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.

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, marginalized or simply buried.”

His testimony reminded me of this Tom Tomorrow cartoon from February 27, 2007.

Meanwhile, Secretary of Homeland Security Michael Chertoff’s extraordinary statement, also this week, that he felt ‘in his gut’ that a terrorist attack might occur in the US this summer reminded me of astronomer Carl Sagan’s reply when an interviewer pressed him for his ‘gut feeling’ as to whether there was life elsewhere in the universe. Sagan replied, “But I try not to think with my gut. Really, it’s okay to reserve judgment until the evidence is in.” (Richard Dawkins, The God Delusion, p. 47.)

Chertoff would be well-advised to follow Sagan’s advice.

Evolution-8: The sufficiency of the mutation rate

(Please see here for previous posts in this series.)

One of the challenges faced by Darwin was whether the rate at which mutations creating new favorable varieties would occur was sufficiently rapid for his purposes. Since during his time the laws of inheritance were not known and neither was the mathematics involved, advocates of natural selection had to assume that things would work out eventually.

In his excellent book The Making of the Fittest (2006), Sean B. Carroll demystifies the various numbers and calculations involved in natural selection using our current knowledge.

Recall from the previous post in this series that DNA is made up of a string of bases A, C, T, and G. New genetic information is created when there is a change in the DNA and the most basic (but not the only) way that this can occur is by mutations acting at the level of a single base site in the DNA, changing one of the bases A, C, T, and G to a different one.

This long string of bases that constitute DNA is split into chromosomes. As one travels down the length of a chromosome, one encounters strings of bases that are called genes and these contain the code for manufacturing the vital proteins. Proteins are made up of strings of amino acids and the genes specify the arrangement of amino acids that are to be lined up, one after another, in each protein. The code for specifying which amino acid is to be added on is made up of three consecutive base sites, each triplet being either a code for one of the twenty amino acids or a code to stop the manufacturing process and release what has been created so far. Think of the whole process as a tape recorder with the DNA string being the tape being read and the tape recorder as a machine that produces the amino acids depending on what it reads in sequence on the tape.

There are 64 possible combinations of three sites made up of four distinct bases (64=4x4x4). But since there are only twenty amino acids, this allows for some redundancy to be built into the system. For example, the amino acid serine is coded for by any of the six triplets TCT, TCC, TCA, TCG, AGT, and AGC, while the amino acid cysteine is coded for by just two triplets TGT and TGC. The three triplets TAA, TAG, and TAA represent the ‘stop’ code that says that the process of adding on amino acids is to be halted and the completed molecule released into the body.

Because of this redundancy, some random single site mutations (say from TCT to TCG) will have no effect on the coding of the amino acid or the resulting protein. This is a good thing since it reduces the chances of the production of ‘good’ proteins being destroyed by a random mutation. Alternatively, a single base switch from TGT (cysteine) to TGA (stop) will result in the protein manufacture being prematurely halted and could be calamitous for the organism.

But if there is a random mutation at a single site that changes AGT to TGT, then we see that a cysteine amino acid will be added on instead of a serine in the creation of the protein. It turns out that which of these two codes for amino acids occupies the sites numbers 268-270 of the gene to produce an opsin protein determines whether the organism’s eye is sensitive to violet light or to ultraviolet (UV) light. Certain birds (ducks and ostriches) are sensitive to violet while others (zebra finch, herring gull, budgerigar) are sensitive to UV light. There are four different orders of birds that contain both violet or UV sensitive species, suggesting that this switch between base A and base T in location 268 of this opsin gene has occurred on at least four different occasions in evolutionary history. Given that there are over one billion base sites in the genome of birds, is this switch in one particular site likely to occur even once, let alone on four different occasions?

The instinctive conclusion is of course ‘very unlikely’, but Carroll (p. 156-158) says we need to get beyond that initial guess and actually crunch the numbers to see what is involved, taking into account the size of populations and the long time scales involved.

The per site rate of mutation averages between 1 per 500,000,000 bases in DNA in most animals – from fish to humans. This means that the exact A in position in position 268 in one copy of the bird SWS [short wavelength sensitive] opsin gene will be mutated, on average, about once every 500 million offspring. It has two copies of the gene, so this cuts the average to 1 in 250,000,000 chicks. However, there are three possible kinds of mutations at this site: A to T, A to C, and A to G. Based on the genetic code, only the A to T mutation will create a UV-shifting cysteine. If the probability of each mutation is similar (they aren’t but we can ignore the small difference), then one out of three mutations at this position will cause the switch. One A to T mutation will occur in roughly 750,000,000 birds (that’s 750 million).

