Natural Selection & Allele Frequencies

• A mathematical model is built to predict how natural selection changes allele frequencies over time.
• Rock pocket mice in the Sonoran and Chihuahuan deserts live on either light-colored or dark lava rocks.
• Mice with fur that matches their environment survive better.

Color Camouflage

• Light fur provides better camouflage on light rocks.
• Dark fur provides better camouflage on dark lava fields.
• Natural selection favors dark-colored mice in lava fields because predators spot light-colored mice more easily,

Genetics of Coat color

• The Mc1R gene controls coat color.

Alleles of Coat Color

• A1 = Dark fur (dominant).
• A2 = Light fur (recessive).

Genotypes & Phenotypes of Mice

• A1A1 (dark).
• A1A2 (dark).
• A2A2 (light).
• Natural selection reduces the frequency of A2 over time because predators can spot light-colored mice more easily in dark environments.
• The selection coefficient (s) measures how strongly selection acts against the A2 allele.
• s is the fitness reduction of the A2A2 genotype relative to the dark-colored mice.

Fitness values

• A1A1 fitness = 1 (full survival).
• A1A2 fitness = 1 (full survival).
• A2A2 fitness = 1 - s (reduced survival).
• Lighter mice had survival rates between 60% to 98% of dark-colored mice. Selection coefficients ranged from s=0.02 to s=0.40.
• The model assumes s=0.1 (10% disadvantage for A2A2 individuals).

Calculation Example

• Before selection: 100 A1A1, 100 A1A2, 100 A2A2.
• After selection: 60 A1A1, 60 A1A2, 54 A2A2.

Fitness of A2A2

• 54/60=0.9 (90% survival).
• Since 1-s=0.9, we get s=0.1.
• Light-colored mice in dark lava fields had a 10% lower survival rate.
• The Hardy-Weinberg model assumes no natural selection, so the model modifies it to include selection.
• A1A1 Before Selection: p^2, After Selection: p^2
• A1A2 Before Selection: 2pq, After Selection: 2pq
• A2A2 Before Selection: q^2, After Selection: q^2(1-s)
• Both A1A1 and A1A2 have full survival, so their frequencies remain the same.
• The A2A2 frequency is reduced by (1 - s) because of selection.
• After selection, the total population size shrinks, so we need to renormalize the frequencies using the formula: p^2+2pq+q^2(1-s)=1
• New frequency of A1 in the next generation.
• The rate of change in A1 is: p'-p=pq^2s/(1-q^2s)
• This helps understand how quickly the A1 allele increases due to selection.

Predictions from the Model

• The model helps predict how quickly A1 (dark fur allele) will spread in the population.
• If s = 0.1, A1 increases slowly.
• If s = 0.4, A1 increases faster.
• If s = 0.7, A1 increases very fast.
• If the initial frequency of A1 is 0.005 (very rare), and s = 0.1, within 400 generations, A1 will reach nearly 100% in the population.
• Natural selection favors dark-colored mice in dark lava environments.
• The A1 allele (dark fur) spreads because A2A2 individuals suffer higher predation.
• The selection coefficient (s) quantifies the disadvantage of A2A2.
• The higher the selection strength (s), the faster A1 increases in the population.
• Mathematical models help predict how allele frequencies change over generations.
• The study helps understand how species evolve in response to environmental pressures.
• Why some traits become dominant in populations.
• How to predict evolutionary changes using mathematical models.
• Frequency-independent selection means that the fitness of a trait does not depend on how common or rare it is in the population; instead, natural selection acts based on how beneficial the trait is, no matter its frequency.
• There are three main types of frequency-independent selection: Directional Selection, Overdominance (Heterozygote Advantage), and Underdominance (Heterozygote Disadvantage).

