In very small populations, rare alleles can become common or disappear because of genetic drift—random changes in gene frequency that are not due to selection, gene mutation, or immigration. We can explain this as follows. When flipping a coin 1,000 times, it is likely to get 50 percent heads and 50 percent tails (if it's a fair coin). But flip it only five or ten times, and it is unlikely to get exactly half heads and half tails. Chances are good that the results will be something quite different. In the same way, if 10,000 people mate and produce children, the bb genotype will pretty much conform to the Hardy-Weinberg equation described above (provided the other assumptions are approximately true). For example, in a sample of just twenty people, instead of getting a group of children of whom 4 percent have blue eyes, the result could end up none with blue eyes, or maybe half having blue eyes. It all depends on how the alleles happen to combine when eggs meet sperm.
Because of genetic drift, small, isolated populations often have unusual frequencies of a few alleles. Although similar to other people in most important respects, such isolated populations may harbor high frequencies of one or more alleles that are rare in most other populations. For example, in 1814, fifteen people founded a British colony on a group of small islands in the mid-Atlantic, called Tristan de Cunha. They brought with them a rare recessive allele that causes progressive blindness, and the disease, extraordinarily rare in most places, is common on Tristan de Cunha. Such "inbreeding" produces more homozygotes than usual and increases the probability of children born with genetic diseases. The Old Order Amish have a high frequency of Ellis-van Creveld syndrome, and Ashkenazi Jews were, until a few years ago, susceptible to Tay-Sachs disease. Fortunately, genetic testing has greatly reduced the incidence of Tay-Sachs and many other such genetic diseases.
Population genetics also provides information about evolution. It is known, for example, that populations that have unusual allele frequencies must have been isolated from other populations. And we can surmise that populations that share similar frequencies of certain rare alleles may have interbred at some point in the past. Human populations in sub-Sarahan Africa show the greatest diversity of all human populations. On the basis, in part, of this diversity, one theory of human evolution suggests that all humans originated in Africa, and then emigrated to Asia, Europe, and the rest of the world.
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Klug, W. S., and M. R. Cummings. Concepts of Genetics, 6th ed. Upper Saddle River, NJ: Prentice Hall, 2000.
Lewontin, R. Human Diversity. Redding, CT: W. H. Freeman, 1982.