Question

A group of 500 unicorns have magically appeared at Griffith Park. Researchers have speculated social distancing restrictions have enabled them to grace our lands. Interestingly, the genetic makeup of unicorns is unlike that of humans. They are triploid species, meaning that 3 alleles make up a given genotype. Researchers have observed variation in their coat colors with 40 unicorns having red coats (WWw), 250 white coats (www), 110 black coats (WWW), and 100 blue coats (wwW).

A. Calculate the genotype frequency for each given genotype: WWw, www, WWW, and wwW.

B. Calculate the allele frequency for each given allele: W and w.

C. Fast forward 50 years into the future, a new generation of unicorns have emerged with a total of 150. Researchers make the following observation: 5 red coats (WWw), 130 white coats (www), 7 black coats (WWW), and 8 blue coats (wwW). Compare this generation to the parent generation. Is the new generation of unicorns undergoing Hardy Weinberg Equilibrium? If not, list at least 2 evolutionary forces that may have occurred.

Answer 1

B. Frequency of W =Number of W alleles/Total number of alleles =[ (2*40)+(3*110)+(1*100)]/[3*(40+250+110+100)]

=(80+330+100)/1500 =0.34 (p)

Frequency of w = Number of w alleles/Total number of alleles =(1*40)+(3*250)+(2*100)/[3*(40+250+110+100)]=(40+750+200)/1500= 0.66 (q)

A.Hardy weinberg equation for triploids = (p+q)3=p3+q3+3p2q+3q2p where p and q are frequencies of dominant allele and recessive allele respectively.

Frequency of genotype WWw = 3p2q =3*0.34*0.34*0.66 =0.076*3 =0.229=22.9%

Frequency of genotype www =q3= 0.66*0.66*0.66 =0.287=28.7%

Frequency of genotype WWW=p3= 0.34*0.34*0.34= 0.039 =3.9%

Frequency of genotype wwW =3q2p =0.66*0.66*0.34 = 0.148*3=0.444=44.4%

C.In the new generation,

Frequency of W allele = [(2*5)+(3*7)+(1*8)]/(3*150)=(10+21+8)/450=39/450=0.087 (p)

Frequency of w allele =[(1*5)+(130*3)+(2*8)]/450=(5+390+16)/450=411/450=0.913 (q)

p+q=0.087+0.913 =1. This implies that the new generation is also undergoing Hardy Weinberg equilibrium similar to the parent generation 50 years ago.

The evolutionary forces that disturb the population from undergoing Hardy Weinberg equiliibrium include inbreeding, mutations, imigration or emmigration.