The relative fitness values of three genotypes are wA / A=...

The relative fitness values of three genotypes are $w_{A / A}=$ $1.0, w_{A / a}=1.0,$ and $w_{a / a}=0.7$ a. If the population starts at the allele frequency $p=$ $0.5,$ what is the value of $p$ in the next generation? b. What is the predicted equilibrium allele frequency if the rate of mutation of $A$ to $a$ is $2 \times 10^{-5}$ ?

The relative fitness values of three genotypes are $w_{A / A}=$ $1.0, w_{A / a}=1.0,$ and $w_{a / a}=0.7$
a. If the population starts at the allele frequency $p=$
$0.5,$ what is the value of $p$ in the next generation?
b. What is the predicted equilibrium allele frequency if the rate of mutation of $A$ to $a$ is $2 \times 10^{-5}$ ?

Key Concepts

Mutation-Selection Balance

Mutation-selection balance is the equilibrium state achieved in a population when the rate at which deleterious alleles are removed by selection is balanced by the rate at which they are reintroduced by mutation. This balance determines the stable frequencies of alleles under opposing forces of mutation and selection, helping predict the long-term genetic structure of a population.

Mutation

Mutation is a change in the genetic material that can introduce new genetic variation into a population. In the context of allele frequency changes, mutation can create or substitute alleles and counteract the effects of natural selection, especially when there is a constant rate of mutation in one direction.

Natural Selection

Natural selection is the process by which genotypes with higher relative fitness increase in frequency over time due to their enhanced reproductive success. It acts on the variation present in a population, and changes allele frequencies in a way that tends to increase the overall fitness of the population.

Relative Fitness

Relative fitness is a measure of the reproductive success of a genotype compared to other genotypes within a population. It quantifies how differences in survival and reproduction contribute to changes in allele frequencies, with higher relative fitness indicating a greater contribution to the next generation.

Allele Frequency

Allele frequency refers to the proportion of a given allele among all alleles for a gene in a population. It is a key concept in population genetics as it provides insights into the genetic composition of populations and serves as a basis for predicting changes due to evolutionary forces such as selection, mutation, migration, and genetic drift.

Transcript

00:01 I was asking us about a situation where there's natural selection acting against the small a allele, that's the homosigous recessive.

00:08 So we need two equations because we're asked to find the frequency in a in the next generation.

00:14 And so that's going to be p prime.

00:15 So that'll be the frequency of big a in the next generation.

00:18 Equals p times p with the fitness of the homosigous dominant plus q times the heterocygous fitness.

00:28 And all of that divided by the average fitness.

00:33 Now, so obviously we need to have the average fitness.

00:36 And average fitness is simply p squared times the fitness plus 2pq times the heterozygous fitness and q squared times the homozygous recessive fitness like that.

00:55 And that's the way to calculate the average fitness.

00:58 And so we'll need this to plug into that.

01:00 So let's do that first.

01:02 We just have to plug our numbers in here.

01:06 So it's 0 .5.

01:09 That's what we get from the question squared times one.

01:12 That's the fitness of the homozygous dominant plus two, that two right there, times 0 .5.

01:19 Again, the frequency of p and q are both 0 .5 in this equation.

01:23 And then the heterozygous fitness is 1 .0.

01:27 And then finally we get to the q squared.

01:31 Which is 0 .5, and that's the frequency of the q allele squared, and then the fitness here.

01:37 And that was 0 .7.

01:38 So that's where we see the decrement of loss of fitness.

01:42 So if you do all of that math, and if i did it correctly, you get a value of 0 .925.

01:49 So we take that number and put it in there.

01:52 So that means that p prime equals 0 .5, and that's this p, and that's going to be times.

02:02 I think i'll put a bracket here to make this clearer.

02:06 0 .5 times the fitness, the average fitness, which is one, or not the average fitness, but the fitness of the hummus zygd dominant...

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