Difficulty: Intermediate | Prerequisites: Part 1 study notes (allele frequency calculations, HW equilibrium basics).
This set of notes builds on Hardy-Weinberg equilibrium by looking at what happens when HW assumptions are violated, specifically through mutation and natural selection. The central question is: how do allele frequencies change when some genotypes survive better than others?
The problems here cover the relationship between mutation and selection, how to work backwards from phenotype counts to allele frequencies when dominance patterns vary, and how to use mortality data to infer pre-selection genotype frequencies. These are the kinds of applied problems that show up on exams, and they require you to combine HW maths with biological reasoning about what selection is doing.
You should be comfortable calculating allele frequencies, using p² + 2pq + q² = 1, and naming the five HW assumptions before working through this material.
Mutation creates new genetic variation ("proposes"), while natural selection determines which variants persist ("disposes"). You can use HW maths backwards, starting from survival or mortality data to infer allele and genotype frequencies before selection acted. When selection pressure changes over time (e.g. pesticide resistance), shifts in allele frequencies explain why a treatment becomes less effective.
Natural selection
The process by which individuals with certain heritable traits survive and reproduce at higher rates than individuals with other traits. Over generations, this changes allele frequencies in the population.
In simple terms, this means: some versions of a gene help organisms survive or reproduce better, so those versions become more common over time.
Mutation
A heritable change in DNA sequence. Mutations are the ultimate source of all new genetic variation. They are random with respect to fitness: a mutation does not arise because the organism "needs" it.
Think of it as: mutation is the raw material. It generates the options that selection then sorts through.
Incomplete dominance
A pattern where the heterozygote has a phenotype intermediate between the two homozygotes. Neither allele fully "dominates" the other.
In simple terms, this means: if SS is short and LL is long, then SL is medium. You can tell all three genotypes apart by looking at the phenotype.
Resistance allele
An allele that confers survival advantage against an environmental pressure (e.g. a pesticide, an antibiotic). Often recessive, meaning it only protects in homozygous individuals.
Think of it as: the genetic variant that lets an organism survive something that kills most of the population.
Directional selection
Selection that consistently favours one extreme phenotype, shifting the population's allele frequencies in one direction over time.
In simple terms, this means: one allele keeps getting more common because it helps organisms survive or reproduce better than the alternative.
This is one of the most commonly quoted principles in evolutionary biology. It captures the distinct roles of two evolutionary forces.
Mutation "proposes": Mutation is the only source of new alleles. Without mutation, there would be no genetic variation for selection to act on. Mutations arise randomly, not in response to environmental need. A bacterium does not "decide" to mutate for antibiotic resistance; the mutation either already exists in the population or arises by chance.
Selection "disposes": Natural selection determines which of those mutations persist and spread. A beneficial mutation increases in frequency because carriers survive and reproduce at higher rates. A harmful mutation decreases because carriers leave fewer offspring. A neutral mutation drifts randomly.
The key insight: mutation and selection have fundamentally different roles. Mutation generates the raw variation. Selection filters it. Neither works without the other. A population with no mutation eventually runs out of variation for selection to act on. A population with mutation but no selection accumulates variation without direction.
Bird's eye primrose plants have short or long flower stalks, determined by a single gene with two alleles (S and L). The dominance pattern is incomplete:
SS = short stalks
SL = intermediate stalks
LL = long stalks
Because each genotype produces a distinct phenotype, you can identify genotypes directly from the plants' appearance. This is the advantage of incomplete dominance for population genetics: no hidden heterozygotes.
How to solve: Count the phenotypes in the population image, assign genotypes, then calculate allele frequencies by counting alleles.
From the practice problem image, counting the plants gives approximately: 4 short (SS), 4 intermediate (SL), 1 long (LL). Total = 9 plants = 18 alleles.
freq(S) = (2 × 4 + 4) / 18 = 12/18 = 0.67
freq(L) = (2 × 1 + 4) / 18 = 6/18 = 0.33
Check: 0.67 + 0.33 = 1.00.
The method is identical to the standard allele frequency calculation. The only difference from a complete dominance system is that you can distinguish heterozygotes from dominant homozygotes by phenotype, so you do not need to use q² to back-calculate allele frequencies.
This is a classic applied HW problem type. You are given survival data after a selective event (pesticide spraying) and asked to work backwards to find allele and genotype frequencies before selection.
Setup: The allele r confers pyrethrin resistance, but only in homozygous (rr) individuals. The other allele is R. Assume HW proportions before spraying. Two alleles at this gene: R and r.
Problem 5a: 1955, pyrethrin killed 99% of the population.
The 1% that survived must be rr (the only resistant genotype). So:
freq(rr) before spraying = q² = 0.01
q = freq(r) = sqrt(0.01) = 0.100
p = freq(R) = 1 - 0.100 = 0.900
Genotype frequencies before spraying (HW):
freq(RR) = p² = (0.900)² = 0.810
freq(Rr) = 2pq = 2(0.900)(0.100) = 0.180
freq(rr) = q² = (0.100)² = 0.010
Check: 0.810 + 0.180 + 0.010 = 1.000.
Problem 5b: 2005, pyrethrin killed only 28% of the population.
The 72% that survived = rr individuals. So:
freq(rr) before spraying = q² = 0.72
q = freq(r) = sqrt(0.72) = 0.849
p = freq(R) = 1 - 0.849 = 0.151
Genotype frequencies before spraying (HW):
freq(RR) = p² = (0.151)² = 0.023
freq(Rr) = 2pq = 2(0.151)(0.849) = 0.256
freq(rr) = q² = (0.849)² = 0.721
Check: 0.023 + 0.256 + 0.721 = 1.000.
Problem 5c: Why did pyrethrin become less lethal?