Directional Selection (One Allele is Always Better)

• One allele (gene variant) is always better than the other, so natural selection pushes the population toward the "better" allele.
• Eventually, the better allele will take over completely, called fixation.
• If A1 is better than A2, then over time, A1 will replace A2.
• Once A1 reaches fixation, the population stops changing (it's at equilibrium).
• If the population somehow gets a few A2 alleles back (mutation or migration), selection will quickly remove them again.
• A1 is Dominant -> Both A1A1 and A1A2 individuals have the same advantage, while A2A2 is weaker.
• A1 and A2 show Incomplete Dominance -> All three genotypes have different fitness, with A1A1 being the best, A1A2 intermediate, and A2A2 the worst.
• A1 is Recessive -> Only A1A1 individuals have the advantage, while A1A2 and A2A2 have the same lower fitness.

Overdominance (Heterozygote Advantage)

• The A1A2 heterozygote has the highest fitness, meaning better survival and reproduction than either A1A1 or A2A2.
• This leads to a balanced polymorphism, meaning both A1 and A2 stay in the population at stable levels rather than one allele taking over completely.
• Sickle cell allele (A1) causes serious disease in A1A1 individuals.
• Normal allele (A2) makes A2A2 individuals more vulnerable to malaria.
• A1A2 individuals (carriers) don't get sickle cell disease AND have resistance to malaria.
• Because of this, both A1 and A2 remain in the population in areas with malaria.
• Unlike directional selection, neither allele reaches fixation, and both stay present at an intermediate frequency.

Underdominance (Heterozygote Disadvantage)

• The A1A2 heterozygote has lower fitness than either A1A1 or A2A2.
• This creates an unstable situation where selection pushes the population toward losing one allele completely (either A1 or A2).
• Which allele wins depends on starting conditions.
• A crossbreed between two mouse strains (NZB and NZW) leads to severe autoimmune disease in heterozygotes (A1A2).
• Because the mixed mice are sick, selection pushes the population toward either pure NZB (A1A1) or pure NZW (A2A2)—one allele eventually disappears.
• Unlike overdominance, where a mix is stable, underdominance causes the population to "choose" one allele and eliminate the other.
• Directional Selection = One allele is best -> it takes over.
• Overdominance = A mix is best -> both alleles stay.
• Underdominance = A mix is bad -> one allele wins, the other disappears.
• At equilibrium, the average fitness of the A1 allele equals the average fitness of the A2 allele.
• Equilibrium helps determine the stable frequency of the A1 allele (denoted as ppp).

Define Fitness Values

• w11 = fitness of A1A1
• w12 = fitness of A1A2
• w22 = fitness of A2A2

Average fitness

• The average fitness of the A1 allele is: pw11+(1-p)w12
• The average fitness of the A2 allele is: pw12+(1-p)w22
• Equilibrium: pw11+(1-p)w12=pw12+(1-p)w22
• Solving for p gives the equilibrium frequency.
• The heterozygote A1A2 has the highest fitness, where the population stabilizes at a mix of A1 and A2 (neither goes extinct).
• The heterozygote A1A2 has the lowest fitness, and The population moves toward either A1A1 or A2A2 (one allele is lost).
• Hybrid sterility happens in some animals.
• Even though selection direction depends on allele frequencies, the fitness of each genotype is constant and does not change based on how common it is.
• Frequency-dependent selection occurs when the fitness of a trait depends on how common or rare it is in the population.

Types of Frequency-Dependent Selection

• Positive Frequency-Dependent Selection: Common traits are favored, like warning coloration in toxic species; predators will learn to avoid common colors.
• Negative Frequency-Dependent Selection: Rare traits are favored in Drosophila (fruit fly) foraging behavior.
• Positive frequency dependence -> One allele wins, the other disappears.
• Negative frequency dependence -> Both alleles are maintained.
• Viability Selection favors traits that help an organism survive better, whereas Fecundity Selection favors traits that help an organism produce more offspring. Viability Selection: Surviving to Reproduce.
• Selection is based on who survives better given individual traits that help escape predators, resist diseases, or find food, which results in a higher chance of staying alive long enough to reproduce. Fecundity Selection: Producing More Offspring.
• Selection is based on who produces more offspring which will contribute much to the gene pool, so fecundity selection favors those who produce more offspring that survive.
• Mutation is a key process in evolution because it creates genetic variation. However, mutations happen randomly, and an organism cannot control whether a mutation is beneficial or harmful.
• Mutation can change allele frequencies where allele is a version of a gene and over generations.
• Mutations can go both ways where the change is from A1 -> A2 happens at a mutation rate of μ and where the change is from A2 -> A1 happens at a mutation rate of v.
• The frequency of each allele in a population will change over time depending on these rates, which is the rate of mutation.
• Equilibrium happens when the frequency of each allele is: A1 equilibrium frequency = v / (μ + v) and A2 equilibrium frequency = μ / (μ + v).

