Sunday, 4 November 2007

The Hardy-Weinberg equation (Part 3) - Genetic equilibrium

As promised, we have to do a little rounding-off of the topic.

So far, we've shown how the Hardy-Weinberg equation describes the frequencies of genotypes in terms of the frequencies of the alleles that make up those genotypes. We've seen how useful this can be in determining the frequencies of genotypes about which we'd otherwise have no clue.

The second major implication of the Hardy-Weinberg equation is that the frequencies of the various alleles, and thus the frequencies of the various genotypes, tend to remain constant across the generations, unless the population is not at genetic equilibrium.

For just a minute, don't worry about what we mean by "genetic equilibrium"; concentrate instead on the rest of the sentence. Many people assume that if a trait is recessive, it will tend to die out; that dominant genes will tend to gradually conquer the recessive ones until the latter are pushed to extinction. Not so! Or consider a rare gene: all things being equal, will it tend to disappear from the gene pool over time? Not at all!

I still think that the gene pool of a species is best visualised as an actual pool containing balls representing the various alleles. In making an organism, two alleles for each gene are randomly scooped up from the pool. (To make the next generation, all the balls would be placed back in the pool, and then selected again at random.) Now it's obvious when you picture the scene this way that the most common alleles will tend to be picked most commonly. But it is also obvious that the rare alleles, although rare, will not tend to die off. Once an allele is part of the species' gene pool, it'll stay there unless something upsets this trend. Nothing automatically tends to banish balls from the pool.

Similarly, since the allele frequencies tend to stay the same, the genotype frequencies tend to stay the same. A recessive trait is not simply 'bred out' by some quirky law of nature. The phrase (so often repeated by students) "If O is a recessive blood type, how can it be the commonest one?" simply makes no sense. Nothing automatically pushes the o allele towards oblivion - and so the OO genotype could be anywhere from the commonest to stone last as regards frequency.

I think I've made my point. I don't mean to imply that allele frequencies don't change as the generations go by (changing allele frequencies is almost the definition of evolution). What I do mean to say is that allele frequencies will tend to stay fixed, unless acted on by some other factor. This tenet is sometimes referred to as the Hardy-Weinberg principle.

If the allele frequencies are tending to stay fixed, the population is said to be in genetic equilibrium (or Hardy-Weinberg equilibrium). However, there are several important factors that can disrupt this equilibrium. Put another way, a population needs to have five characteristics if it is be capable of being in genetic equilibrium. Briefly, there are as follows.
  • The population needs to be large. How large? Large enough to avoid chance disrupting gene frequencies. For instance, if some freak accident kills 4 animals, this won't do much to alter the gene pool if the species contains a million animals. However, if it only contains 6 animals, allele frequencies could be dramatically altered (e.g. What if a rare allele was housed solely in the body of one of the dead animals?).

  • There needs to be random mating. If albinos, say, tended to mate only with other albinos, this would obviously increase chances of creating albino children (recessive homozygotes) quite dramatically, and simultaneously reduce the number of carriers of the albino gene.

  • There can't be any mutations. Clearly, mutations are a constant source of increased variability within the gene pool. Put another way, mutating one allele into a new one must alter the allele frequencies. (However, without a positive selection, the effect of the new mutation will be tiny, especially in a large population. Consider taking one ball out the pool of a million balls, and altering it. Clearly, not much change will occur.)

  • There can be no migration. In a similar way to mutations, allele frequencies will obviously be altered by having one population of birds fly in and start mating with another population at genetic equilibrium.

  • There can't be any natural selection. Natural selection will tend to automatically favour some alleles over their counterparts, resulting in more copies of the former, at the expense of the latter, as the generations go by. Natural selection is usually by far the most potent force capable of disrupting a genetic equilibrium.

All five factors must usually be met for the population to be in genetic equilibrium. As a corollary, if a population is not in genetic equilibrium (i.e. the genotype frequencies are changing), one of the five criteria must have been violated.

That's about it, folks. If you need more help with the five criteria, try this website, which illustrates the concepts very nicely. Otherwise, leave a message or email a query, and I'll get back to you!

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