One thousand Individualsfrom Britain typed for the alleles at two different bloo

Question

One thousand Individualsfrom Britain typed for the alleles at two different blood group loci, the MN and ST groupsrevealed the allele frequencies given below: f(M) = 0.5425f(S) = 0.3080f(N) = 0.4575f(T) = 0.6920Assuming starting genotypes in the population of MS/NT and the number of each haplotype is: f(MS) = 474f(MT) = 611f(NS) = 142f(NT) = 773a)Given the above haplotype numbers, what is the frequency for each haplotype in this population? b)What is the percentage of recombinant to parental haplotypes? c)What is the amount of disequilibrium (coefficient of linkage disequilibrium) among these loci? To calculate the theoretical maximum value of disequilibrium (Dmax), multiply the frequencies of each allele that forms a recombinanthaplotype (e.g., M*T and N*S). The theoretical maximum disequilibrium is the value of these multiplications that is less than 0.25. d)What is the theoretical maximum disequilibrium?e)What is the percentage of observed disequilibrium relative to the theoretical maximum you calculated? f)Calculate the recombination frequency for theabove gametes.g)What is the frequency of each haplotype in the next generation? h)Is the percentage of recombinant to parental haplotypes increasing or decreasing? i)Provide a biological explanation for your answer in part h).j)If calculations for haplotype frequencies were made for subsequent generations, what would be the equilibrium value for the recombinant to parental haplotype ratio? k)What would be the final value for the coefficient of linkage disequilibrium?l)Given the original allele frequencies atthe beginning of Problem 2, calculate the expected genotype frequencies and numbers of individuals (x1000) at each locus, i.e., MM, MN, and NN as well as SS, ST, and SS

Explanation / Answer

Given data: It is a 2 loci case
allele frequencies : f(M) = 0.5425, f(S) = 0.3080, f(N) = 0.4575, f(T) = 0.6920
No. of haplotypes : MS = 474, MT = 611, NS = 142, NT = 773, Total haplotypes = 2000
starting parent genotype MS/NT

a) frequency of each haplotype in the population:
f(MS) = 474/2000 = 0.237
f(MT) = 611/2000 = 0.3055
f(NS) = 142/2000 = 0.071
f(NT) = 773/2000 = 0.3865

b) since starting parent genotype is MS/NT the recombinant haplotypes are MT and NS.
% of recombinant to parent haplotype = [(total recombinant haplotypes)/(total parental haplotypes)] * 100
= [(MT + NS) / (MS + NT)]*100
= [(611+142)/(474+773)]*100
= (753/1247)*100 = 60.38%

c) the coefficient of linkage equlibrium D:
D = f(MS) - f(M)*f(S)
= 0.237 - (0.5425*0.3080) = 0.237 - 0.1671 = 0.067

d) Theoretical maximum of disequilibrium Dmax:
according to the question we calculate f(M)*f(T) = 0.5425*0.6920 = 0.3754 > 0.25 therefore we ignore this
f(N)*f(S) = 0.4575*0.3080 = 0.1409 < 0.25 therefore Dmax = 0.1409

e) % of observed disequilibrium to theoretical maximum = (D/Dmax) * 100
= (0.067/0.1409) * 100
= 47.55%

f) recombination frequency = (total recombinant haplotypes)/(total haplotypes)
=(MT + NS)/2000
= (611+142)/2000 = 753/2000 = 0.3765

g) I will be using a ( ' ) to denote next generation frequencies and I will assuming random mating for:
f '(MS) = f(M)*f(S) = 0.5425*0.3080 = 0.1671
f '(MT) = f(M)*f(T) = 0.5425*0.6920 = 0.3754
f '(NS) = f(N)*f(S) = 0.4575*0.3080 = 0.1409
f '(NT) = f(N)*f(T) = 0.4575*0.6920 = 0.3166

h) % of recombinant to parent haplotype in next generation = [(f '(MT)+f '(NS))/(f '(MS)+f '(NT))]*100
= [(0.3754+0.1409)/(0.1671/0.3166)]*100
= (0.5163/0.4837)*100 = 106.73%
This implies there are more recombinants in next generation than parent haplotypes.
The % of recombinant is increasing in the next generation.

i) We know that linkage disequilibrium converges to zero after several generations due to recombination. Here the linkage disequilibrium coefficient being nonzero is resulting in more recombinant haplotypes in the next generations.

j) the recombinant to parent haplotype ration will ratio will go to infinity at equilibrium point.

k) As stated in ' i ' the value of D will converge to zero.

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