Seems like a long shot?

Not really. It is important to factor in the number of offspring produced per year. According to long-term population surveys, many species consist of 1 million to more than 20 million individuals. With annual reproduction, a plentiful species like herring gull will produce at least 1 million offspring in a year (probably a very conservative number). Divide this into the rate of one mutation per 750 million birds; the result is that the serine-to-cysteine switch will arise once every 750 years. This may seem like a long time in human terms but we need to think on a much longer timescale. In 15,000 years, a short span, the mutation will have occurred 20 separate times in this species alone.

The four orders that these birds belong to are ancient – their ancestors have had tens of millions of years to evolve UV or violet vision. At the rate calculated in gulls, the A to T mutation will occur more than 1200 times in 1 million years in just this one species. Getting the idea?

Steve Jones (Almost Like a Whale, p. 149) estimates that among domestic cats there occur around 200,000 genetic changes each year in London alone. He adds, “Worldwide, any mutation is almost a certainty. If it is useful it will at once be picked up by natural selection.” He also discusses (p. 176) how a mutation in a single base site (similar to the serine to cysteine switch) enables the bar-headed goose better able to bind oxygen to haemoglobin and thus enables it to migrate at an altitude of over five miles (i.e., the height of Mount Everest), a height where humans would collapse and die within a few hours.

So small probability events cannot be considered in isolation. When factored in with large populations and long time scales, they not only become likely, they become almost inevitable.

But changes in single sites are not the only way that changes in DNA occur. They can also occur when entire chunks of the DNA molecule are changed during reproduction in the formation of the sex cells (meiosis) because of copying errors, duplication, recombination, insertional mutations, transposition, and translocation. (See here for fuller descriptions for some of these mutations.)

For example, humans have three kinds of opsin genes that code for three different proteins that are important for color vision. LWS [long wavelength sensitive] opsin enables us to see in the long-wave or red portion of the spectrum of light, MWS enables us to see in the medium-wave or green portion of the spectrum, and the already mentioned SWS type works for the short wave or blue region. It is the presence of all these three opsin proteins that gives us the full color spectrum vision humans enjoy. We share this ability with colobus monkeys, chimpanzees, and other primates such as all apes and all African and Asian monkeys.

But most other mammals have only dichromatic vision, having only two (SWS and MWS) opsin genes and consequently seeing only blue and yellow. They cannot distinguish between red and green. How humans and other primates achieved tricolor vision is by one of the dichromatic genes (the entire gene, which can consist of hundreds of thousands of bases) being erroneously duplicated during the copying process, resulting in three genes being created, and then one of the duplicate genes later undergoing changes in its bases similar to the way the violet-to-UV switching occurred, resulting in the creation of red-sensitivity in our eyes. (Carroll, p. 97)

But although this calculation shows that favorable mutations are by no means as rare as one might naively think, and are in fact quite likely when the large size of populations and long times are taken into account, how likely is it that a mutation that occurs in a single organism will succeed in ending up dominating the species? After all, even a few hundred mutations in a population of millions may not seem like a significant amount.

That question will be examined in the next posting in this series.

POST SCRIPT: Michael Moore blasts CNN and Wolf Blitzer

Michael Moore goes on CNN and blasts Wolf Blitzer and their resident medical apologist for the health industry Dr. Sanjay Gupta for effectively acting as shills for the medical industry, not to mention their abandonment of any real journalism prior to the invasion of Iraq. This is a must-see video.

Moore followed up with a detailed analysis of Gupta’s shallow reporting.

Evolution-7: Genes, chromosomes, and DNA

(Please see here for previous posts in this series.)

In order to understand how inheritance works and the mathematics involved, it may be helpful to have a quick summary of some basic facts about genetics (a little simplified), using the human genome for concreteness.

All the genetic information in our bodies is found in the DNA, whose famous double helix structure was discovered in 1953. Thanks to the Human Genome Project, we now have a complete map of the DNA of humans, called the human genome, and know that it consists of a sequence of 3.1647 billion sites arranged in a row, each site containing one of four complex molecules (called bases) labeled A, C, T and G. It is this long arrangement of the four bases that define each of us genetically. Almost 99.9% of the arrangement of these bases is identical in all humans, and about 98% is identical between chimpanzees and us.
[Read more…]

Evolution-6: The probabilities of natural selection

(Please go to ‘Categories’ and choose ‘Science’ to see the previous posts in this series.)

