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 3,398 blue lupins, for a total of 3,441.

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)

Answer 1

Given that Blue colour allele is dominant over pink allele. Blue allele(B) and pink (b). Relative fitness of all possible genotypes are also provided. Wbb represents relative fitness or Survival or reproductive rate of pink lupins is 0.667. so 0.667 is the survival rate of pink lupins relative to maximum Survival rate of blue lupins in population.

To predict how the composition of the lupin population will change over time due to natural selection.

We will first calculate the allele frequencies of pink and blue lupins.

According to Hardy-Weinberg equilibrium p^2 + q^2 + 2 p*q =1

So first we are calculating q^2 ( white lupins)

Pink lupins population= 43

Total = 3441.

q^2 = 43/3441

= 0.012496 = 0.0124

q = 0.1113 = 0.111 ( 3 significant figures).

Frequency of p = 1- q (according to Hardy-Weinberg equation)

p= 1- 0.111 = 0.889

p^2= 0.7903 = 0.790

Now we will find mean relative fitness =

Relative fitness of one genotype * genotype frequency and then add up all.

P^2 * wBB + q^2*wbb + 2pq * wBb

= 0.790 * 1 + 0.012 * 0.667 + 2*0.889*0.111 * 1

= 0.790 + 0.008 + 0.197

= 0.995

Now we will calculate expected genotype frequency in the next generation.

p^2= frequency in older population*relative fitness/0.995 (total population as predicted above)

p^2 =( 0.790 * 1)/ 0.995

p^2 = 0.793

wBB = 0.793

q^2 =( 0.012 * 0.667)/0.995

q^2 = 0.008/0.995

q^2 = 0.008 = wbb

2pq =( 2* 0.889 * 0.111 *1)/0.995

2pq= 0.197/0.995

2pq= 0.197 = wBb

So these represent the change in composition of lupin population over time due to natural selection.

Thank you....

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