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 TGA 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.