Natural Selection Change of Allele Frequency

• If A1 mutates to A2 much more often than the reverse, A2 will become more common in the population.
• Mutation is a Slow Process Compared to Natural Selection, it can take thousands of generations for allele frequencies to stabilize. ,
• Mutation alone is not the main driver of rapid evolutionary change as natural selection plays a much bigger role in shaping populations over short timescales.
• Mutation-Selection Balance is when harmful mutations stay in a population.
• Natural selection tries to eliminate A2, but new A2 mutations keep appearing which is where the population reaches a steady state of balance.

Types of Mutations

• A1 (wild-type, normal gene) = fully functional
• A2 (mutant gene) = causes harm.
• Selection removes harmful mutations but mutation keeps introducing new ones until the two forces balance each other out.
• If A2 is recessive, its frequency at equilibrium is √(μ/s) whereas If A2 is dominant, its frequency is μ/s
• Mutation creates new genetic variation, but it happens randomly.
• Mutation alone is a slow process, and natural selection is usually much faster at changing allele frequencies.
• Harmful mutations persist because new ones keep appearing, balancing natural selection's efforts to remove them (mutation-selection balance).
• Recessive harmful mutations are harder to eliminate than dominant ones because they can hide in carriers.
• Mutation continuously introduces new copies of the harmful allele.
• Natural selection removes them because individuals with harmful alleles have lower fitness.
• Equilibrium is reached where the rate of mutation introducing the allele matches the rate of selection removing it.

Mutation and Selection

• Two alleles at a single gene (locus): A1 = normal and A2 = harmful recessive allele
• Where the fitness of each genotype is: A1A1 (normal individuals): Fitness = 1 or A1A2 (carriers) = 1 or A2A2 (affected individuals): Fitness = 1 - s
• Where s is the selection coefficient, which measures how much a harmful allele reduces fitness.
• The frequencies of both alleles is: p = frequency of A1 (So, q = 1 - p)
• After selection for A1A1 and A1A2 the frequency increases, where as A2 decreases( because the A2 individuals have reduced fitness)
• Mutation adds new copies of A2, and some Alleles A1 mutate into A2 at rate μ per generation.
• If the mutation rate μ is high, q will be higher (because more harmful alleles stay in the population).
• If the selection pressure s is strong , then the disease reduces fitness), q will be lower (because selection removes the allele more effectively).

Example

• Familial Adenomatous Polyposis (FAP) is a genetic disorder that causes colon polyps and eventually cancer
• It is caused by mutations in the APC tumor suppressor gene; where People with even one mutated copy of the gene develop the disease (dominant inheritance) which Reduces fitness, but the mutation keeps reappearing in the population.
• In the estimated (μ): Researchers studied 154 people with FAP in Denmark finding 39 cases were due to new mutations.
• The allele equilibrium frequency is: =13,000 so approximately 1 in 13,000 people should carry a change.
• After a Danish study that observed the numbers: Mutation constantly reintroduces harmful alleles into a population BUT natural selection removes harmful alleles, only if mutation is not happening more often. If both are happening, then the balance between them both will determine the populations allele change.
• If there is a dominant disease like FAP; you can calculate how rare each is based upon their own factors.
• Harmful genetic diseases persist because of balancing both factors.
• Under normal circumstances that selection removes harmful mutations becauseIndividuals with them have lower survival or reproductive success SO, because new mutations arise, bringing back allele changes constantly, there never stops being a cycle. Over time, a perfect equal balance is to never have an overall allele mutation change.