mr. Darwin as the book that all incoming first-year students in fall 2008 read, and will also try to expand the program to make it a campus-wide reading experience.
Quammen has agreed to be the fall convocation speaker in September 2008. There are also plans to have E. O. Wilson (one of the most eminent evolutionary biologists and author of Sociobiology), Sean B. Carroll (The Making of the Fittest), and Rosemary and Peter Grant also give talks during that year.
July 25, 2007
Evolution-14: How a single mutation spreads everywhere
In the previous post, we saw that if we start with a trait that is present in just 0.1% of the population (i.e., f=0.001), and if this has a small selection advantage of size s=0.01, this will grow to 99.9% (F=0.999) in just under 1,400 generations, which is a very short time on the geological scale.
But in a population of one million, an initial fraction of f=0.001 means that we are starting with about 1000 organisms having the favorable mutation. But it could be argued that new mutations usually start with just a single new kind of organism being produced in one single organism. How does that affect the calculation?
Suppose that you have a population of organisms of size N and they all start out having the same gene at a particular position (called the 'locus') on one of the chromosomes that make up the DNA. Now suppose a random mutation occurs in just one organism, the way that it was described in an earlier post in this series describing the shift from violet to UV sensitive sight in some birds. Most of the time, even a favorable mutation will disappear because of random chance because (say) that mutated organism died before it produced any offspring or it did produce a few and that particular gene was not inherited. But on occasion that mutation will spread. How likely is it that such a single mutation will spread to every single organism (i.e., become 'fixed' in the population)?
When one is not dealing with deterministic systems involving smoothly varying numbers (as was done in the previous case), a different kind of calculation (based on probabilities and known as 'stochastic') has to be done, and in this case the expectation value for the number of generations T taken for the single new mutation to spread all over and become fixed in the population (i.e. to spread to 100% of the organisms) is given by T=(2/s)ln(2N) generations, where 'ln' stands for natural logarithms. (Molecular Evolution, Wen-Hsiung Li, 1997, p. 49)
Even if s is taken as a very small advantage of size 0.01, for a population of N=one million, the average time taken for just a single mutation to become fixed is just 2,900 generations. So we see that mutations occurring in a single organism can become universal in a very short period on the geological time scale.
There are two important points that need to be emphasized.
There first is that even a very small selection advantage is sufficient to have that mutation dominate the species. This means that the advantage may not be even visible in the organism itself, which may look like every other organism in the species. For example, an eye mutation that works better by just a tiny bit may look like every other eye. Thus we should not think in terms of big changes for natural selection to work.
The second point is that even starting from a single mutation, as long as it takes hold (which has a probability of 2s of happening) and does not disappear and has an selection advantage however small, the mutation can spread surprisingly rapidly in the population and become universal and form the basis for future mutations.
It is interesting that even if there is no survival advantage to the new gene (i.e., s=0 and the mutation is said to be 'neutral'), the mutation can on occasion still spread and become fixed, except that now the average time taken is much longer and given by T=4N generations. So that for a population of one million it would take on average about 4 million generations for a neutral mutation to spread everywhere, as compared to just 2,900 generations for a selection advantage of 0.01.
Darwin did not have access to this kind of mathematical analysis, which came long after his death. It is a tribute to his genius that he intuitively sensed the power of cumulative change over long time scales.
So far, I have shown how the first two items in the three components of natural selection, although seeming to have small probabilities of occurring, actually are quite likely. The third aspect of natural selection that has to be looked at is how the cumulative effects of small changes lead to big changes.
POST SCRIPT: Some real fact-checking
In yesterday's post, I spoke about how the media does almost no fact-checking on Bush. Well, except for Jon Stewart who catches Bushies making up stuff about Iraq.
July 23, 2007
Evolution-13: Differential rates of survival
(Please see here for previous posts in this series.)
Of the three stages of natural selection outlined before, the only one that occurs purely by chance is the first one, that of the occurrence of mutations. I discussed how although the chances of producing a favorable mutation by changes in any individual site in the DNA (called 'point mutations') on an individual member of the species is very small, when the number of individuals in a species and the long times available for the changes to occur are factored into the calculation, the result is that such mutations are not only likely, they are almost inevitable to occur and furthermore are likely to occur many times.