There are three mathematical ideas that one needs to come to terms with in order to get the full flavor of how natural selection works.

  1. One is the rate at which favorable mutations occur in organisms. These do occur by chance and the question is whether the frequency of such occurrences is sufficient to explain evolution.
  2. The second is the rate at which favorable mutations become more numerous in the population. It is not enough to produce a single favorable organism. The population of varieties with advantageous properties has to eventually grow to sufficiently high numbers that it dominates the population and can form the basis for yet further mutations.
  3. The third is whether the rate at which repeated small and favorable mutations build on each other is sufficient to produce major changes in complex systems (the eye, ear, and other organs for example) and even entirely new species.

It is only the very first item that works by pure chance. The other two are highly directed processes, not because there is an external intelligence at work but because they are subject to the pressures of natural selection, which considerably reduces the contributions of chance to the outcome.

Now it is undoubtedly true that the chance of producing a favorable mutation is small. Most mutations are deleterious to the organism. The chance of a favorable mutation, once produced, taking hold and becoming widespread in a species population is also small. And the chance of favorable mutations building on each other to produce complex organisms is also small. So if we leave things at this high level of generality, skeptics of natural selection can (and do) argue that the complexity of life as we know it is too unlikely to have occurred and that therefore some intelligence must be behind it. To get beyond that superficial argument and appreciate the power of the theory, one has to actually do the calculations.

Darwin himself was well aware of these difficulties but also had the intuitive sense that even events with very small individual probabilities have a good chance of occurring if you wait long enough and have large enough populations. Although he could not quantify it, Darwin knew that he needed a very long time for his theory to work, which is why he viewed with such interest research on the age of the Earth. All three processes listed above must be able to fit within the timeline allowed by the age of the Earth, which is why research in geology and physics have had important implications for the theory of evolution. But since the time scales involved are well beyond our own lifetimes, people have a hard time comprehending the workings of evolution.

As an example of this, take the lottery. The chance of buying one ticket and selecting six numbers from 1 to 49 that match the winning numbers is incredibly small (to be precise 1 in 13,983,816). But you can greatly improve your chances if you buy many tickets and plan to play week after week. The greater the number of tickets you buy, the shorter the time in which you can expect to hit the jackpot. Of course, even if you live long enough and invest enough, the total amount you spend on your tickets will almost always be much more than the amount you win but that is because the organizers of the lottery have pegged the prize money that way so that they can make a profit.

Only the first of the three items listed above for natural selection (the occurrence of favorable mutations) works the same way as the lottery, except that nature hasn’t rigged the system against you. Nature just doesn’t care. And this means that if there are large enough populations and long enough times available, natural selection will repeatedly hit the jackpot and produce the wonderful complexity we see.

One of the fundamental features of the theory is that mutations, or changes in organisms, occur at random. Most of these mutations are either fatal or sufficiently harmful to the organism so that the mutated variety dies away. After all, if you make random changes in anything (say the wiring of your computer or even your toaster) there is a much greater chance of making it worse than making it better. But on rare occasions, a beneficial mutation will occur that results in that new variety flourishing because it is better adapted to succeed in its current environment.

We now know something that Darwin did not, that these mutations occur at the level of the genes. Although the work that led to the discovery of the genetic laws of inheritance was done by Gregor Mendel at roughly the same time as Darwin and provided the material basis for understanding inheritance, Darwin was not aware of that cloistered monk’s research, although Mendel was aware of Darwin’s work. Mendel published his seminal paper in 1865 (Darwin’s On the Origins of Species appeared in 1859) but it went largely unnoticed until 1900 when several biologists who had been working on the problem of inheritance, independently came across Mendel’s work.

The synthesis of Mendel’s work on genetics with Darwin’s theory of natural selection is one of the great advances in modern science and the next post in this series will discuss that relationship.

Next in the series: The effect of Mendel’s work on Darwin’s theory

POST SCRIPT: Onion parody on evolution

The nice thing about this parody is that it captures very well the central problem with the arguments of intelligent design creationists and other religious believers who want to preserve a role for god by carving out a little niche for god to intervene in evolution.

Evolution-5: How probability intuition can lead us astray

(See part 1, part 2, part 3, and part 4.)

One of life’s ironies is that the difficulty in understanding the mathematics of Darwin’s theory of natural selection may actually be caused by natural selection itself.