Between 1955 and 2005, the frequency of the resistance allele (r) increased dramatically, from 0.100 to 0.849. This happened because pyrethrin use exerted strong directional selection: every generation, susceptible individuals (RR and Rr) died at higher rates, leaving rr individuals to reproduce. Over 50 years of this selection pressure, the r allele became the majority allele, so most bedbugs were now resistant and pyrethrin killed far fewer of them.
The pyrethrin resistance problem is a textbook case of a real phenomenon. Pesticide resistance in insects, herbicide resistance in weeds, and antibiotic resistance in bacteria all follow this same logic: a chemical kills most of the population, the resistant individuals survive and reproduce, and within years or decades the population is dominated by resistant genotypes.
This is why hospitals rotate antibiotics, why farmers rotate pesticides, and why public health officials worry about overuse of antimicrobials. The evolutionary mechanism is exactly what you calculate in these HW problems.
Students often think organisms "develop" resistance in response to a pesticide. They do not. The resistance allele already exists (or arises by mutation) before the pesticide is applied. The pesticide selects for pre-existing resistance; it does not cause it.
Students sometimes forget that heterozygotes (Rr) are NOT resistant when resistance is recessive. Only rr individuals survive. This is a common error in the bedbug problem: if you accidentally count Rr as resistant, your answer will be wrong.
Students confuse the direction of the calculation. In the pyrethrin problem, you start from the survival percentage and work backwards to allele frequencies. The percentage killed is not q²; the percentage that survived (if only rr survive) is q².
Students assume that because the r allele was rare in 1955, it must have arisen by mutation between 1955 and 2005. More likely, the r allele was already present at low frequency, and strong selection (killing 99% of the population every generation) rapidly increased its frequency.
⚠️ "Mutation proposes, selection disposes" is a favourite short-answer question. Know it cold and be able to explain each half in one sentence.
⚠️ Incomplete dominance problems are popular because they let examiners test whether you can identify genotypes from phenotypes without needing to use q² back-calculation. Count carefully.
⚠️ Pesticide/antibiotic resistance is a standard exam scenario. The setup is always: given survival data, assume HW before selection, find allele and genotype frequencies. Practice the backwards calculation (survival % = q², then q = sqrt, then p = 1 - q, then HW genotype frequencies).
⚠️ Be ready to explain in two sentences why a pesticide becomes less effective over time, using the language of allele frequency change and directional selection.
True or false: Mutations arise in response to environmental pressures such as pesticides.
Answer: False. Mutations arise randomly. Selection then favours the ones that happen to be beneficial.
Fill in the blank: In a system with incomplete dominance between alleles S and L, the heterozygote SL has a ____ phenotype.
Answer: Intermediate (between the two homozygote phenotypes).
True or false: If pyrethrin kills 40% of a bedbug population, and only rr individuals are resistant, then q² = 0.40.
Answer: False. q² = 0.60 (the 60% that survived, since survival = rr frequency).
Fill in the blank: "Mutation ____; selection ____."
Answer: Proposes; disposes.
True or false: If the resistance allele r increases from 0.10 to 0.85 over 50 years of pesticide use, this is an example of directional selection.
Answer: True.
Q: Explain what "mutation proposes, selection disposes" means in your own words.
A: Mutation is the only source of new genetic variation. It introduces new alleles into a population at random, without regard to whether they are helpful or harmful. Natural selection then determines which of those alleles increase in frequency (because they improve survival or reproduction) and which decrease or disappear. Mutation provides the raw material; selection shapes the outcome.
Q: A population of moths has incomplete dominance at a wing-colour gene. BB = dark, Bb = medium, bb = light. You count 16 dark, 48 medium, and 36 light moths. What are the allele frequencies?
A: Total = 100 moths = 200 alleles. freq(B) = (2 × 16 + 48)/200 = 80/200 = 0.40. freq(b) = (2 × 36 + 48)/200 = 120/200 = 0.60.
Q: A fungicide kills all susceptible (SS and Ss) fungi, and only ss individuals survive. After spraying, 36% of the population is alive. Assuming HW before spraying, what were the allele frequencies?
A: Survivors = ss = q² = 0.36. So q = sqrt(0.36) = 0.60, p = 0.40. Before spraying: freq(SS) = 0.16, freq(Ss) = 0.48, freq(ss) = 0.36.
Q: After 20 years of heavy fungicide use, 81% of the population now survives spraying. What are the new allele frequencies, and what evolutionary process explains the change?
A: Survivors = ss = q² = 0.81. So q = 0.90, p = 0.10. The resistance allele (s) increased from 0.60 to 0.90 over 20 years because directional selection by the fungicide killed susceptible genotypes each generation, leaving resistant individuals to reproduce.
Q: Why can you tell all three genotypes apart in an incomplete dominance system but not in a complete dominance system?
A: In incomplete dominance, the heterozygote has a phenotype intermediate between the two homozygotes, so all three genotypes produce distinct, identifiable phenotypes. In complete dominance, the heterozygote looks identical to the dominant homozygote, so you cannot distinguish AA from Aa by phenotype alone.
This connects to Hardy-Weinberg equilibrium (Part 1 notes), because every problem here uses HW as either the starting assumption or the null model to test against. Selection is the most biologically important violation of HW.
This connects to antibiotic resistance in microbiology. The mechanism is identical: a selective agent (antibiotic or pesticide) kills susceptible genotypes, leaving resistant ones. The maths is the same, whether you are studying bedbugs, bacteria, or weeds.
This connects to adaptation and fitness, because natural selection is the mechanism by which populations adapt to their environments. The shift from q = 0.10 to q = 0.85 in the bedbug resistance allele is adaptation in action, measured quantitatively.
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