The Hardy-Weinberg law showed that if natural selection was not at work (along with some other conditions), populations settled into stable equilibrium values after just one generation of random mating. The next question to be addressed is to see how the populations change when natural selection is allowed to act. How likely is it that favorable mutations produced in the set of genes (the genotype) that characterize the organism (the phenotype) will end up with that actual organism predominating in the species? (Recall that natural selection acts on the phenotype and not the genes directly, while mutations act only on the genes and inheritance is passed on purely via the genes. A genetic change that has no effect on the phenotype will not influence the fitness of the organism.)
It is not the case that this happens every time. Most mutations are deleterious and do not spread and even favorable changes usually disappear by chance before they can spread to become a significant number in the population. But when the favorable mutations do take hold, that particular variety becomes widespread and dominates the population.
There are many such cases that have occurred in nature. The most famous and widely quoted example of this kind of growth of a favored phenotype is the case of the peppered moths in industrial areas of England and America. As a result of the pollution that created dark backgrounds on the lichen covering the trees where the moths rested, the darker varieties of the moths were camouflaged better from predators than the lighter ones and thus had a significant survival advantage. From 1848 to 1896, the darker forms grew to as much as 98% of the population. Subsequently, with the advent of pollution control measures that cleaned up the environment and reduced the soot pollution, the dark moth population decreased to as low as 10%. In The Making of the Fittest (2006, p. 52-53), Sean B. Carroll points out that peppered moths are not the only such examples, that many similar changes in coloration due to selection pressures have occurred in land snails, ladybird beetles, desert mice, and other species.
The way that even a very small natural selection advantage can result in that variety dominating a species can be appreciated using the more familiar example of compound interest. Suppose a parent gives each of two children $1,000 at the same time. One of the children invests in a bank that offers an interest rate of 5.0% while the other, being slightly more thrifty, shops around and invests in a different bank at 5.1%. Although they start out with the total money being split 50-50, in 7,000 years the second child (or rather that child's descendents) will have 99.9% of the total money, thanks to that very small advantage in the annual rate of return.
It is exactly this kind of differential survival rate that plays such an important role in natural selection. Even minute differences in fitness can result, over the long term, in the runaway domination of a preferred variety. To see how fast this can happen, population geneticists have carried out calculations.
Suppose one variety has a mutated gene that has a very slight fitness advantage over the existing gene. 'Fitness advantage' can be quantified by defining the fitness w as the measure of the individual's ability to survive and reproduce. (The concept of fitness is a combination of the organism's ability to survive for any length of time (at least until its reproducing age is over) and its fecundity in terms of the number of offspring it produces.) Suppose the original gene has fitness w=1 and the new mutation has fitness w=1+s, where s is the selection advantage.
The selection advantage is a measure of how much more likely it is that that particular variety will propagate itself in future generations when compared with the standard type. So if, on average, the new mutated variety produces 101 fertile adult descendents while the same number of the standard organism produces 100, then s=0.01.
When this selection advantage is included in the calculation, the number of generations T it will take for a mutation to increase its frequency in the population from an initial value of f to a final value of F is given by the formula T=(1/s)ln[F(1-f)/f(1-F)], where 'ln' stands for the natural logarithm. (Molecular Evolution, Wen-Hsiung Li, 1997, p. 39)
So if we start with a trait that is present in just 0.1% of the population (i.e., f=0.001), and if this has a small selection advantage of size s=0.01, this variety will grow to 99.9% (F=0.999) of the population in just under 1,400 generations, which is a very short time on the geological scale.
But in a population of one million, an initial fraction of f=0.001 means that we are starting with about 1000 organisms having the favorable mutation. In reality, we are likely to begin with just one mutation in one organism. How does that affect the calculation?
That will be discussed in the next post in the series.
POST SCRIPT: Lil George and evolution
This clip from a cartoon show I had never heard of (probably because it is on cable) is pretty funny.
July 20, 2007
Evolution-12: Population genetics and the Hardy-Weinberg law
(Please see here for previous posts in this series.)
In the previous post, I discussed the puzzle posed by a naïve understanding of Mendelian genetics, which was that one might expect that organisms that displayed recessive gene traits would slowly disappear in a population while those with dominant gene traits would grow in number. But if that were true that would prevent new mutations from gaining a foothold in the population and growing in number, if it happened to be a recessive trait.
