Effective genetic population size:
Professional geneticists are able to look at the genetic makeup of a number of animals or plants and announce that the effective population size is such and such a number. We have been looking at the genetics of populations with sizes, so it is natural to ask whether we mean the same thing. Alas, we do not.
If you want to sprain your brain, there is a most engaging book, John H. Gillespie Population Genetics, The Johns Hopkins University Press, Baltimore, 2004. If you can make your way through it with serenity then you can inform me on these matters, but I shall try to give a notion of what effective population size means to a geneticist.
Suppose you select a gene, a good old fashioned sequence of DNA that codes for building a protein. Different genes in one place on a chromosome are called alleles, while the place itself is called a locus. I have heard both of them called “genes” as in “gene for eye color,” which would be a locus and “gene for blue eye color,” which would be an allele. The book makes even stricter definitions.
So suppose you take a swab of your mouth and chemically isolate the DNA. Then with a kit that lets you do so, you make the DNA replicate itself using the same enzymes that nature uses until you have a useable sample, large enough for analysis. Then through steps fathomless to moi you isolate your alleles, of which we assume there will be two since you have two of most loci, and determine the sequence of each, that is to say the base pairs that code for the amino acids that will make of the protein. The two alleles will have the same length, which you probably already knew, and the vast majority of the bases in the same places will be identical. But a number of them will be different bases.
That does not necessarily mean that one is wrong and the other is right. In fact, we shall assume that the differences are neutral, that there is absolutely no preferred alternative base at the sites in question. Using that assumption, we can employ a mathematical technique called the Wright-Fisher theory.
So we have a number of sites where the bases are the same and a few where they are different. No as it turns out, alleles at a given locus have a certain mutation rate, and this rate is the same throughout the locus although different for different loci. And such mutations rates are pretty well known.
The presence of the variation, the different base pairs, is due to mutations, uncorrected copying errors that can substitute one base (of which there are four possible ones) for another.
While mutations are pumping variability into the population, variability is being reduced by something called random drift. If you take a bucket of marbles, half black and half white, mix them well and grab a handful, you will probably get some black and some white. But if you mix and grab often enough, eventually you get all black or all white. The other shade has been excluded because of randomness. Similarly, some of the variant base pairs will be excluded from the population because they chanced not to make it into the next generation.
So the frequency of those variant base pairs, the number that are different compared with the number that are the same, is a balance between mutation rate and rate of genetic drift. Mutation rate is independent of population size, the copying mechanism having no clue as to what is going on in other individuals in the population, but the rate of genetic drift is quite dependent on population size. If you were bailing marbles out of a tub with a bucket it would take a lot longer to come up with all black marbles than if you were grabbing handfuls.
Taking these two factors into consideration, and waiting until things come to equilibrium, you can infer from the frequency of differences in base pairs and the mutation rate, the size of the population. That is the effective population size at equilibrium.
It would be a lucky good thing if you could simply look at a fifty year old, check out his or her effective population size and ask how many children there were. Then you could decide whether gene pool size and fertility were related.
Unfortunately, it does not seem to be likely. The model we presented indicates, and I believe it to be the approximate truth, that if you take a population of 20,000 randomly mating individuals and follow them for 10 generations you will see a population crash. That is only 200,000 individuals.
The mutation rate for hemoglobin is, for instance 10-9 substitutions per amino acid site per year or 3 X 10-10 per generation. There are probably something like 150 amino acids in a hemoglobin protein polypeptide, if it is anything like myoglobin, so there should be 4.5 X 10-8 mutations per chain per generation. There are 4 protein chains, and two alleles per individual, so that rate is about 3.6 X 10-7 mutations in hemoglobin per individual per generation. That is 1 per .00000036. Multiply that times 200,000, and I think you get .72 mutations during the entire history. Indeed, you might get one, probably would. And it would occur somewhere along line of 10 generations, after which it might even survive genetic drift. But it would probably not even be in the majority of the individuals. However, fertility in the first generation might be enormous and disastrously low in the last generation. Even if the mutation was found and traced, it would be of no use in predicting fertility.
The time to equilibrium is very long. The effects we are looking at are but a few generations long. Alas, what seemed at one point to be a slam dunk to demonstrate the relationship between population size and fertility turns out to look like another fool’s errand.
On the other hand, such things are popular some times.
The book (and I do mean it as a plug. If you enjoy a good hard think, you know how rare they are, and this is one) does say on page 39 that one ought to be “uncomfortable” with the fact that the heterozygosity (read effective population size) of so many widely different species lie in a narrow range. That is deft understatement. As we pointed out on July 10 of this year, in the long run populations are the same size because they operate under the same ceiling of population size because we all have the same basic genetic structure.
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