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.
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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.

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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. [Read more…]

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.
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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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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.
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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.
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