The crucial work that formed the breakthrough that revived the theory of natural selection was done in 1908 by G. H. Hardy (a Cambridge University mathematician and author of a fascinating book A Mathematician's Apology) and Wilhelm Weinberg (a German physician), working independently. What is nice is that the result is quite simple to derive, and surprising.
The main result is that whatever the distribution of gene pairs AA, Aa, and aa you start with in a population, after just one generation the number of people with those distributions will reach an equilibrium value that will never subsequently change. In other words, the numbers of the different types of genes in a population are stable. So traits, once they appear, do not disappear simply because of the accidents of random mating. This counters the 'blending inheritance' objections to Darwin's theory.
The proof of this result assumes that certain conditions apply so that only mating effects are at play: that the total population is large enough (effectively infinite for statistical purposes) to avoid the phenomenon of genetic drift, whereby the ratio of a particular gene varies purely due to statistical fluctuations (i.e., say the population with a particular gene happens to breed disproportionately, thus causing that gene's frequency to change), is diploid, that the population reproduces sexually and that mating within the population is totally random, that natural selection is not working to change the distributions of the genotypes, and that other factors like genetic mutations and migrations in or out of the population are not occurring (i.e., no gene flow).
Here's the result. Suppose that you start with a population in which AA types occur with probability p, Aa types occur with probability 2q (where the 2 is inserted just to make the arithmetic a little simpler), and aa types account occur with probability r. Since the total population must add to 100%, this means that the total probabilities p+2q+r=1.
Under the conditions given above, the Hardy-Weinberg result says that: (1) after just one generation, the AA types occur with probability P where P=(p+q)2, Aa with probability 2Q where Q=(p+q)(q+r), and aa with probability R where R=(q+r)2; and (2) these new probabilities will remain unchanged with each succeeding generation.
As an example, if we started with the population of AA being 50% (p=0.5), Aa being 40% (2q=0.4), and aa being 10% (r=0.1), then after just one generation, the Hardy-Weinberg result predicts that the proportions will be P=0.49 or 49% for AA, 2Q=0.42 or 42% for Aa, and R=0.09 or 9% for aa, and remain fixed at these values forever afterwards.
The proof of this result is quite simple and elegant and here it is:
If there is random mating, then the probability of any particular mating combination is just the product of their individual probabilities.
The probability of an AA mating with another AA is p2. The offspring will get just one gene from each parent, and in this case the result will always be AA.
The probability of an AA mating with an Aa is 4pq (the extra factor of 2 comes from the fact that this mating combination can occur two ways, that either the father could be AA and the mother Aa, or the father could be Aa and the mother AA) and there is a 50% chance that the offspring will be an AA and 50% chance of being an Aa.
Similarly, the probability of an AA mating with an aa is 2pr. The offspring will get just one gene from each parent, and in this case the result will always be Aa.
The probability of an Aa mating with an Aa is 4q2 and there is a 25% chance that the offspring will be AA, 50% chance of being an Aa, and 25% of being an aa.
The probability of an Aa mating with an aa is 4qr and there is a 50% chance that the offspring will be Aa and 50% chance of being an aa.
The probability of an aa mating with another aa is r2. The offspring will get just one gene from each parent, and in this case the result will always be aa.
When you add all the probabilities for each type of offspring together, the probabilities of getting AA and Aa and aa are just the expressions for P, 2Q, and R given above.
What Hardy and Weinberg noticed was that if, by some chance, the starting values p, q, and r were such that they satisfied the equation q2=pr, then after one generation, P=p, Q=q, and R=r. In other words, if the starting values satisfied that particular relationship, the probabilities are unchanged from one generation to the next.
Of course, the values of p, q, and r we actually start with for a random population can have any value, as long as p+2q+r=1. But after the first generation of mixing, the values P, Q, and R actually do satisfy the relationship Q2=PR, irrespective of the starting values of p, q, and r.
Since the values of P, Q, R that are obtained after one generation become the starting values to calculate the distributions for the subsequent generation, and since P, Q, R satisfy the required relationship Q2=PR, these values will remain the same for every succeeding generation after the first.
What I found particularly surprising is that usually equilibrium conditions tend to be approached gradually and even asymptotically. Here, whatever the starting point, you get equilibrium after just one iteration.
The stability of population distributions under conditions of random mating is an important result. It implies that gene distributions do not change due to mating but only under some kind of pressure to do so..