As we saw earlier, natural selection does not try for maximum benefit but instead works on a ‘just good enough for now’ principle. Steven Pinker in his book How the Mind Works (1997) is a cognitive scientist who believes that natural selection has been the driver for most aspects of our bodies and our behavior, and that the brain, being just another organ, has evolved to do what it does to effectively meet the challenges it faced at various times in our somewhat distant past. Pinker points out that humans, when compared with other animals, have unusually large brains compared to body size but that this rapid expansion in brain size occurred more than 100,000 years (or about 5,000 generations) ago (Pinker, p. 198) and then leveled off after that. This means that the structure of our present brains has been largely determined by a time when humans were hunter-gatherers and foragers.

This means that although modern life is undoubtedly very complex and require us to meet a vast array of challenges, our brains are best suited to meet the challenges of our ancient forebears, not those of driving on a highway or learning to operate a computer or solving sudoku puzzles. Thus we are very good at identifying faces and shapes, seeing things in depth, reacting to predatory dangers, and acting on instincts such as ducking when an object is thrown at our heads, etc, because our brains have probably evolved modules that handle such things efficiently. But we are not so good at solving quadratic equations. The kind of mathematics that helped our hunter-gatherer ancestors survive did not require much beyond an elementary sense of number. As for probability, simple concepts largely based on induction and extrapolating from past experiences, are sufficient.

But as culture developed in the last 10,000 years with the advent of more settled agrarian societies and written language, we now find ourselves having to struggle a bit to master the concepts needed to face today’s challenges. They do not come ‘naturally’ to us, by which I mean that there are no brain modules that have evolved to enable us to quickly grasp and understand and respond to them.

This is especially true of probability and statistics. There was no need for our ancestors to develop modules to make Bayes’ Theorem or the Central Limit Theorem easily understandable, which explains why our intuitions are so often led astray. For example, many people fall prey and lose money because of the ‘gambler’s fallacy’ because they put their faith in a spurious ‘law of averages’, believing that the more repeated occurrences you have of the same thing (say getting heads on a coin toss or coming up black in a roulette wheel), the more likely a different outcome becomes on the next play. Similarly people who play the lottery numbers tend to avoid numbers that have won recently.

While mathematical sophisticates may look down on such naïvete , Pinker points out that such expectations are perfectly consistent with the kinds of probability experiences our hunter-gatherer ancestors experienced and which we still experience in most everyday life. After several days of rain, a dry day is more likely. After seeing several elephants appear in a line, it was more likely not to see one. In fact, event repetitions that are finite and terminate and change are the norm in nature, not the exception. Hence believing such things and acting upon such beliefs has some survival value that makes it plausible that our brains evolved modules that encoded those expectations, making us instinctively sympathetic towards believing things like the gambler’s fallacy.

The reason that so many are fooled by the gambler’s fallacy is that the creators of the gambling devices go to great lengths to make each event independent of the previous ones, thus violating our natural expectations. We thus have to consciously learn to sometimes go against our ‘natural’ instincts and this takes effort and is not easy.

Even though I consider myself fairly adept at mathematical manipulations, I am often humbled by how easily my intuition is led astray when confronted with a novel statistics problem. Take for example this case, which may be familiar to people who have taken an elementary statistics course, but fooled me when I first encountered it.

Suppose the incidence of some disease is fairly rare in a population, say about one in a thousand. You are told that there is a test for this disease that is pretty good in that it that has a ‘false positive’ rate of only 5%, meaning that if a randomly selected group is tested, only 5% of the people who do not have the disease will have test results that come out positive. Also you are told that the false negative rate is zero, meaning that if someone does have the disease, the test will definitely come out positive.

Suppose you are among those who are part of this random testing. To your dismay, the result is positive. What do you think are your chances of actually having the disease?

Most people would think that it is very high. They may put it as high as 95%, thinking that if there is a 5% false positive rate and 0% false negative rate, that means that the likelihood of someone testing positive having the disease is 95%. This sounds eminently reasonable.

But the actual chance of you having the disease despite testing positive is just 1 in 51 or less than 2%! How come? This becomes easier to understand if we shift from talking in terms of probabilities (which I have pointed out are not so intuitive) to talking about numbers. Suppose you are one of 1000 people being randomly tested. (Any size will do. I have chosen 1000 because it is a nice round number.) Then an incidence of 1 in 1000 means that we expect only one person to actually have the disease (and who will test positive), and 999 to be free of the disease. But a 5% false positive rate will result in about 50 of the 999 people who do not have the disease also testing positive. So your chance of actually having the disease is the chance that you happen to be that one person with the disease out of the 51 testing positive.

