Question

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

Suppose that several centuries ago, a Spanish galleon with a load of conquistadors' horses was shipwrecked by a large grassy island. Just by chance, the horses that survived the shipwreck and swam to shore were 10 chestnut roans (eeRr) and 10 nonroan homozygous blacks (EErr). On the island, they interbred with each other and established a wild population. The island environment exerts no direct selection on either locus.

1. What was D, the coefficient of linkage disequilibrium, in the initial population of 20 horses? Was the initial population in linkage equilibrium or not? If not, what chromosomal genotypes were underrepresented?

2. Do you expect the frequency of the chestnut allele, e, to increase or decrease in the first crop of foals? Would your answer be different if the founding population had been just 10 horses (5 of each color)? Explain your reasoning.

Answer 1

Genotype	Phenotype
EE and Ee	black pigment
ee	reddish chestnut
Rr	Roan (a scattering of white hairs throughout the basic coat color)
rr	not roan
RR	die during fetal development

10 chestnut roans (eeRr) x 10 nonroan homozygous blacks (EErr).

1. To solve first part, we need to calculate the frequencies of each haplotype.

	.e	.e		E	E
R	Re	Re	r	Er	Er
r	re	re	r	Er	Er

From the above crosses, we can know the frequency of haplotypes

So, we will get     eR=0.25, er=0.25, Er=0.5 and ER=0

Now use the above data to calculate the coefficient of linkage disequilibrium (D)

                             D = fAB fab – fAb faB

i.e D = (0)(0.25) – (0.5)(0.25) = -0.125.

With the above obtained results we can say that the population is in linkage disequilibrium, so the population is not in linkage equilibrium. Here we can find too many rE and no RE chromosome, so this population is not certainly at equilibrium.

B) Obviously the population will decrease because half of the chestnut alleles in this population are linked to the R allele. So it will end up in RR, so these will die during fetal development.

As we all know that genetic drift will have its effect on small populations, 20 horses’ means its small population only.

As mentioned in the second question if the number of horses are only 10, then the genetic drift will try to show greater effect on this small population.