From the year 1908 onwards, mathematical biologists proceeded to make rapid advances in the embryonic field now known as population genetics. The names of R. A. Fisher, Sewall Wright, and J. B. S. Haldane are the ones associated with the birth of this field and by the 1930s or so, their work had put Darwinian natural selection and Mendelian genetics on a firm scientific and mathematical footing (William B. Provine, The Origins of Theoretical Population Genetics, 2001).
In the next post in the series, I will look at how natural selection causes the population distributions to shift.
POST SCRIPT: Iraq war lies
Watch this video to see the brazenness with which the country was lied into war.
July 18, 2007
Evolution-11: The rise of population genetics and the neo-Darwinian synthesis
(Please see here for previous posts in this series.)
The joining of Darwin's theory of natural selection with the Mendelian theory of genetics is one of the great triumphs of biology, now called somewhat grandly the 'neo-Darwinian synthesis'. It forms the basis of all modern biology, and was strengthened by the discovery of DNA as the structure of genetic information and which explained how Mendelian genetics worked on a microscopic scale. The modern ability to map out the entire genome of humans and other species has produced overwhelming evidence in support of Darwin's theory of how organisms evolve and branch out into different forms. The rough tree of life that Darwin sketched out in his book based on the anatomy of biological species has now been made more precise and detailed by the mapping of the DNA of species, showing ever more clearly how species are related to one another and when they separated from a common ancestor.
Mendel showed that genes were discrete objects that retained their identity as they were handed down from generation to generation and that thus any changes in genes, however small, did not get blended away in a regression towards the mean. So you would have thought that the rediscovery and rapid popularization of Mendel's ideas in 1900 would have signaled a resurgence of Darwin's idea that natural selection worked on very small, almost continuous changes, and the defeat of those who argued that one needed discontinuous changes for evolution to occur.
Ironically, the exact opposite happened. Because Mendelian genetics was a discrete mechanism with the genetic information seeming to occur in small lumps that remained intact, it superficially seemed to support the discontinuous model of natural selection, and the proponents of discontinuous changes were able to co-opt Mendel's theory to their cause. By around 1908 or so, it seemed like Darwin's own favored model of small continuous changes leading to large changes was in almost total retreat, actually doomed by the arrival of Mendel. While there was a sprinkling of mathematicians like Udny Yule (what a wonderful name!) who argued that Mendel's theory was compatible with Darwin's model of continuous evolution, their voices were lost in the volume of controversy generated by the competing biological schools. (The Origins of Theoretical Population Genetics, William B. Provine, 2001, p. 85)
Part of the problem was that scientists were still struggling to understand the workings of both Darwin's theory and Mendelian genetics and many misunderstanding of each were then prevalent. For example, one thing that was puzzling about genetics (and puzzled me for a long time too) was this whole business of dominant and recessive genes and how it affected population distributions.
It was Mendel's work that argued for the existence of these two types of characteristics, the actual mechanism of which became better understood with the discovery on DNA and increased understanding of the way that chromosomal information was handed down from parent to child.
Simply put, each person has pairs of genes, one from each parent on the respective inherited chromosome. To be concrete, we can look at the gene for eye color. Each gene may be of a dominant type (denoted by A, for say brown eyes) or a recessive type (denoted by a, for say blue eyes). So a person would have one of the pairs AA, Aa, or aa on the pair of chromosomes that contain the genes for eye color. Since A is the dominant one, it always wins, and so those people with either AA or Aa will have the characteristic A (brown eyes) manifest itself in their features, and only the person who has aa will display the characteristic a (blue eyes). Each parent will also have AA, Aa, or aa, and will randomly pass on just one of the pair of genes it possesses to the child.
It seems intuitive that if a population starts out with some distribution of AA, Aa, and aa types, and there is random mating in the population, then the number of people displaying the dominant characteristic A will steadily increase in the population, while the manifestation of the recessive characteristic a will decrease and perhaps eventually even disappear altogether, since only someone possessing the relatively unlikely combination aa will manifest it. Since regressive characteristics did not seem to be disappearing in real life populations, and in fact seem quite stable in their numbers, early geneticists had some doubts about whether they were interpreting Mendel's model correctly.
