Question

A wildflower native to California, the dwarf lupin (Lupinus nanus) normally bears blue flowers but occasionally bears pink flowers. Flower color is controlled by a single diploid locus, with the blue allele (B) completely dominant over the pink allele (b). In a wild population of lupins, there are 43 pink lupins and 3398 blue lupins, for a total of 3341.

Calculate the genotype and allele frequencies of this population, assuming that the population is in Hardy-Weinberg equilibrium:

Genotype frequency of bb assuming the Hardy-Weinberg equilibrium (i.e. the frequency of pink flowers in the population): q2 =

Frequency of allele b: q =

Frequency of allele B: p =

Genotype frequency of BB: p2 =

Genotype frequency of Bb: 2pq =

Seed pods, which is an indicator of fecundity, was counted from the blue and pink lupins in the population. Based on the data, the relative fitness of each genotype were determined to be as follows:

WBB = 1 WBb = 1 Wbb = 0.667

Given these data, what can you say about how well blue lupins survive and reproduce compared to pink lupins in this environment?

Now, you want to predict how the composition of the lupin population will change over time due to natural selection. First, calculate the mean relative fitness of the parental population using the allele frequencies that you found above.

w=

Next, use the relative fitness and the mean relative fitness to calculate the genotype frequencies expected to be found in the next generation.

p2’ =

2pq’ =

q2’ =

Which phenotype of the flower color does natural selection favor in this environment? How can you tell? (1 pt)

Answer 1

frequency of pink flowers in the population): q2 = 43/3341 = 0.0129

Frequency of allele b: q = √q2 = √0.0129 = 0.1136 =0.11

Frequency of allele B: p = 1-q = 1-0.11 = 0.89

Genotype frequency of BB: p2 = 0.89 * 0.89 = 0.7921 = 0.79

Genotype frequency of Bb: 2pq =2*0.89*0.11 = 0.1958 = 0.196

WBB = 1 WBb = 1 Wbb = 0.667,

According to this data fitness of the homozygous dominant and heterozygous genotype is more than the recessive homozygous. Thus blue lupins survive and reproduce more than the pink lupins.

Mean relative fitness =

p2(wBB) + 2pq(wBb) + q2(wbb)

= 0.79*1 + 0.196 *1+ 0.0129*0.667 = 0.995 = 0.995

The genotype frequency calculated by using relative fitness and mean relative fitness

P2(1/0.995) + 2pq(1/0.995) + q2 ( 0.667/0.995)

0.794 + 0.197 + 0.009

Thus the value of p2 = 0.794

2pq' = 0.197

q2' = 0.009