What the positive test result has done is provide a twenty-fold increase in the odds of your having the disease from 1 in 1000 (or 0.1%) to 1 in 51 (or slightly less than 2%), but your chances are still extremely good (over 98%) of not having the disease. I suspect a lot of people get unduly terrified by test results of this kind because doctors may not know how to present the data in ways that give them a better sense of estimating the probability. (Of course, I am assuming that you were selected randomly for this test. If the doctor recommended that you get the test because you had other symptoms that caused her to suspect you had the disease, then that would further increase the odds of you having the disease.)

The lesson here is to be wary of our ‘gut’ feelings when dealing with certain mathematics concepts, especially involving probability and statistics. This may partially explain why Darwin’s theory of natural selection, dealing as it does with small probabilities and long time scales, is so hard for many to digest because they are outside the range of things we experience on a daily basis. In future postings, I will look at some of the issues that come up.

POST SCRIPT: Sicko opening nationwide on Friday

Michael Moore’s new documentary on the health care system Sicko will be at the Cedar-Lee (2163 Lee Rd) in Cleveland Heights starting on Friday, June 29, 2007. The show times are noon, 2:30, 5:00, 7:30, and 10:00 but you should check before you go.

Moore also appeared on The Daily Show to point out once again what a scandal the health care system in the US is, where it is actually in the interests of the profit-driven health insurance companies to deny health care to patients.

Evolution-4: Darwin gets an idea from Malthus

(See part 1, part 2, and part 3.)

In Darwin’s travels to distant lands from 1831 to 1836 on the Beagle, the different climates and environmental conditions he encountered made him aware of the weakness of the existing theory of ‘special creation’, where god was assumed to have created creatures best suited for their environment. Darwin saw for himself that very similar climates could produce hugely different kinds of species, and that the nature of these species seemed to be more influenced by the species in nearby areas than by anything else. This seemed to him to suggest that new species arose from the modifications of the old.

The discovery that the Earth was much older than had been previously thought, and the evidence for which was in the geology book by Charles Lyell that he had read on the boat, told him that it may be possible for these changes to occur gradually by very small steps provided that there was enough time for the changes to accumulate.

But why should species change at all? Why shouldn’t they stay the same forever? Or if they changed, why wouldn’t they change randomly instead of seeming to have a direction towards increasing complexity?

What Darwin still lacked was a mechanism that drove the change in organisms. The idea for this came in September 1838 when, after his return from his voyage and he was thinking about all the evidence he had gathered, he read Thomas Malthus’s Essay on the Principle of Population in which that political economist argued that the only thing that kept the population of anything (humans, other animals, plants) from experiencing runaway exponential growth was the limitation of essential resources (such as food and suitable habitats), and deprivations such as cruel climates, predators, and the like. (David Quammen, The Reluctant Mr. Darwin (2006), p. 42.)

Darwin knew that the size of plant and bird and animal populations in nature were fairly stable and he reasoned that the factors identified by Malthus might act differentially on members of the population, being more likely to remove the ones less suited and thus increasing the proportions of those more suited to the conditions. This kind of selection pressure, he felt, must be the driver of evolutionary change. Here at last was the mechanism that he had been seeking.

For the next twenty years, he carefully studied this process, starting with the breeding practices of pigeon owners and moving on to many others species. He even spent eight years studying barnacles. While breeders had the ability to artificially control the selection process, Darwin had the insight that the forces at work in nature might produce the same effect in the wild, hence his term ‘natural selection’.

Darwin eventually arrived at the basic tenets of evolution by natural selection. (The Advancement of Science, Philip Kitcher, 1993, p. 19. I have mentioned these before but reproduce them here for completeness.)

1. The Principle of Variation: At any stage in the history of a species, there will be variation among the members of the species: different organisms belonging to the species will have different properties.

In other words, children are never identical with their parents. Within each species there is considerable diversity in properties (the larger the population, the greater the diversity) and in support of this position, Darwin took great pains to point out how hard it was to distinguish between different varieties within the same species, and between species.

2. The Principle of the Struggle for Existence: At any stage in the history of a species, more organisms are born than can survive to reproduce.

If there is an abundance of food and other resources, the population of any species would multiply exponentially, as suggested by Malthus. The fact that it doesn’t is due to limitations in these necessary elements and this is what results in only some surviving and populations reaching more or less stable values.

3. The Principle of Variation in Fitness: At any stage in the history of a species, some of the variation among members of the species is variation with respect to properties that affect the ability to survive and reproduce; some organisms have characteristics that better dispose them to survive and reproduce.