But starting around 1908, things started to change as better experiments were done and more mathematical versions of the two theories started being used. Mendelian and Darwinian theories started to get quantified and people began to realize that Darwin's version of natural selection with continuous changes was in fact compatible with Mendel's theory. By 1918, the reversal was complete and Darwin was ascendant and has remained so ever since. This was largely due to the rise of the field now known as population genetics, whose practitioners developed mathematical models that looked at the consequences of Mendelian genetics in natural selection.
What started the shift was the result now known as the Hardy-Weinberg law, which will be discussed in the next posting in this series.
POST SCRIPT: American beliefs about evolution
Gallup has done one of its periodic surveys about Americans views on evolution
These results show that:
- 24% of Americans believe that both the theory of evolution and the theory of creationism are probably or definitely true.
- 41% believe that creationism is true, and that evolution is false.
- 28% believe that evolution is true, but that creationism is false.
- 3% either believe that both are false or have no opinion about at least one of the theories.
That first group of 24% is definitely confused, since there is no way that evolution could have occurred in the 10,000 years or less allowed by creationism. The survey creators speculate that these were people who believed that god influenced evolution and somehow wanted to incorporate that view and responded in contradictory ways depending on which question was asked.
Also:
- The reasons for rejecting evolution were mostly religious.
- The more regularly you attended church, the less likely you were to believe in evolution.
- Republicans were less likely to believe evolution (30%) than Democrats (57%).
Summary:
It is apparent that many Americans simply do not like the idea that humans evolved from lower forms of life. This appears to be substantially based on a belief in the story of creation as outlined in the Bible -- that God created humans in a process that, taking the Bible literally, occurred about 10,000 years ago.
July 16, 2007
Evolution-10: The debate over natural selection in Darwin's own time
(Please see here for previous posts in this series.)
In Darwin's own time, there was a three-way dispute concerning the theory of evolution. Strange as it may sound these days in the US where so many question whether evolution even occurs at all, the idea that evolution had occurred and new species were being created and old ones dying out was not such a major problem in the mid-to-late 19th century. Elite opinion of that time had been exposed to that idea and had accepted it even before Darwin because of all the fossil records that were being discovered all the time. Even Darwin's own grandfather Erasmus Darwin, a freethinker, had around 1795 published a book Zoonomia that had floated the idea that species had evolved, but he used a Lamarckian model. What religious people mostly shied away from was the idea that human beings were also part of the evolutionary process and shared common ancestors with other species, a reluctance that still persists.
In Darwin's time what the dispute mainly centered on was the mechanism of evolution and how it operated.
Apart from Biblical literalists and believers in special creation, there were those of a religious bent who argued that god had to intervene somehow at least occasionally to create new species (especially humans) and this view persists down to this day among people who seek a tangible role for religion. At the very least, believers in an immortal soul needed a god to insert it into humans at some point in that person's development.
But the more interesting dispute was among those scientists who were not invoking religious ideas. Their dispute centered on the scale of the mutations necessary for natural selection to work.
Due to all the buffeting that Darwin's theory had received from those who argued that the age of the Earth was too short for evolution to have occurred and that mutations would get blended away, in the later editions of his book, Darwin himself started qualifying some of the more ambitious claims that he had forthrightly stated in the 1859 edition. As a result, his later editions lost some of the directness and clarity of his first edition, and scholars now recommend reading the first edition as being the best. I personally found it a fascinating book, remarkably accessible to the layperson.
For example, his first edition contained a rough estimate by him, based on geological phenomena he observed in England, that the Earth was about 300 million years old, which was in his view sufficient time for evolution to have occurred. He arrived at this by assuming that the Weald, a valley in the south of England, had been created by erosion that had always occurred at the same rate it was occurring now. He removed this claim in later editions, presumably due to unease over physicist William Thomson's calculations that the Earth was only 30 million years old. As it turns out, Darwin had no need to be worried since the current age of the Earth is calculated to be more than ten times his own estimate.
But while willing to give ground on some peripheral issues, Darwin steadfastly stuck until his death (in 1882) to one central idea, and that was that natural selection was able to act on even extremely small advantages in the fitness of some organisms, causing them to grow in the population, and that it was the cumulative effect of these minute changes that led to new species.
Contrasted with Darwin's continuous model of change were those scientists (including even Darwin's staunch defender and ally Thomas Huxley) who argued that natural selection could not really work with very tiny changes because they would get washed away because of blending inheritance. These people argued in favor of a discontinuous model which only valued those mutations that produced significant changes in the organism that represented a new and stable phenotype whose qualities were robust enough that they would not get blended away by breeding.
