In horses, the coat color is governed by the E locus.  EE and Ee horses are black and ee horses are chestnut.  A different locus, the R locus, can cause roan, a scattering of white hairs throughout the background coat color.  However, the roan allele has a serious drawback:  RR embryos always die during development, Rr embryos survive and are roan, while rr horses survive and are not roan.  The E and R loci are tightly linked.

Suppose that several centuries ago, a Spanish galleon with a load of horses was shipwrecked on a large, grassy island.  The horses that made it to shore were 20 chestnut roans (eeRr) and 20 nonroan homozygous blacks (EErr).  On the island they interbred with eachother and established a wild population.  The island environment exerts no direct selection pressure on either locus.

Before doing any calculations, make a prediction about what you think will happen to the frequency of the e allele in the first generation of foals – will it increase, decrease, stay the same?

1.     Confirm that the initial population of 20 horses are in linkage disequilibrium by calculating the observed haplotype frequencies, the allele frequencies of all four alleles, and the predicted haplotype frequencies based on the allele frequencies if the population were in linkage equilibrium.

2.     Next, calculate the diploid genotype frequencies in the first generation produced from these horses using the haplotype frequencies.  First, write out the ten possible diploid genotypes, then use the observed haplotype frequencies and the equations from lecture 23.   Remember, diploid genotypes that are homozygous at both loci (e.g. ER:ER) have frequencies of the haplotype frequency squared (g_ER²) and diploid genotypes that are heterozygous at either locus (e.g. ER:Er) have frequencies of two times the product of the two haplotype frequencies (2 x g_ER x g_Er).

3.     Assume 100 zygotes were created from these parents.  Eliminate any zygotes with the deadly RR genotype at the R locus and calculate how many foals will have each of the remaining diploid genotypes by multiplying the diploid genotype frequencies from the last step by 100.

4.     Using the numbers of individuals with each genotype from above, count alleles to compute the new allele frequencies of all four alleles in the first generation of foals.

5.     Compare the allele frequencies for all four alleles in the original population of 20 horses to the allele frequencies in the first generation of foals.  Explain why selection against RR homozygotes changed the allele frequencies at the E locus.  Would this have happened if these loci were in LE?  Why or why not?