The members of a species that are more likely to survive and pass on their properties to the next generation are those that have properties that give them some survival advantage in the environment in which they find themselves. It is important to note that only some of the properties need to be advantageous for the organism to have preferential survival. Other properties may also flourish not because they have an advantage but because they are somehow linked to advantageous properties and are thus carried along. Thus some properties may simply be byproducts of selection for other properties.

4. The Strong Principle of Inheritance: Heritability is the norm; most properties of an organism are inherited by its descendents.

Most properties that we have (five fingers, four limbs, one heart, etc.) are inherited from our ancestors.

All these four things were not controversial and were not hard to accept even for religious people. What gave Darwin’s theory its uniqueness and created controversy was that from these four principles, he inferred the crucial fifth. It was this extrapolation that is the key to Darwin’s theory of natural selection.

5. The Principle of Natural Selection: Typically, the history of a species will show the modification of that species in the direction of those characteristics which better dispose their bearers to survive and reproduce; properties which dispose their bearers to survive and reproduce are likely to become more prevalent in successive generations of the species.

So natural selection will favor those organisms that, by chance mutation, have properties that give them better chances for survival, and thus these characteristics will appear in the next generation in greater abundance. And from this he inferred that as these changes accumulate, eventually new species emerge.

But it was one thing to have a theory that satisfied him. It was quite another to convince others that it was the explanation for the diversity of life. There were many obstacles he had to overcome, not the least of which was the scale of time he was asking people to envisage was much longer than they were used to, the size of the mutations that underlay the process were so small as to be mostly invisible, and there was no agreement at that time on the whole question of how characteristics were inherited and how variations occurred in species.

It was to try and meet these objections that Darwin spent the rest of his life accumulating vast amounts of evidence from all over the world. Darwin, great scientist that he was, knew that just having a good idea wasn’t enough in science, however beautiful the idea was. You had to have evidence to support it.

Next in the series: How probability ideas can lead us astray

POST SCRIPT: How can we miss you if you won’t go away?

I was looking forward to British Prime Minister Tony Blair leaving office today. I found his preening pieties, his obsequious behavior toward Bush, and his self-righteous attitude irritating in the extreme and was looking forward to not having to see that on public display. But now comes the alarming news that Bush is thinking of making him some kind of special envoy to the Middle East, so we will be forced to endure even more of his grating presence.

Maybe Bush likes having his ‘pet poodle’ (which is actually an insult to a fine and dignified breed of dogs) around but as long-time Middle East correspondent Robert Fisk points out in the British newspaper The Independent, those who think that Blair, whom he describes as “this vain, deceitful man, this proven liar, a trumped-up lawyer who has the blood of thousands of Arab men, women and children on his hands,” has any credibility at all in the Middle East are woefully mistaken.

Evolution-3: Natural selection and the age of the Earth

(See part 1 and part 2.)

It is clear that many people find it hard to accept Darwin’s theory of evolution by natural selection. One reason is of course because it completely undermines the need to believe in a creator, making god superfluous when it comes to explaining the nature and diversity of life, and thus people may have a negative emotional reaction that prevents them from seeing the power of the theory. As I have discussed earlier, people are quite able to develop quite sophisticated reasons to believe what they want and reject what they dislike.
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Evolution-2: The lack of evidence for perfect design

In the first post in this series, I showed with the example of a soap spray nozzle how natural design could come up with systems whose intricacy and complexity is such that it was superior to the efforts of intelligent human designers. But what about the argument that a god-like designer would be able to come up with an even better nozzle design? It is true that if we allow for the existence of such a designer, we could get the best possible design for a nozzle. The catch is that assuming that god is a perfect designer opens up a whole set of new problems, not the least of which is why if god is so powerful he would need any kind of nozzle at all and not simply create any kind of spray he/she needed.

Let me start with a limitation of natural selection. There is a well known result about any method of solving a problem that starts (like natural selection does) with some state, tries out small variations, selects the one that shows the greatest improvement over the starting point, tries out variations based on that new state, selects the best one again, and so on, which is exactly the way that natural selection works. The problem is that while you will end up with a better result than the one with which you started, it may not be the very best solution that is conceivable. Such algorithms result in finding a locally optimal solution but not a globally optimal one.

As an example, suppose you are in open ground and totally in the dark. For some reason, you need to get to the highest point in the ground, say because flooding is occurring and you know the water is rising very slowly. (The specific reasons are not important. The point is to have some kind of external pressure that drives the selection process in one direction.) You could gingerly take small steps in every direction, see which way went up the most, and move one step in that direction. Then you again take tiny steps in all directions and select the one direction that moved up most, and move to that position. And so on. By repeatedly doing this, you are guaranteed to arrive at a peak.