To better understand the difference, compare a sphere and (say) a twenty-sided die, which is almost a sphere, both resting on a table. The sphere can be shifted by any small amount and would stay in that new position. The die on the other hand, if tilted slightly and released, would revert to its original position unless the tilt were sufficient to topple it to rest on the adjacent flat face. Then it would be stable in the new position and would resist any further shift, even back to its original state. One faction led by Darwin was arguing that natural selection could act on the continuous changes represented by the sphere while others said that only the changes beyond a certain critical amount and represented by the die were stable enough for selection to work on.
It must be emphasized that both sides supported the mechanism of natural selection for driving evolution. They simply disagreed on its ability to act on very small changes. While we may think that this was a small issue to disagree on, in actual fact the debate was fierce and very acrimonious, with both sides trying to marshal evidence for their side and picking holes in the evidence of their opponents. William B. Provine in his book The Origins of Theoretical Population Genetics (2001) gives a fascinating account of this controversy, the personalities involved, and the heated nature of the exchanges, which grew increasingly bitter by the time 1900 rolled around.
The rediscovery of Mendel's work on genetics (he was a monk who lived from 1822-1884 and published his major work in 1865, but it remained obscure until it was rediscovered in 1900) provided new fuel to the controversy. Scientists quickly recognized the significance and importance of Mendel's work. While Mendel's model was accepted as having finally produced the correct theory of how inheritance works, this did not immediately resolve the dispute because there was still disagreement about what Mendel's theory actually implied and how it fitted into Darwin's theory.
Next in this series: The synthesis of Mendelian genetics and natural selection.
POST SCRIPT: Why a secular public sphere works best
As I understand it, both US houses of Congress open with a ceremonial prayer which hardly any members bother to attend. Although each house has an official chaplain, it has become the practice to make this event more inclusive and ecumenical by having people of diverse faiths give the prayer.
For the first time last week, a Hindu was invited but his prayers were disrupted by hecklers from a Christian group, who saw this as an affront to their own god. See the video here.
Steve Benen provides some background on what happened.
Interestingly, some Christians see the saying of Hindu prayers in Congress as a sign that the end of the world is almost upon us, and their anger about this act of sacrilege is mixed with eager anticipation at seeing Jesus any day now.
One doesn't know whether to laugh or cry. I think I'll laugh.
July 13, 2007
Evolution-9: Early challenges to Darwin's theory
(Please see here for previous posts in this series.)
In an earlier post in this series, I listed the three stages involved in natural selection, each of which seemed to have seemingly small probabilities. In the previous post, I showed how because of the large numbers of organisms and long time scales involved, the first item got converted into a very high probability event.
The next item in the list, the issue of how a mutation with a small advantage in the properties of an organism can end up with that property dominating the species, was both Darwin's greatest challenge and his greatest triumph.
The triumph came from a crucial insight that Darwin had concerning the importance of varieties within species. Recall that Platonic ideas were dominant at that time, and that laid the emphasis on the idealized forms of things. So for example while a real triangle drawn on paper would contain imperfections, these were considered incidental, the drawing being a mere approximation to the idealized triangle that one could envision in some abstract space.
In Darwin's time, the biological equivalent of this thinking was that while it was plain to see that (say) chickens were different from one another in small ways, these differences were not considered important. They were considered mere approximations to an idealized chicken that represented the essence of chickenhood (so to speak), and it was the latter that was important.
But Darwin realized that the variety that he saw in species, rather than distracting from an understanding of the ideal, was important in its own right. In fact, he recognized that the diversity within a species was so vast that it was often hard to say what was a variety within a species and what was a different species altogether. As he wrote, "[I]t will be seen that I look at the term species, as one arbitrarily given for the sake of convenience to a set of individuals closely resembling each other, and that it does not essentially differ from the term variety, which is given to less distinct and more fluctuating forms" (Charles Darwin, On the Origin of Species (1859) p. 52). It was this wide variety that allowed some animals to survive better than others and was the driver of natural selection. The existence of variety lay at the heart of his theory.
(The problem with all classification schemes is that it is often impossible to specify both necessary and sufficient conditions to make unerring judgments as to which category some organism belongs. The fact that there is often no sharp line that can be drawn between varieties within species and differences between species should put to rest the artificial distinction made by intelligent design creationists who say they have no trouble with what they call 'microevolution' (what they define as change within a species) but cannot accept 'macroevolution' (the creation of new species). This is a distinction without much merit.)
