β-thalassemia is a human genetic disease that is inherited in an autosomal recessive manner. Individuals with β-thalassemia produce abnormal hemoglobin which results in a reduced ability to carry oxygen in their blood. The severity of symptoms depends on several genetic and environmental factors and can vary from mild to fatal.
In this problem, we will use the letter "A" to represent the normal allele and the letter "a" to represent the β-thalassemia allele.
a) In Delhi, India, the frequency of the a allele is 0.03. Using the mathematics from lecture, estimate the following:
i)The frequency of β-thalassemia carriers (genotype Aa) in the Delhi population. Please express your answer as a number between 0.0000 and 1.0000. You may use as many significant digits as necessary.
ii)The frequency of people with β-thalassemia (genotype aa) in the Delhi population. Please express your answer as a number between 0.0000 and 1.0000. You may use as many significant digits as necessary.
b) Individuals with β-thalassemia are often partially resistant to malaria, a severely debilitating disease. Malaria is common in Delhi, India. In contrast, malaria is extremely rare in Iceland. Based on this, would you expect the frequency of the β-thalassemia allele to be higher, lower, or the same in Iceland as compared to Delhi?
Higher in Iceland than DelhiThe same in both placesLower in Iceland than Delhi
c) In Sardinia, approximately one in every 200 people has β-thalassemia. Using the mathematics from lecture, estimate the following:
i)The frequency of the β-thalassemia allele in the Sardinian population. Please express your answer as a number between 0.0000 and 1.0000. You may use as many significant digits as necessary.
ii)The frequency of β-thalassemia carriers (genotype Aa) in the Sardinian population. Please express your answer as a number between 0.0000 and 1.0000. You may use as many significant digits as necessary.
iii) Consider the following situation in the Sardinian population. An individual with β-thalassemia marries an unaffected individual of unknown genotype. On average, considering many such couples, what is the chance that their first child will have β-thalassemia? Please express your answer as a number between 0.0000 and 1.0000. You may use as many significant digits as necessary.
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In population genetics, we deal with traits in large groups of humans. We therefore use frequencies of alleles and genotypes rather than the genotypes of individual humans.
For a gene with two alleles, A and a, we can define:
p = the frequency of the A allele
q = the frequency of the a allele
Since there are only these two alleles, p + q = 1 always.
We can often make the following approximations:
The frequency of AA individuals = p2
The frequency of Aa individuals = 2pq
The frequency of aa individuals = q2
We will make these assumptions
its really easy...just do it like probability and keep in mind that p+q=1 and 2pq= Aa
i = 0.0582
ii=0.0009
b) 3
ai) 0.0582 ii) 0.0009
b) Lower
ci) 0.0582
ai) 0.0582 ii) 0.0009
b) Lower
ci) 0.0582 ii) 0.1 iii)0.05
To solve part a) of the problem, we will use the information given that the frequency of the "a" allele in Delhi is 0.03.
i) The frequency of β-thalassemia carriers (genotype Aa) in the Delhi population can be calculated using the formula 2pq, where p is the frequency of the "A" allele and q is the frequency of the "a" allele. Since p + q = 1, we can substitute q = 0.03 into the formula:
Frequency of Aa = 2pq = 2(0.97)(0.03) = 0.0582
Therefore, the frequency of β-thalassemia carriers in the Delhi population is 0.0582.
ii) The frequency of people with β-thalassemia (genotype aa) in the Delhi population can be calculated using the formula q^2, where q is the frequency of the "a" allele:
Frequency of aa = q^2 = (0.03)^2 = 0.0009
Therefore, the frequency of people with β-thalassemia in the Delhi population is 0.0009.
Now let's move on to part b) of the problem.
b) Based on the information given that individuals with β-thalassemia are often partially resistant to malaria and that malaria is common in Delhi but extremely rare in Iceland, we can infer that the frequency of the β-thalassemia allele might be higher in Iceland than in Delhi. This is because the β-thalassemia allele confers an advantage in regions with high malaria prevalence, as it provides some resistance against the disease. In contrast, in regions with low malaria prevalence, there is no selective advantage for the β-thalassemia allele, resulting in a lower frequency.
So, the correct option is: Higher in Iceland than Delhi.
Moving on to part c) of the problem.
i) The frequency of the β-thalassemia allele in the Sardinian population can be calculated using the formula q = √(frequency of aa). We are given that approximately one in every 200 people has β-thalassemia, so the frequency of aa can be calculated as 1/200 = 0.005.
Frequency of q = √(0.005) = 0.0707
Therefore, the frequency of the β-thalassemia allele in the Sardinian population is approximately 0.0707.
ii) Using the formula 2pq, where p is the frequency of the "A" allele and q is the frequency of the "a" allele, we can calculate the frequency of β-thalassemia carriers (genotype Aa) in the Sardinian population:
Frequency of Aa = 2pq = 2(0.9293)(0.0707) = 0.1319
Therefore, the frequency of β-thalassemia carriers in the Sardinian population is approximately 0.1319.
iii) For this part, we assume that the unaffected individual is heterozygous (Aa), as we don't know their genotype. The probability that their first child will have β-thalassemia can be calculated using the formula 1/4, as the unaffected individual has a 1/2 chance of passing on the "a" allele, and the β-thalassemia individual will always pass on the "a" allele.
Therefore, the chance that their first child will have β-thalassemia is 1/4 or 0.25.