(This is how natural selection works, though to be a more accurate analogy, we need to start with many people at the starting point, have couples move in each direction, have only the couples that get to higher ground survive while the others drown, have those successful couples produce lots of children at that location, who then move as couples in different directions, and so on.)

The catch is that the peak you arrive at may not be the highest peak in the vicinity. If a yet higher peak were to be separated from your initial starting point by even a small dip in the ground, you would miss it using this algorithm, since it does not allow you to make a short-term disadvantageous change in anticipation of future benefits. Natural selection is not guaranteed to produce the very best or the most perfect solution or design. It instead works on a ‘just good enough for now’ basis. This means that biological systems do not necessarily make progress towards perfection even though they do become more complex over time.

Now a god-like designer would presumably be able to see all the possible solutions (even in the dark) and pick the one that is best overall and guide you to that point. But the interesting thing is that the results of nature are more consistent with the ‘just good enough for now’ strategy of natural selection than that of a perfect designer. After all, we know that while nature’s designs (by which I mean designs arrived at by natural selection) are marvelously adapted and successful for many things, they are by no means perfect.

As Sean B. Carroll says in his book The Making of the Fittest (2006) which examines the DNA evidence for natural selection:

Modern species are not better equipped than their ancestors, they are mostly just different. They have often gained some coding information in their DNA and, as I have shown throughout this chapter, they have often lost some, or even many, genes and capabilities along the way.

The fossilization and loss of genes are powerful arguments against notions of “design” or intent in the making of species. In the evolution of the leprosy bacterium, for example, we don’t see evidence that this pathogen was designed. Rather, we see that the organism is a stripped-down version of a mycobacterium, which still carries around over a thousand useless, broken genes that are vestiges of its ancestry. Similarly, we carry around the genetic vestiges of an olfactory system that was once much more acute than what we have today.

The patterns of gain and loss seen species’ DNA are exactly what we should expect if natural selection acts only in the present, and not as an engineer or designer would. Natural selection cannot preserve what is not being used and it cannot plan for the future. (p. 136)

The very fact that it is estimated that over 99% of all the species that ever existed are now extinct is powerful evidence against perfect creation. The only way out of this for the religious believer is to think that god, although perfect, is somehow holding back and deliberately creating imperfections and thus making it merely look like something like natural selection is at work. Or god does not interfere at all, ever in the natural selection process once it began way back at the beginning of life. Or is simply careless and produces sloppy designs.

Darwin himself, based on his careful study of plants and animals, found it hard to believe in the idea of an intelligent designer. His biographer David Quammen in the book The Reluctant Mr. Darwin (2006, p. 120) highlights the kinds of questions that troubled Darwin, and which he expressed in letters to the Harvard botanist Asa Gray, who believed in the idea of special creation of humans.

I cannot see, as plainly as others do, evidence of design & beneficence on all sides of us. There seems to me too much misery in the world.
. . .
Why would a benevolent God design ichneumon wasps, for instance, with the habit of laying eggs inside living caterpillars, so that the wasp larvae hatch and devour their hosts from inside out? Why would such a God design cats that torture mice for amusement? Why would a child be born with brain damage, facing a life of idiocy?
. . .
An innocent & good man stands under [a] tree & is killed by [a] flash of lightning. Do you believe (& I really shd like to hear) that God designedly killed this man? Many or most persons do believe this; I can’t and don’t.

The question of pointless suffering and loss were not hypothetical issues for Darwin. He had been devastated when his own beloved daughter Annie had, at the age of ten, died after a long and mysterious and undiagnosed wasting illness. Darwin seemed to feel that such things were incompatible with a benevolent deity. As Quammen writes, “Any god who controlled events on Earth closely enough to preordain such an occurrence – or to permit it, if permission was necessary – wasn’t one that Darwin could take seriously.”

Darwin’s theory of evolution by natural selection, although not aimed at doing so, ultimately provided the basis on which belief in a designer god, and thus god itself, could be abandoned.

Evolution-1: The power of natural selection

We are rapidly approaching 2009, a year that marks a major scientific milestone that is going to be commemorated worldwide. It is both the 150th anniversary of the publication of the landmark book On the Origin of Species that outlined the theory of evolution by natural selection, and the 200th anniversary of the birth of its author Charles Darwin.

