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 100 pink lupins and 2291 blue lupins, for a total of 2391.

1) Calculate the genotype and allele frequencies of this population, assuming that the population is in Hardy-Weinberg equilibrium. Show the answers in three significant figures. (0.2 pts each)

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

q² =

Frequency of allele b assuming Hardy-Weinberg equilibrium:

q =

Frequency of allele B assuming Hardy-Weinberg equilibrium:

p =

Genotype frequency of BB assuming Hardy-Weinberg equilibrium:

p² = ­­

Genotype frequency of Bb assuming Hardy-Weinberg equilibrium:

2pq =

2) 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:

ω_BB = 1                                 ω_Bb = 1                                 ω_bb = 0.667

Given these data, what can you say about how well blue lupins survive and reproduce compared to pink lupins in this environment? (1 pt)

(Continued on page 2)

Now, you want to predict how the composition of the lupin population will change over time due to natural selection.

3) First, calculate the mean relative fitness of the parental population using the provided relative fitness and genotype frequencies that you calculated above. Show the answer in three significant figures. Show your work (1 pt)

ϖ =

4) Next, use the current genotype frequencies, relative fitness and the mean relative fitness to calculate the genotype frequencies expected to be found in the next generation. Show the answer in three significant figures. Show your work. (0.67 pts each, total 2 pts)

p²’ =

2pq’ =

q²’ =

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

Answer 1

2) population is in Hardy-Weinberg equilibrium

Number of pink lupins=100

Number of Blue lupins= 2291

Genotypic frequency of pink bb (q^2)= number of pink / total number

= 100/2391

= 0.042

Frequency of pink allele (q)= square root of Genotypic frequency of pink

= square root of (0.042)

= 0.205

Frequency of Blue allele (p) + Frequency of pink allele (q)=1

Frequency of Blue allele (p) = 1-  Frequency of pink allele (q)

= 1- 0.205

= 0.795

Genotypic frequency of blue BB (p^2) = (Frequency of Blue allele)^2

= (0.795)^2

= 0.632

Genotypic frequency of heterozygote Bb ( 2pq)= 2* Frequency of Blue allele (p)* Frequency of pink allele (q )

= 2* 0.795*0.205

= 0.326