Population Allele-Frequency Charts (Hardy-Weinberg)
Read a bar chart of allele or genotype frequencies, use p + q = 1, and predict genotype proportions with p^2 + 2pq + q^2 = 1.
A gene often comes in two versions (alleles), and how common each version is in a population is not a single number about one person: it is a rate for the whole group. Allele-frequency charts turn that idea into a picture you can read. The letter p stands for the fraction of one allele and q for the other, and because those are the only two choices, p + q = 1. Hardy-Weinberg goes one step further and predicts how those alleles pair up into genotypes: p^2 + 2pq + q^2 = 1. Genetic counselors use these numbers to tell a family the chance a child inherits a condition. Public-health epidemiologists use them to compare disease-allele frequencies between populations and to see whether an allele is becoming more or less common over time. Conservation biologists use them to watch whether a small animal population is losing genetic variety. Read the chart correctly and you can answer real risk questions with arithmetic instead of guesswork.
- Common Core · HSS-ID.A.1Represent data with plots on the real number line and summarize distributions, including reading and comparing bar charts of category frequencies.
- Common Core · HSN-Q.A.1Use units and quantities to interpret problems, treating a frequency as a fraction of a whole and checking that parts sum to one.
- NGSS · SEP-4Analyzing and Interpreting Data: read a population frequency chart, compare two populations, and describe change across generations.
- NGSS · SEP-5Using Mathematics and Computational Thinking: apply p + q = 1 and p^2 + 2pq + q^2 = 1 to compute allele and genotype proportions.
- AP · AP Bio SP 6 (Quantitative)Perform quantitative analysis, including the Hardy-Weinberg equations, to predict allele and genotype frequencies in a population.
- Convert between fractions, decimals, and percents: Allele frequencies are written as decimals (0.7) and percents (70 percent), so students must move between the forms.
- Read a value off a bar chart: Every problem here starts by reading a bar height, so students must map a bar to its number on the axis.
- Understand that parts of a whole add to one: p + q = 1 and p^2 + 2pq + q^2 = 1 only make sense if students know all the fractions of a group sum to one.
Prerequisites are inferred: pending teacher review.
Re-learn the skill with worked practice and clear examples.
Read the allele or genotype bars off the chart, then use Hardy-Weinberg to connect them: p^2 is the AA fraction, 2pq is the Aa (carrier) fraction, and q^2 is the aa fraction, and they add to one. You can also work backward from a bar: if the aa bar is q^2, then q is its square root.
Read the allele-frequency chart. What is the frequency q of the a allele?
Reviewed- A.0.7
- B.0.3
- C.0.4
- D.1.0
Show the worked solution ▾
Answer: B. 0.3
- Step 1: Read the A bar: The A bar is labeled 0.7, so p = 0.7.
- Step 2: Use p + q = 1: q = 1 - p = 1 - 0.7 = 0.3, which matches the a bar sitting at the 0.3 line.
Why it's right: The A bar reads 0.7, so p = 0.7, and q = 1 - 0.7 = 0.3.
- A: This is p (the A bar), not q (the a bar).
- C: This misreads the a bar as reaching 0.4 instead of 0.3.
- D: This is p + q, the total, not q by itself.
Aligned to NGSS SEP-4: read a value off a chart and apply p + q = 1 · reading level ~grade 9
In a population, p = 0.6 for the A allele and q = 0.4 for the a allele. Using Hardy-Weinberg, what fraction of individuals are the heterozygous carrier genotype Aa? (Aa = 2pq)
Reviewed- A.0.24
- B.0.36
- C.0.48
- D.0.16
Show the worked solution ▾
Answer: C. 0.48
- Step 1: Write the carrier formula: The heterozygous fraction is 2pq.
- Step 2: Multiply: 2 x 0.6 x 0.4 = 0.48.
Why it's right: The Aa fraction is 2pq = 2 x 0.6 x 0.4 = 0.48.
- A: This is just p x q = 0.24, forgetting the factor of 2.
- B: This is p^2 (the AA fraction), not 2pq.
- D: This is q^2 (the aa fraction), not 2pq.
Aligned to AP Bio SP 6: apply 2pq for the heterozygous fraction · reading level ~grade 9
A recessive condition appears in the aa genotype. In one population the aa fraction is q^2 = 0.09. What is the frequency q of the a allele?
Reviewed- A.0.09
- B.0.30
- C.0.03
- D.0.18
Show the worked solution ▾
Answer: B. 0.30
- Step 1: Recognize the aa bar is q^2: The aa genotype fraction equals q^2, and here that value is 0.09.
- Step 2: Take the square root: q = square root of 0.09 = 0.3.
Why it's right: Since aa = q^2 = 0.09, the allele frequency q is the square root of 0.09, which is 0.3.
- A: This is q^2 itself (the aa fraction), not q.
- C: This is 0.09 divided by 3, not the square root of 0.09.
- D: This doubles 0.09 instead of taking its square root.
Aligned to AP Bio SP 6: work backward from q^2 to q · reading level ~grade 9
- A genetic counselor reads an allele bar of 0.6 for A, computes 2pq = 0.48, and tells a couple that about 48 percent of the population are carriers.
- A student sees the aa bar at 0.09, takes the square root to get q = 0.3, and then finds p = 0.7.
- A biology class checks a chart's three genotype bars (0.36, 0.48, 0.16) add to 1 before using them.
Fill these in as you work through the lesson.
- Allele (one version of a gene (A or a)):
- Allele frequency (p, q) (fraction of gene copies that are that allele):
- Genotype (the allele pair a person has (AA, Aa, aa)):
- Hardy-Weinberg (p^2 + 2pq + q^2 = 1 for genotype fractions):
Because there are only two alleles, p + q = , and the genotype fractions are AA = p^2, Aa = , and aa = q^2, which add up to .
- If the A bar on a chart reads 0.7, what is q, and how did you get it?
- Which genotype does the 2pq term count, and why is there a 2 in front?
- If the aa bar is q^2 = 0.16, how do you find q from it?
A chart shows p = 0.6 for A. First find q = 1 - 0.6 = ____. Then the carrier fraction Aa = 2pq = 2 x 0.6 x ____ = ____.
The vocabulary of this topic, shown in the way you will meet it.