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.
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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?
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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 extinct, 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.

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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.
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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)?
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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.
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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.
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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.
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