## POPULATION GENETICS IN EQUILIBRIUM

We are accustomed to thinking about organisms in a population. To study what is called population genetics, we need to expand this concept and think about alleles in a population. For example, for organisms, we could ask: "Of all the people in the world, what percent have cystic fibrosis?" The corresponding question for alleles is: "Of all the F and f alleles of CFTR in the world (two alleles per person), what percentage are f ?" These two questions have different answers, of course, but they are related. Let's see how.

1. Under what conditions can we expect "allele frequencies" (or "allele percentages") in a large population to remain constant from generation to generation?

In general, allele frequencies will remain constant from generation to generation if . . .

(1) if the members of the large population mate randomly,
and
(2) if all genotypes survive and reproduce equally well,
and
(3) if new alleles are not entering into the population (either via new mutations or migration of individuals).

Obviously, this set of conditions is never met completely. However, in large populations it may be "close enough" such that allele frequencies do not change noticeably over some observable number of generations. When this is the case, we refer to the situation as "Hardy-Weinberg equilibrium". {Named after the two people who first realized this.}

2. In such a randomly mating population, what is the graph of "genotype frequencies" as a function of "allele frequencies" (for the case of two alleles of gene alpha)?

This is the "p&q" graph of Problem S-12. This relationship between allele frequencies and genotype frequencies is an expression of the "Hardy-Weinberg principle". p is the A allele frequency, q is the a allele frequency, p squared is the AA genotype frequency, q squared is the aa genotype frequency, and 2pq is the Aa genotype frequency.

3. What valuable calculation about cystic fibrosis (or any single gene inherited disease) can we make from the "genotype frequency vs. allele frequency" graph?

Page 730 gives the calculation. If we know what fraction of the population has the disease (i.e., how many people are genotype ff ), we can calculate how many people are heterozygous carriers of a defective allele.

4. How can we extend this to a three allele case, such as that for human blood type?

Page 731
Figure 17.12.

5. How can we extend this to X-linked genes?

Page 734.
Figure 17.16.