STUDY GUIDE
Selection, Gene Pools, Hardy-Weinberg Equilibrium
If we define evolution as change in the phenotypes and genotypes of a population over time, then natural selection is the main way that evolution can bring about organisms with adaptations that suit their environment. Natural selection is the tendency of organisms that are better suited to their environment to have more successful offspring, causing them to become more prevalent in a population.
Study Question 1:
Natural selection can select against some genetic variants (alleles) in a population and cause others to take over... but where do these variations in genes come from in first place? In other words, what is the source of the diversity that allows evolution to occur? (Hint: What are genes made of? What do we call a change in that stuff?)
To understand how natural selection can change a population, we need some way of looking at all the alleles in the population. We call the full set of alleles in a population the gene pool. Suppose we have a population of 200 rats with coat color alleles B and b. There are three ways of describing the gene pool:
1) Giving the number of individuals with each genotype. Example: The gene pool consists of 50 BB individuals, 100 Bb individuals, and 50 bb individuals.
2) Giving the percentage/fraction of individuals with each genotype. Example: For the gene pool just given, the fraction of BB individuals is .25, the fraction of Bb individuals is .50, and the fraction of bb individuals is .25. (Or 25%, 50%, and 25%). This is because there are 200 total individuals. 50/200 = 25%, 100/200 = 50%, 50/200 = 25%
3) Giving the frequency of each allele in the gene pool. In that gene pool, half of the alleles are B, and half are b. So p, the frequency of B alleles, is .50, and q, the frequency of b alleles, is .50 as well. Key point: If there are only 2 alleles, p and q must add up to 1! p + q = 1, and 1 - p = q.
In problems, the gene pool will frequently be described using method 1 or 2, and you'll have to calculate the allele frequency (p and q).
If method 1 is used, you can obtain the frequency of an allele by counting the total number of alleles in the population, then dividing by the number of copies of that allele. In this example, the total number of alleles is 400, since there are 200 individuals each with 2 alleles. There are 200 B alleles (50 x 2 total from the BB individuals and 100 from the Bb individuals), and 200 b alleles. So the frequency of each is 200/400.So p = .50, q = .50.
If method 2 is used, and you're given percentages of each genotype, you can use the following logic. Suppose 50% of the individuals are Bb. Only half of those alleles are B, so those heterozygotes only contribute 25% B to the gene pool. If 25% of the individuals are BB, then that adds another 25% B to the gene pool (since all of the alleles of these individuals are B alleles.) In that case, the total percentage of B alleles is 50%, and p = .5.
It takes practice to make sense of this, so let's try two problems.
Practice Problem 2:
A population of 1000 fruit flies contains 160 white-eyed flies with genotype ww, 480 red-eyed flies with genotype Ww, and 360 red-eyed flies with genotype WW. If p represents the fraction the gene pool that consists of W alleles and q represents the fraction of w alleles, what are p and q?
Practice Problem 3:
A population of fruit flies contains 4% ww flies, 32% Ww flies, and 64% WW flies. Calculate p and q.
Once you've found the percentage of the gene pool that consists of each allele, it is possible to make predictions about the next generation, assuming the population is in Hardy-Weinberg equilibrium. Hardy-Weinberg equilibrium only works when you assume large populations of individuals that mate totally randomly, without any natural selection or migration. While these assumptions are unrealistic, they give us a hypothesis to compare to the real-world data. Differences between reality and these predictions can help us figure out how selection and mating are really working!
Under Hardy-Weinberg equilibrium, the frequency of homozygotes for an allele is equal to the square of that allele's frequency. In other words, if p represents the frequency of W alelles, then p2 would give us the expected percentage of WW offspring. Likewise, if q is the fraction of w alleles, then q2 gives the percentage of ww offspring.
To get the percentage of heterozygotes, we need to multiply both frequencies, p and q, and then double the result to take into account that there are two possible ways of being a heterozygote: either inheriting the dominant allele from the mother and the recessive allele from the father, or the other way around. In this case, the expected frequency of Ww offspring is 2 * p * q.
All of these frequencies need to add up to 1, since percentages need to add up to 100%. So p2 + 2pq + q2 = 1.
Practice Problem 4:
A population of cats has two coat color alleles: S and s (for spotted/not spotted). The percentage of S alleles in the gene pool is 30% (or .30). What is the percentage of s alleles? Assuming Hardy-Weinberg equilibrium, what percentage of SS, Ss and ss cats do you expect to see in the next generation?
Practice Problem 5:
A rare autosomal recessive disease might have an allele fraction p = .0001. What is the percentage of offspring in a population that you would expect to be homozygous for this allele, assuming Hardy-Weinberg equilibrium?