Darwin’s theory represents arguably one of the most, if not the most, profound scientific advances of all time, ranking well up with those scientific revolutions associated with the names of Copernicus, Newton, and Einstein. And yet it is widely misunderstood, or more appropriately, under-understood because most discussions of it remain on too high a level of generality, enabling critics to make statements about the theory that are not valid but yet seem plausible.

In order to create a better awareness of what the theory involves, today I will begin an occasional series of posts that looks at the details of the theory, including the mathematics that underlies it and which was developed later by people like J. B. S. Haldane, Sewall Wright, and R. A. Fisher.

One of the most common misconceptions about evolution by natural selection is that it works purely by chance. After erroneously assuming that notion, people then look around them, see the wonderful complexity of nature, and conclude that this simply could not have occurred by chance and that therefore this points to the existence of a designer who must be god. This is exactly the explicit argument of intelligent design creationists, but also the implicit argument of some people who want to somehow find evidence for the necessity of god’s existence.

It seems as if no amount of reiteration (by those who have studied the theory of evolution) that this basic assumption of chance is not true, seems to have any effect. I recently had a correspondence with someone who, despite my repeatedly pointing out that chance was not the sole driver of natural selection, kept saying things like “How can you think all this came about by chance?”

Now chance does play a role in the way that genetic changes occur, externally from the occurrence of mutations due to things like ultraviolet radiation, and internally in the way that genetic shuffling occurs in the copying of the genetic information during reproduction. You cannot be sure, for example, what genetic features you will inherit from your mother and what from your father. But these chance variations are then acted upon by selection forces that are the very opposite of chance in that they pick out only those varieties that are beneficial for future propagation. This is a highly directed process that acts without an intelligent director and it is these selection forces that are behind the complexity of the systems that have evolved.

In response to the “evolution is just chance and is very unlikely to produce complexity” argument, those who understand the theory of evolution sometimes argue in its defense that the theory is just as good at producing complex things as any conscious designer. But such people are really selling the theory short. In actual fact, the theory of evolution by natural selection produces results that are often much better than those produced by conscious design.

A wonderful example that illustrates this point is given by biologist Steve Jones, as recounted in his book Almost Like a Whale: The Origin of Species Updated (1999) (Chapter IV, Natural Selection). (Thanks to Heidi Cool for alerting me to the podcast of a talk by Jones which is where I first heard this story.)

I once worked for a year or so, for what seemed good reasons at the time, as a fitter’s mate in a soap factory on the Wirral Peninsula, Liverpool’s Left Bank. It was a formative episode, and was also, by chance, my first exposure to the theory of evolution.

To make soap powder, a liquid is blown through a nozzle. As it streams out, the pressure drops and a cloud of particles forms. These fall into a tank and after some clandestine coloration and perfumery are packaged and sold. In my day, thirty years ago, the spray came through a simple pipe that narrowed from one end to the other. It did its job quite well, but had problems with changes in the size of the grains, liquid spilling through or − worst of all − blockages in the tube.

Those problems have been solved. The success is in the nozzle. What used to be a simple pipe has become an intricate duct, longer than before, with many constrictions and chambers. The liquid follows a complex path before it sprays from the hole. Each type of powder has its own nozzle design, which does the job with great efficiency.

What caused such progress? Soap companies hire plenty of scientists, who have long studied what happens when a liquid sprays out to become a powder. The problem is too hard to allow even the finest engineers to do what enjoy the most, to explore the question with mathematics and design the best solution. Because that failed, they tried another approach. It was the key to evolution, design without a designer: the preservation of favourable variations and the rejection of those injurious. It was, in other words, natural selection.

The engineers used the idea that moulds life itself: descent with modification. Take a nozzle that works quite well and make copies, each changed at random. Test them for how well they make powder. Then, impose a struggle for existence by insisting that not all can survive. Many of the altered devices are no better (or worse) than the parental form. They are discarded, but the few able to do a superior job are allowed to reproduce and are copied − but again not perfectly. As generations pass there emerges, as if by magic, a new and efficient pipe of complex and unexpected shape.
Natural selection is a machine that makes almost impossible things.

In other words, by mindlessly applying an algorithm based on the principle of natural selection, they were able to come up with a complex design for a superior spray nozzle that was inconceivable to the scientists trying to design one using engineering and science principles.

Believers in a god-like designer might argue that what natural selection did here was outperform mere mortal designers and that god, being a perfect designer, would be able to come up with a better design. But that argument doesn’t work that well, either, as I will discuss in the next posting in this series.