Study Questions - Evolution at Multiple Loci
1) The selective value of an allele can be influenced by the genotype at other loci. Explain.
2) If two loci are assorting independently (NOT PHYSICALLY linked) and they have the following gene frequencies, how likely would each of the gamete types (haplotypes) be? Would there be any "linkage disequilibrium" in this case? D = ad - bc
| Gene frequencies | Probability of gametes |
| f(A) = p1 = 0.8 | a = AB = |
| f(a) = q1 = 0.2 | b = Ab = |
| f(B) = p2 = 0.7 | c = aB = |
| f(b) = q2 = 0.3 | d = ab = |
OK, so hopefully you proved to yourself that independently assorting genes, which are NOT LINKED, have no "linkage disequilibrium". Good. That should make sense. Note, there was no selection here.
3) Now, consider two linked loci, A and B. Suppose we have a population that is homozygous for A (p = 1.0) and is polymorphic for B such that f(B) = .6 and f(b) = .4. So, initially, the only two haplotypes in the population are AB (0.6) and Ab (0.4), and they MUST occur at these frequencies. Is this population in linkage disequilibrium?
| Gene frequencies | Probability of gametes | observed haplotypes |
| f(A) = p1 = 1.0 | a = AB = | a = 0.6 |
| f(a) = q1 = 0.0 | b = Ab = | b = 0.4 |
| f(B) = p2 = 0.6 | c = aB = | c = 0.0 |
| f(b) = q2 = 0.4 | d = ab = | d = 0.0 |
4) OK, so hopefully, you just discovered that "linked genes" do not HAVE to be in "linkage disequilibrium... disequilibrium describe a situation where the expected frequency of haplotypes differs from what is observed. Now, continuing the example, above, suppose we have a population of 50 diploid individuals (100 haplotypes) and new mutation occurs at the A locus on an AB chromosome, changing an AB to an aB. Is this population in linkage equilibrium? What is D?
| Gene frequencies | Probability of gametes | observed haplotypes |
| f(A) = p1 = 0.99 | a = AB = | a = 0.59 |
| f(a) = q1 = 0.01 | b = Ab = | b = 0.4 |
| f(B) = p2 = 0.6 | c = aB = | c = 0.01 |
| f(b) = q2 = 0.4 | d = ab = | d = 0.0 |
5) For the problem above, what are the equilibrium haplotype frequencies? If there are NO MORE MUTATIONS, what is the only way that we can create ab haplotypes in this population from zero, and thus approach linkage equilibrium?
So, if you answered correctly, that is why that process (your answer, above) takes a population from disequilibrium to equilibrium, even for linked genes.
6) So, a population will tend towards equilibrium. What reasons might it not be in equilibrium (yet)?
7) So, how might one use this as a tool for determining whether a given locus is under selection?
8) What is the down side of this? Suppose you observe that a gene is not in HWE with ITSELF... could it be influenced by selection on another closely linked gene? Explain.