MathBench > Population Dynamics

Mutation and Equilibrium

>Episode 3: Revenge of the Mutants

Best of the Hardy-Weinberg Show

Do equilibrium and rates of change
matter for subjects other than genetics?

Yes, absolutely! Mutation is an example of a linear change process. The number of changes is directly proportional to the amount of raw material. These same relationships are true of all linear rates of change – for example, birth or death rates in ecology, or amount of products and reactants in a chemical equation. Linear models are the simplest models, although often we also use more complicated models.

Remember that equilibrium does not mean that no change is taking place! The number of mutations taking place can be quite high, and yet if they balance each other out, there is still a dynamic equilibrium. In other words, the frequencies of different alleles change the fastest when the number of forward and backward mutations is the most UNBALANCED. This tends to be true when we are farthest from equilibrium.

Also, remember that the RATE of forward and backward change does not need to be equal in order to have equilibrium. Rather, the NUMBER of forward and backward changes must balance out.

How is the mutation-equilibrium
different from the Hardy-Weinberg equilibrium?

woman at Rennfest with blue hairRemember that the Hardy-Weinberg 'Law' makes two predictions:

  1. allelic equilibrium: p and q will not change, and
  2. genotypic equilibrium: the proportions of genotypes will conform to p2/2pq/q2.

Under mutation, the allelic frequencies do change, approaching a new equilibrium gradually. In the long run, the starting conditions don't matter -- the same equilibrium is obtained no matter where you start.

But just because a population is undergoing mutation does not mean that it is not mating randomly. Therefore, the H-W GENOTYPIC frequencies should still occur. Remember that the genotypic equilibrium occurs in a single generation! That is, genotypic equilibrium is a FAST process, while allelic equilibrium under mutation is a SLOW process.

So if you are asked to "show that a given population is in Hardy-Weinberg equilibrium", it is NOT enough to show that the genotypic ratios conform to p2/2pq/q2! All populations which are reasonably large and mate randomly will conform to p2/2pq/q2, because genotypic equilibrium is such a fast process. Instead, in order to show that a population is in Hardy-Weinberg equilibrium, you need to show that p and q are not changing over at least one generation.

What were those assumptions again?

blue guy Here they are:
  1. the population is reasonably large
  2. the alleles assort randomly (random mating)
  3. there is no mutation (this would change p and q)
  4. there is no migration (this would also change p and q)
  5. there is no differential reproduction / natural selection (this would also change p and q)

Notice the last 3 are all processes that change p and q. Mutation, because if the alleles mutate their frequencies can change. Migration, because if the migrant pool if different from the population, then p and q will change. And natural selection, which would favor one of the alleles over the other.

Meeting all five of these conditions exactly is pretty hard. BUT, natural populations are often ALMOST in Hardy-Weinberg equilibrium. For example, mutation might be almost zero, and migration very similar to the current allelic frequencies.

Also, the Hardy-Weinberg equilibrium gives us a "normal" expectation (sometimes called a "null" expectation) of what the genotypic frequency in a population should look like -- so if the population does not resemble this equilibrium, we know that something else is going on.

The assistant handed over his report to the ME, who filed it under the corner of his desk that was uneven. “Just give me the punchline,” he growled.

“Only thing I'm sure of,” said the Assistant , “Is we're all going to dye.”








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