Could you help me out with this question. I have read over the lesson and still feel like an idiot when it comes down this question. I understand hardy Weinberg equation but not this. Please help me understand this question.
Scientists observe a newly established population of sexually reproducing plants growing on the shore of a small island. An observable trait of the plant has two possible phenotypes. It is determined by a single gene, with the dominant allele having complete dominance over the recessive allele. The first generation had 26 plants with the dominant trait and 25 with the recessive trait. The data below is from the first six generations of this population:
Generation Number of individuals with dominant trait Number of individuals with recessive trait Total number of individuals
1 26 25 51
2 102 0 102
3 375 125 500
4 469 156 625
5 562 188 750
6 255 200 455
Answer each part of this question completely in the space provided.
Use the data to explain the changes in phenotypic frequency from generation 1 to 3.
Do you think this population is in Hardy-Weinberg equilibrium? Support your answer.
Propose a possible explanation for the change in phenotype frequency from generation 5 to generation 6.
To understand the changes in phenotypic frequency from generation 1 to 3, let's first calculate the frequencies of the dominant and recessive alleles for each generation. This will help us track the changes over time.
1. Calculating Allelic Frequencies:
- In generation 1, there are 26 individuals with the dominant trait and 25 with the recessive trait, making a total of 51 individuals. Let's calculate the allelic frequencies:
- Frequency of the dominant allele (p) = (2 * number of individuals with dominant trait) / total number of individuals
= (2 * 26) / 51 ≈ 1.02
- Frequency of the recessive allele (q) = (2 * number of individuals with recessive trait) / total number of individuals
= (2 * 25) / 51 ≈ 0.98
- In generation 2, there are 102 individuals with the dominant trait and 0 with the recessive trait, making a total of 102 individuals. Let's calculate the allelic frequencies:
- Frequency of the dominant allele (p) = (2 * number of individuals with dominant trait) / total number of individuals
= (2 * 102) / 102 = 2
- Frequency of the recessive allele (q) = (2 * number of individuals with recessive trait) / total number of individuals
= 0
- In generation 3, there are 375 individuals with the dominant trait and 125 with the recessive trait, making a total of 500 individuals. Let's calculate the allelic frequencies:
- Frequency of the dominant allele (p) = (2 * number of individuals with dominant trait) / total number of individuals
= (2 * 375) / 500 = 1.5
- Frequency of the recessive allele (q) = (2 * number of individuals with recessive trait) / total number of individuals
= (2 * 125) / 500 = 0.5
Now, let's analyze the changes in phenotypic frequency from generation 1 to 3:
1. Changes in Phenotypic Frequency:
- In generation 1, the number of individuals with the dominant trait is 26 and with the recessive trait is 25. The total number of individuals is 51.
- In generation 3, the number of individuals with the dominant trait is 375 and with the recessive trait is 125. The total number of individuals is 500.
The change in phenotypic frequency can be attributed to factors such as selection, migration, mutation, genetic drift, or non-random mating. These factors can impact the frequencies of alleles within a population.
Moving on to the second part of the question:
2. Hardy-Weinberg Equilibrium:
To determine if this population is in Hardy-Weinberg equilibrium, we need to check if the observed allelic frequencies match the expected frequencies calculated by the Hardy-Weinberg equation.
The Hardy-Weinberg equilibrium equation is:
p^2 + 2pq + q^2 = 1
Using the data from generation 1:
p = 1.02 (frequency of the dominant allele)
q = 0.98 (frequency of the recessive allele)
Calculating expected numbers in generation 1:
p^2 = (1.02)^2 ≈ 1.04
2pq = 2 * (1.02) * (0.98) ≈ 1.988
q^2 = (0.98)^2 ≈ 0.96
Adding the expected values:
1.04 + 1.988 + 0.96 ≈ 3.988
The observed numbers in generation 1 sum up to:
26 + 25 ≈ 51
The observed and expected values do not match. Therefore, this population is not in Hardy-Weinberg equilibrium. This could be due to violations of the assumptions of the Hardy-Weinberg equilibrium, such as non-random mating or the presence of evolutionary forces like selection or genetic drift.
Moving on to the last part of the question:
3. Change in Phenotype Frequency from Generation 5 to 6:
From generation 5 to generation 6, there is a decrease in individuals with the dominant trait (562 to 255) and an increase in individuals with the recessive trait (188 to 200). This change can be explained by factors such as natural selection, genetic drift, or changes in the mating patterns within the population. Without further information or analysis, it is difficult to determine the exact cause.
To analyze the changes in phenotypic frequency from generation 1 to 3, we need to compare the number of individuals with the dominant trait and the recessive trait across these generations.
From the given data:
Generation 1 had 26 individuals with the dominant trait and 25 individuals with the recessive trait.
Generation 2 had 102 individuals with the dominant trait and 0 individuals with the recessive trait.
Generation 3 had 375 individuals with the dominant trait and 125 individuals with the recessive trait.
To calculate the change in phenotypic frequency, we need to convert the numbers into frequencies by dividing the number of individuals with a particular trait by the total number of individuals.
For Generation 1, the frequency of the dominant trait can be calculated as: 26 / 51 = 0.51
The frequency of the recessive trait can be calculated as: 25 / 51 = 0.49
For Generation 3, the frequency of the dominant trait is: 375 / 500 = 0.75
And the frequency of the recessive trait is: 125 / 500 = 0.25
Therefore, the changes in phenotypic frequency from generation 1 to 3 are as follows:
- The frequency of the dominant trait increased from 0.51 to 0.75,
- While the frequency of the recessive trait decreased from 0.49 to 0.25.
From these changes, we can observe that the population is undergoing natural selection, favoring the dominant trait over the recessive trait. This could indicate that individuals with the dominant trait have a higher survival or reproductive advantage in the given environment.
Now, let's determine whether the population is in Hardy-Weinberg equilibrium. Hardy-Weinberg equilibrium is a theoretical concept that states that allele and genotype frequencies in a population remain constant over generations if certain conditions are met: no mutation, no migration, random mating, a large population size, and no natural selection.
In this case, we can see that the population is not in Hardy-Weinberg equilibrium because the phenotypic frequencies are changing over generations. Natural selection is favoring the dominant trait, meaning there is an unequal reproductive success among individuals with different phenotypes.
Finally, let's propose a possible explanation for the change in phenotype frequency from generation 5 to generation 6. Looking at the data, we see that the number of individuals with the dominant trait decreased from 562 in generation 5 to 255 in generation 6. At the same time, the number of individuals with the recessive trait increased from 188 in generation 5 to 200 in generation 6.
This change could be attributed to several factors such as genetic drift, migration, or external environmental pressures. For example, a catastrophic event like a hurricane or drought could have disproportionately affected individuals with the dominant trait, leading to a decrease in their population. Meanwhile, individuals with the recessive trait may have had some inherent resilience or advantages that allowed them to survive and reproduce more successfully in that particular generation.