Hardy-Weinberg problem set
Hardy-Weinberg Theorem states that if a population is NOT evolving then the frequencies of the alleles in the population will remain stable across generations - it is in equilibrium.
We can use the Hardy-Weinberg equation to make predictions about the relative frequency of the different alleles (as well as the associated genotypes), even if there is population growth, as long as the five conditions we discussed in class hold true. Think about what those five conditions are.........
no mutations, no natural selection, no gene flow, large population size, random mating
Alternatively, Hardy-Weinberg equation can be a means to determine if a population is indeed evolving - that the allele frequencies are changing and therefore NOT at equilibrium.
The trick to using the Hardy-Weinberg equation to help evaluate the frequency of a particular allele frequency at time X, or to make a prediction about the frequency of a particular genotype/phenotype in future generations, is to go through the math is a step-by-step manner.
For the problems below assume all genes have only two alleles and there is a simple dominant recessive relationship.
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1. Lets say that brown fur coloring is dominant to gray fur coloring in mice. If you have 168 brown mice in a population of 200 mice........
Again start with what you know -- if 168 out of 200 are brown, that means 32 mice must be gray. There are only two phenotypes (three genotypes). So the first step is to determine q2.
Why don't you start with p2 since I given you the frequency of the dominant phenotype?
Think about it -- you have two DIFFERENT genotypes that can give you the dominant phenotype. Homozygous dominant and heterozygotes. So the frequency of the dominant phenotype would be:
frequency of dominant phenotype = p2 + 2pq
You can't solve for p, if both p and q are unknown. So solve for q first ---
q2 = (32/200) = 0.16
q = 0.4
p = 1 - (0.4) = 0.6
What is the predicted frequency of heterozygotes?
2pq = 2 (0.6)(0.4) = 0.48
What is the predicted frequency of homozygous dominant?
p2 = (0.6)(0.6) = 0..36
What is the predicted frequency of homozygous recessive?
q2 = (0.4)(0.4)= 0.16
p2 + 2pq + q2 = 1
0.16 + 0.48 + 0.36 = 1.0
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2. If 81% of a population is homozygous recessive for a given trait.......... Note questions are out of order in how you should figure out the answers -- I have indicated the order in which I would answer the questions.
(STEP 2) What is the predicted frequency of homozygous dominant?
p2 = p * p or 0.1 * 0.1 = 0.01
(STEP 3) What is the predicted frequency of heterozygotes?
2pq = 2(0.1)(0.9) = 0.18
(STEP 1) What is the frequency of the dominant and recessive alleles in the population?
In order to figure this out you need to know what p (frequency of the dominant allele) -
You know q2 = .81 (frequency of homozygous recessive)
q = square root of 0.81 or 0.9 = the frequency of the recessive allele
p = 1-q or 1-0.9 = 0.1 - the frequency of the dominant allele
(STEP 4) DOUBLE CHECK:
p2 + 2pq + q2 = 1
0.01 + 0.18 + 0.81 = 1
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3. If 51% of the population carries at least one copy of the recessive allele....... Note questions are out of order in how you should figure out the answers -- I have indicated the order in which I would answer the questions.
(STEP 2) What is the predicted frequency of individuals in the population that express the dominant phenotype?
the predicted frequency of individuals who express the dominant phenotype are:
frequency of homozygous dominant + the frequency of heterozyotes or
p2 + 2pq
(0.7 * 0.7) + (2(0.7)(0.3)
0.49 + 0.42 = 0.91
(STEP 3) What is the predicted frequency of individuals in the population that express the recessive phenotype?
frequency of individuals with the recessive phenotype is the frequency of homozgyous recessive or q2
q2 = q * q or 0.3 * 0.3 = 0.09
Note the above answer and this one equals 1 which is a good double check
p2+2pq+q2 = 1
0.49 + 0.42 + 0.09 = 1
(STEP 1) - the information in the question gives you the % of individuals who are homozygous dominant, but not who expressive the dominant phenotype (which would be homozygous dominant and heterozygotes).
So need to solve for q and p and then answer the questions above:
p2 (frequency of homozygous dominant) would be equal to 100%-51% or 49% or 0.49
p = the square root of 0.49 or 0.7
q = 1-p or 1-0.7 = 0.3