Genetic drift is always occurring, even when an allele is advantageous or disadvantageous. Randomness is still at work — lightning is still hitting the occasional deer, for example — but these random events don't make much difference to the outcome. The slow deer will get eaten by wolves, and the fast deer will pass their genes on to the next generation. If a lightning bolt happens to hit one of the fast deer, the outcome won't change. But sometimes, it's not so clear cut when natural selection is the main force and when genetic drift is.
In a small population, the weakly advantageous allele could be eliminated by random genetic drift before it could be fixed by natural selection, or a weakly deleterious allele could increase to fixation. For example, a cheetah with a mutation that made it just a tiny bit faster might be expected to catch a few more antelope and have a slightly better chance at leaving more descendents than its neighbor. This new mutant would tend to increase in frequency in the population through time, but it would increase very slowly because the difference between the mutant gene and the other cheetahs is miniscule.
It might also increase or decrease in the population purely as a result of chance events. It's possible that even though it's selectively advantageous (you get to catch a couple more antelope, just not very many more), it might be eliminated by chance events before it could sweep through the population.
Whether a particular neutral allele increases to fixation is a function of population size. In small populations, random factors can be of greater importance. But — and this is a big but — the probability that there will be a neutral mutation that will increase to fixation is independent of population size. The key is that larger populations have more individuals and, as a result, more errors in DNA replication (errors by the mutations). So although it's true that any particular mutation has a much lower chance of increasing to fixation in a large population, that population has proportionally more mutations. Mathematically, everything pretty much cancels out. The effect of large population size on slowing fixation as a result of genetic drift is balanced out by the fact that a large population also has more mutations.
Here's why this little tidbit is important: Knowing that the overall rate of accumulation of neutral mutations doesn't have anything to do with population size lets scientists estimate the time since two lineages diverged. Neutral mutations in particular genes sometimes accumulate at a relatively constant rate. Therefore, the differences between two lineages can be used to determine the time since their divergence — a subject covered in more detail in Chapter 15.
Natural selection doesn't operate at the same strength at all times. Imagine a gene that allows an organism to survive extremely dry conditions. Natural selection will result in an increase in the frequency of this gene in environments with very dry conditions. Now imagine that those conditions occur only once every ten generations. During the other nine generations, changes in the frequency of that particular gene from generation to generation will be due entirely to drift.
If a new allele is neutral, random forces determine its future frequency. It may disappear, or it may increase in frequency. Consider the gene that determines which of your thumbs is on top when you interlace your fingers. As it turns out, you always put the same thumb on top. Try interlacing your fingers so that the other thumb is on top. Feels weird, doesn't it? Yep, a locus with two alleles actually determines your thumb preference.
Assuming that both alleles have always been identical with respect to fitness (scientists can't be certain, but neither can they think of the slightest reason why they wouldn't be), both alleles exist in the human population because of random events — an initial mutant increasing in frequency as a result of chance in the absence of any effects of natural selection. The relative frequency of the two genes is still subject to the process of genetic drift, but human populations are so large that both alleles will persist in the population for the foreseeable future.
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