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.
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There is a strong (negative) correlation between infant mortality and life expectancy, as can be seen from this graph, where each dot represents the data for a country, along with a linear regression line. The implication is clear that the best way to improve life expectancy is to reduce infant mortality. The reason that many developing countries have high infant mortality rates and resulting low life expectancy is that lack of access to clean water results in diarrhea and this leads to dehydration, which is often fatal for infants. (As an aside, the international conglomerate Nestle deserves widespread condemnation for its