Answer :
To understand which set of genotype fitnesses would lead to the eventual loss of [tex]\( A_1 \)[/tex] but take a very long time to be lost, we need to analyze the fitness values for each genotype.
1. Fitness of [tex]\( A_1A_1: 0.1 \)[/tex], fitness of [tex]\( A_1A_2: 1.0 \)[/tex], fitness of [tex]\( A_2A_2: 0.80 \)[/tex]:
- [tex]\( A_1A_1 \)[/tex] has a relatively low fitness of 0.1, indicating that [tex]\( A_1 \)[/tex] homozygotes are at a disadvantage.
- [tex]\( A_1A_2 \)[/tex] has the highest fitness (1.0), suggesting heterozygotes have a selective advantage.
- [tex]\( A_2A_2 \)[/tex] also has a reasonable fitness of 0.80.
- Given these values, [tex]\( A_1 \)[/tex] would be selected against, but its presence in the heterozygote [tex]\( A_1A_2 \)[/tex] would slow down its loss over time due to the high fitness of heterozygotes.
2. Fitness of [tex]\( A_1A_1: 0.05 \)[/tex], fitness of [tex]\( A_1A_2: 1.0 \)[/tex], fitness of [tex]\( A_2A_2: 0.85 \)[/tex]:
- [tex]\( A_1A_1 \)[/tex] has an even lower fitness of 0.05, indicating [tex]\( A_1 \)[/tex] homozygotes are at an even greater disadvantage compared to the first option.
- [tex]\( A_1A_2 \)[/tex] maintains the selective advantage with a fitness of 1.0.
- [tex]\( A_2A_2 \)[/tex] has a slightly higher fitness of 0.85 compared to the first option.
- Similar to the first set, [tex]\( A_1 \)[/tex] would be selected against, but the further reduced fitness of [tex]\( A_1A_1 \)[/tex] suggests [tex]\( A_1 \)[/tex] would be lost more quickly than in the first set.
3. Fitness of [tex]\( A_1A_1: 0.80 \)[/tex], fitness of [tex]\( A_1A_2: 1.0 \)[/tex], fitness of [tex]\( A_2A_2: 0.1 \)[/tex]:
- Here, [tex]\( A_1A_1 \)[/tex] has a high fitness of 0.80.
- [tex]\( A_1A_2 \)[/tex] again has the highest fitness of 1.0.
- [tex]\( A_2A_2 \)[/tex] has a very low fitness of 0.1, indicating that [tex]\( A_2 \)[/tex] homozygotes are at a significant disadvantage.
- Under these conditions, [tex]\( A_2 \)[/tex] would be the allele selected against, not [tex]\( A_1 \)[/tex].
4. Fitness of [tex]\( A_1A_1: 0 \)[/tex], fitness of [tex]\( A_1A_2: 1.0 \)[/tex], fitness of [tex]\( A_2A_2: 0.80 \)[/tex]:
- [tex]\( A_1A_1 \)[/tex] has a fitness of 0, meaning [tex]\( A_1 \)[/tex] homozygotes have no chance of survival or reproduction.
- [tex]\( A_1A_2 \)[/tex] has the highest fitness of 1.0.
- [tex]\( A_2A_2 \)[/tex] has a decent fitness of 0.80.
- With a fitness value of 0 for [tex]\( A_1A_1 \)[/tex], [tex]\( A_1 \)[/tex] would be lost quite rapidly as any [tex]\( A_1 \)[/tex] homozygote would not contribute to the next generation.
By comparing these options, it's clear that the set of genotype fitnesses which would lead to the eventual loss of [tex]\( A_1 \)[/tex] but take the longest time is:
- Fitness of [tex]\( A_1A_1: 0.1 \)[/tex], fitness of [tex]\( A_1A_2: 1.0 \)[/tex], fitness of [tex]\( A_2A_2: 0.80 \)[/tex].
Thus, the correct answer is the second option listed. This set of fitness values ensures [tex]\( A_1 \)[/tex] is eventually lost but retains enough presence in the population through [tex]\( A_1A_2 \)[/tex] heterozygotes to slow down the overall rate of loss considerably.