But Darwin faced a serious problem. Even though people might accept his idea that one variety of an species might be more suited to survive than another, the lack of a real understanding at that time of the mechanism of inheritance worked against him. It was believed that sexual reproduction resulted in features being mixed (called 'blending inheritance'), with the child of parents being intermediate in terms of properties such as height, skin color, etc. Hence even if an occasional particular mutation had better chances for survival, it was believed that its advantageous properties would soon get diluted and disappear by mating with those animals that did not have this same property. This is the well-known phenomenon of 'regression towards the mean,' first articulated by the polymath Francis Galton, a cousin of Darwin.
In artificial breeding one could avoid this blending outcome by simply restricting the breeding of animals to those organisms with the desired properties and thus preserve and enhance desired changes. But in the wild, organisms would mate more indiscriminately and this raised the question of how advantageous mutations could be preserved.
Around the same time that Darwin's theory was already reeling from estimates of a short age of the Earth from William Thomson (aka Lord Kelvin), Fleeming Jenkins wrote a long article in 1867 criticizing Darwin's theory on precisely the blending inheritance issue. In addition, the co-discoverer of natural selection Alfred Wallace (who had initially been seen as an even more zealous advocate of natural selection than Darwin) had become interested in spiritualism and in 1869 unexpectedly published a paper in which he asserted that natural selection, although it could explain everything else, couldn't account for the human brain, and he even went so far as to espouse an early version of intelligent design creationism saying that while the living world is governed by laws, "an Overruling Intelligence has watched over the action of those laws, so directing variations and so determining their accumulation" in order to produce the wonderful thing that is the human brain (David Quammen, The Reluctant Mr. Darwin (2006), p. 215). (The idea that the workings of the human brain, and that the mind and consciousness lie outside the realm of natural selection and the laws of biology, is something that persists down to this day, a topic I will examine in the future when I look at what we are now learning about the nature of consciousness.)
There was nothing much that Darwin could do about Thomson's criticism but hope that someone else would prove the physicist wrong, which did happen with the discovery of radioactivity in the first decade of the 1900s. There was also nothing that Darwin could do about Wallace going against one of the fundamental precepts of natural selection, although Darwin felt that the whole idea of natural selection was meaningless if an outside 'intelligence' could drive organisms towards a pre-ordained result. Darwin simply wrote "No!!!" in the margins of Wallace's paper.
As for Jenkins's criticisms, Darwin had not been unaware that this would be a problem for his theory and had tried to anticipate it by suggesting that successful mutations would take hold in only those cases where the mutations appeared concurrently in numerous individuals and that these would then breed with each other, allowing that variety to grow and take root in the population. (Quammen p. 212)
Darwin's defense was not very persuasive but it was all he had. Although the real defense against Jenkins's critique was already at hand in the form of Mendel's theory of genetics (which showed that genes are discrete entities that remain intact on breeding and do not get blended away), Mendel's work was not widely known at that time and Darwin's theory had to wait until its rediscovery in 1900 to fully overcome objections of the type put forward by Jenkins.
Darwin the man and the scientist are fascinating character studies. He was painstakingly thorough in his work and conscientious about the need to amass evidence to buttress the main argument he was making. But once he felt convinced by the evidence that the theory of natural selection was sound, he was determined. While he was willing to give ground on the periphery of his theory, he was firm in his commitment to its core ideas, and one of these was that his theory would make no sense if you allowed an outside agency (an 'intelligence' or whatever name you gave to a god-like power) to intervene in the process at any time in any way. He was a methodological naturalist, a necessary condition for any good scientist.
But it is a very thin line that separates methodological naturalism from philosophical naturalism (or atheism) and this, at heart, which is why Darwin's theory is so subversive to beliefs about god.
Next in this series: The debate over natural selection in Darwin's own time
POST SCRIPT: Science? Evidence? Who cares?
In congressional testimony this week, outgoing US Surgeon-General Richard Carmona spoke of how in the Bush administration, ideology trumped science every time, with constant political interference muzzling him on scientific issues like embryonic stem cell research. He said, "Anything that doesn't fit into the political appointees' ideological, theological or political agenda is ignored, m