Question

A population in Chile that lives in a harsh desert environment had an outbreak of cholera during the summer that killed many people. This population was tested for the presence of CFTR alleles. The numbers of each genotype are shown below.

                     + / +             + / ∆ F508               ∆F508 / ∆F508          Total

Spring          1489             570                         91                          2150

Fall              780             570                         0                            1350

a. What is the fitness of each genotype?

b. What are the allele frequencies in the Fall population?

c. Assuming no further disease outbreaks occur, what will be the allele frequencies in the next generation?

d. What will be the genotype frequencies in this next generation?

e. Provide a biochemical, cellular, or molecular hypothesis as to why the three different genotypes should have different fitness.

Answer 1

Lets calculate the survival rate of each genotype first:

+ / + = 780/1489= 0.52 52%

+ / ∆ F508 = 570/570= 1 100%

∆F508 / ∆F508 = 0/91= 0 0%

Genotype with highest survival rate has highest fitness

fitness of +/+ = survival rate of genotype/maximum genotype= 0.52/1 =0.52

fitness of  + / ∆ F508 = 1/1= 1

fitness of ∆F508 / ∆F508= 0/1= 0

Now lets calculate allele frequencies in Fall population:

frequency of  + / + (p) = [780 +( 570/2)] / 1350 = 0.7889

frequency of  ∆F508 (q) = [0+(570/2)]/1350= 0.211..it can also be also 1-p as per hardy weinberg equation according to which  the sum of the allele frequencies for all the alleles at the locus must be 1, so p + q = 1

Now talking about question c) allele frequencies in next generation, The Hardy-Weinberg principle predicts that allelic frequencies remain constant from one generation to the next, or remain in equilibrium. Hence it will be same as previous generation. Unless some outside force is operating to change allele
frequencies, they will remain constant from generation to generation

Initial Genotype frequencies:

f(+ / + ) =p2= 0.7889*0.7889= 0.62

f(+ / ∆ F508 ) =2pq= 2*0.7889*0.2111= 0.33

f(∆F508 / ∆F508) = q2= 0.211*0.211= 0.044

Next generation frequencies=

Frequency of + allele from homozygotes = initial frequency is 0.62 and fractio of +/+ is 1 hence= 0.62*1 = 0.62

Frequency of + allele from hetrozygotes= initial frequency is 0.33 and fraction of +/+ is half= 0.33*0.5= 0.165

Overall frequency of +allele in next generation = 0.785 (0.62+0.165)

Similary for  ∆ F508   allele:

frequency from homozygotes= 0.044*1= 0.044

frequency from heterozygotes=  0.33*0.5= 0.165

Overall frequency of ∆ F508   allele in next generation= 0.044+0.165= 0.209

e.Provide a biochemical, cellular, or molecular hypothesis as to why the three different genotypes should have different fitness.

Ans: As part of a species lifecycle,  zygotes are produced which either become adults or do not survive .Mating happens after becoming adults. If everything is fine then these adults produce some number of offspring and the cycle begins . Differences in fitness among individuals can arise from differences in “performance” at any of these stages. Each of these “fitness components”— in this case, viability, mating success, fecundity— can contribute to differences in total fitness among individuals, i.e., can cause different individuals to leave different numbers of progeny.