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Step 1:
: Identify the false statement regarding sickle-cell alleles and malaria.

The given statements are as follows:

Step 2:

If a genetic disease reduces fertility and the allele that causes the disease offers no other advantage, the allele will likely eventually disappear, due to natural selection.

Step 3:

Natural selection does not favor individuals who are homozygous for the sickle-cell allele, because these individuals typically die before they are old enough to reproduce.

Step 4:

Individuals who are heterozygous $\boldsymbol{H b A} / \boldsymbol{H b S}$ are protected from malaria, and this is why sickle-cell disease persists in wetter, mosquito-prone regions in Africa.

Step 5:

In regions where malaria does not occur, individuals who are heterozygous $\boldsymbol{H b A} / \boldsymbol{H b S}$ have a fitness advantage over those who are homozygous for the normal hemoglobin allele (HbA).

Step 6:
: Analyze each statement.

Statement 1 is generally true. If a genetic disease reduces fertility and the allele does not provide any other advantage, the allele will likely eventually disappear due to natural selection. Statement 2 is true. Homozygous individuals for the sickle-cell allele (HbS/HbS) have sickle-cell anemia, which typically reduces their life expectancy and fertility. Statement 3 is true. Heterozygous individuals (HbA/HbS) have protection against malaria, which is why the sickle-cell allele persists in wetter, mosquito-prone regions in Africa. Statement 4 is false. In regions where malaria does not occur, there is no fitness advantage for heterozygous individuals (HbA/HbS) compared to homozygous individuals for the normal hemoglobin allele (HbA/HbA).

Step 7:
: Identify the false statement regarding the frequency of the HbS allele after malaria is cured.

The given statements are as follows:

Step 8:

People will no longer die from sickle-cell disease in these regions.

Step 9:

Having one copy of the HbS allele will no longer be advantageous in these regions.

Step 10:

Natural selection will no longer act on the HbS allele at all in these regions.

Step 11:

All alleles associated with genetic diseases eventually disappear.

Step 12:
: Analyze each statement.

Statement 1 is true. After malaria is cured, people will no longer die from sickle-cell disease in these regions. Statement 2 is true. After malaria is cured, having one copy of the HbS allele will no longer be advantageous in these regions. Statement 3 is false. Even after malaria is cured, natural selection will still act on the HbS allele, but the direction and strength of selection will change. Statement 4 is generally false. Not all alleles associated with genetic diseases will eventually disappear, as other factors (e.g., balancing selection, genetic drift, etc.) can maintain them in the population.

Final Answer

Statement 1 in Q^5.1 is true, Statement 2 is true, Statement 3 is true, and Statement 4 is false. Statement 1 in Q^5.2 is true, Statement 2 is true, Statement 3 is false, and Statement 4 is generally false.