1. Fitness of [tex]\( A_1A_1: 0.1 \)[/tex], fitness of [tex]\( A_1A_2: 1.0 \)[/tex], fitness of [tex]\( A_2A_2: 0.80 \)[/tex]:
- [tex]\( A_1A_1 \)[/tex] has a relatively low fitness of 0.1, indicating that [tex]\( A_1 \)[/tex] homozygotes are at a disadvantage.
- [tex]\( A_1A_2 \)[/tex] has the highest fitness (1.0), suggesting heterozygotes have a selective advantage.
- [tex]\( A_2A_2 \)[/tex] also has a reasonable fitness of 0.80.
- Given these values, [tex]\( A_1 \)[/tex] would be selected against, but its presence in the heterozygote [tex]\( A_1A_2 \)[/tex] would slow down its loss over time due to the high fitness of heterozygotes.
2. Fitness of [tex]\( A_1A_1: 0.05 \)[/tex], fitness of [tex]\( A_1A_2: 1.0 \)[/tex], fitness of [tex]\( A_2A_2: 0.85 \)[/tex]:
- [tex]\( A_1A_1 \)[/tex] has an even lower fitness of 0.05, indicating [tex]\( A_1 \)[/tex] homozygotes are at an even greater disadvantage compared to the first option.
- [tex]\( A_1A_2 \)[/tex] maintains the selective advantage with a fitness of 1.0.
- [tex]\( A_2A_2 \)[/tex] has a slightly higher fitness of 0.85 compared to the first option.
- Similar to the first set, [tex]\( A_1 \)[/tex] would be selected against, but the further reduced fitness of [tex]\( A_1A_1 \)[/tex] suggests [tex]\( A_1 \)[/tex] would be lost more quickly than in the first set.
3. Fitness of [tex]\( A_1A_1: 0.80 \)[/tex], fitness of [tex]\( A_1A_2: 1.0 \)[/tex], fitness of [tex]\( A_2A_2: 0.1 \)[/tex]:
- Here, [tex]\( A_1A_1 \)[/tex] has a high fitness of 0.80.
- [tex]\( A_1A_2 \)[/tex] again has the highest fitness of 1.0.
- [tex]\( A_2A_2 \)[/tex] has a very low fitness of 0.1, indicating that [tex]\( A_2 \)[/tex] homozygotes are at a significant disadvantage.
- Under these conditions, [tex]\( A_2 \)[/tex] would be the allele selected against, not [tex]\( A_1 \)[/tex].
4. Fitness of [tex]\( A_1A_1: 0 \)[/tex], fitness of [tex]\( A_1A_2: 1.0 \)[/tex], fitness of [tex]\( A_2A_2: 0.80 \)[/tex]:
- [tex]\( A_1A_1 \)[/tex] has a fitness of 0, meaning [tex]\( A_1 \)[/tex] homozygotes have no chance of survival or reproduction.
- [tex]\( A_1A_2 \)[/tex] has the highest fitness of 1.0.
- [tex]\( A_2A_2 \)[/tex] has a decent fitness of 0.80.
- With a fitness value of 0 for [tex]\( A_1A_1 \)[/tex], [tex]\( A_1 \)[/tex] would be lost quite rapidly as any [tex]\( A_1 \)[/tex] homozygote would not contribute to the next generation.
By comparing these options, it's clear that the set of genotype fitnesses which would lead to the eventual loss of [tex]\( A_1 \)[/tex] but take the longest time is:
- Fitness of [tex]\( A_1A_1: 0.1 \)[/tex], fitness of [tex]\( A_1A_2: 1.0 \)[/tex], fitness of [tex]\( A_2A_2: 0.80 \)[/tex].
Thus, the correct answer is the second option listed. This set of fitness values ensures [tex]\( A_1 \)[/tex] is eventually lost but retains enough presence in the population through [tex]\( A_1A_2 \)[/tex] heterozygotes to slow down the overall rate of loss considerably.
