Question

An allele, A₁, in a diploid population of size N, starts at an allele frequency of 0.7. What is the expected allele frequency in the next generation? In the 100^thgeneration? What is the probability that the allele frequency will increase in the next generation? If you follow 100 populations that start with the same conditions for millions of generations, how many would you expect to be fixed for A₁?

Answer 1

ANSWER 1:-

1. In the diploid organism, there will be two alleles for a particular trait and in the above mentioned query, allele A1 is stated to have an allele frequency of 0.7.

2. Lets consider allele A1 as a dominant allele and allele A2 be the recessive allele. Then the value of p=0.7 and q=1-p = 1-0.7 = 0.3. Hence, the genotype frequency will be p² = 0.7×0.7 = 0.49 and q² = 0.3×0.3 = 0.09.

3. Frequency of heterozygous condition will be 2pq = 2 × (0.7) × (0.3) = 0.42. This is calculated taking into consideration that the population is in Hardy-Weinberg equilibrium.

4. After one generation (n), the allele frequency of A1 is given as:-

Allele frequency of A1 ( after n generation ) = p² + 1/2 × 2pq = (0.49) + 1/2 × (0.42) = (0.49) + (0.21) = 0.70.

Conclusion:- Hence, after one generation or in the next generation, the allele frequency will not change taking into consideration the population remains in Hardy-Weinberg equilibrium.

ANSWER 2:-

1. After 100 generation, the allele frequency can be calculated in the form of taking the value in context with (n+1) generation.

2. So, Frequency of allele A1 in 100th generation will also remains constant unless genetic drift or mutation occurs.

A1 frequency = p² + 1/2 (2pq)

= p² + pq

= p (p+q) ...but q=1-p

= p (p+1-p)

= p (1)

= p

Hence the allele frequency will remain constant.

Note:- The answer has been stated on the basis of minimum answering guidelines. For any doubt, please prefer comment section.

Answer 2

To calculate the expected allele frequency in the next generation, we can use the Hardy-Weinberg principle. The Hardy-Weinberg principle states that in an idealized population under certain conditions (such as random mating, no mutation, no migration, and no natural selection), the allele frequencies remain constant from one generation to the next.

Let p be the frequency of allele A1 and q be the frequency of the other allele in the current generation.

1. Expected Allele Frequency in the Next Generation (t = 1): According to the Hardy-Weinberg principle, in the absence of any evolutionary forces, the allele frequencies will remain the same from generation to generation. Therefore, the expected allele frequency in the next generation (t = 1) will be the same as the current frequency:

p(t=1) = 0.7

2. Expected Allele Frequency in the 100th Generation (t = 100): Similarly, in the 100th generation (t = 100), the expected allele frequency will remain the same:

p(t=100) = 0.7

3. Probability of Increasing Allele Frequency in the Next Generation (t = 1): The probability of an allele frequency increasing in the next generation depends on the initial frequencies and the random sampling of alleles during mating. In this case, the allele A1 has an initial frequency of 0.7.

The probability of an increase in frequency (p increase) can be calculated as follows:${�}_{\text{increase}}=2��$

where p and q are the allele frequencies in the current generation. Since we know that p = 0.7 and q = 1 - p, we can calculate:

${�}_{\text{increase}}=2\times 0.7\times (1-0.7)=2\times 0.7\times 0.3=0.42$

So, the probability that the allele frequency of A1 will increase in the next generation is 0.42 (or 42%).

4. Number of Populations Fixed for A1: If we follow 100 populations starting with the same conditions (allele frequency of A1 = 0.7) for millions of generations, the probability that an individual population becomes fixed for allele A1 depends on the initial frequency and random sampling during mating.

The probability of fixation of an allele is equal to its initial frequency (p) in a diploid population. So, in this case, the probability of a population becoming fixed for allele A1 is 0.7 (or 70%).

However, it's essential to note that this probability is only an estimate, and there will still be fluctuations due to random genetic drift in each population.

Keep in mind that the Hardy-Weinberg principle is an idealized model, and in real populations, evolutionary forces such as selection, mutation, migration, and genetic drift can cause changes in allele frequencies over time.

Answer 3

To determine the expected allele frequency in the next generation, we can use the Hardy-Weinberg principle. The Hardy-Weinberg principle describes the relationship between allele and genotype frequencies in an idealized, non-evolving population.

In a diploid population, if we assume random mating, no selection, no mutation, and no migration, the expected allele frequency in the next generation (p') can be calculated using the formula:

p' = (p * (N-AA) + 0.5 * h * (N-Aa)) / N

Where: p = current allele frequency (0.7 in this case, as the A1 allele starts at a frequency of 0.7) N = population size AA = number of individuals homozygous for the A1 allele Aa = number of individuals heterozygous for the A1 allele h = proportion of heterozygotes that contribute one copy of A1 allele to the next generation (0.5 in case of random mating)

Let's calculate the expected allele frequency in the next generation and in the 100th generation:

1. Expected allele frequency in the next generation: Let's assume the population size (N) is 100 individuals for simplicity.

p' = (0.7 * (100-AA) + 0.5 * 0.5 * (100-Aa)) / 100

Since the current generation is the starting generation and there has been no time for evolution to occur, we can assume Hardy-Weinberg equilibrium and the frequencies of genotypes will be given by the Hardy-Weinberg equation:

p^2 + 2pq + q^2 = 1

where p is the frequency of allele A1, q is the frequency of allele A2, and p^2, 2pq, and q^2 are the frequencies of genotypes AA, Aa, and aa, respectively.

In the starting generation (generation 0): p^2 = 0.7^2 = 0.49 2pq = 2 * 0.7 * 0.3 = 0.42 q^2 = 0.3^2 = 0.09

Thus, in the next generation (generation 1): p' = frequency of A1 allele in generation 1 = p^2 + 0.5 * 2pq = 0.49 + 0.5 * 0.42 = 0.7

So, the expected allele frequency in the next generation is 0.7 (same as the current allele frequency).

2. Expected allele frequency in the 100th generation: Since the population is assumed to be at Hardy-Weinberg equilibrium, the expected allele frequency will remain constant over generations. Therefore, the expected allele frequency in the 100th generation will also be 0.7.

3. Probability that the allele frequency will increase in the next generation: Since the expected allele frequency in the next generation is the same as the current allele frequency (0.7), the probability of the allele frequency increasing in the next generation is 0 (as it is not expected to change).

4. Number of populations expected to be fixed for A1 in millions of generations: If the allele frequency is 0.7, then the frequency of the alternative allele (A2) is 0.3. In an idealized, non-evolving population (under Hardy-Weinberg equilibrium), the frequency of A2 will remain constant over generations as well. In the long run, the proportion of populations that become fixed for A1 will be equal to the initial frequency of A1.

So, in millions of generations, we would expect approximately 70% of the populations to be fixed for A1.