Population Genetics I: Deterministic Forces and Allele-Frequency Change
Allele Frequencies as the Fundamental State Variable
Population-genetic framing
Population genetics models evolution by tracking allele frequencies over time. For a two-allele locus with frequencies and , where , deterministic forces alter these frequencies in predictable ways under assumptions about population structure, mating, and fitness.
Selection
If genotypes have fitnesses , , and , then selection changes genotype representation across generations in a way that depends on dominance and relative fitness differences. Selection is directional when one allele consistently increases in frequency because it improves reproductive success in a given environment.
Mutation and migration
Mutation introduces new alleles at low rates, often described by forward and reverse rates. Migration or gene flow moves alleles among populations, often counteracting local divergence. In structured populations, the balance of migration and selection can maintain clines or local adaptation.
Equilibrium insight
Deterministic forces can create stable equilibria, unstable equilibria, or clines depending on the balance among fitness differences, mutation, and migration.
What does a fitness value represent in population genetics?
Fitness is a relative measure of genetic contribution to future gene pools.
Correct answer: Expected relative reproductive contribution to future generations
State the Hardy–Weinberg condition for allele frequencies in a two-allele system.
This is the null model for no evolutionary change at a locus.
Correct answer: If allele frequencies are and , then genotype frequencies at equilibrium are , , and under random mating and no evolutionary forces.
Common deterministic forces
| Force | Typical effect |
|---|---|
| Selection | Increases frequency of alleles with higher relative fitness |
| Mutation | Introduces new alleles, usually at low rate |
| Gene flow | Reduces differences among populations |
| Nonrandom mating | Changes genotype frequencies and can affect homozygosity |
Which condition is NOT required for Hardy–Weinberg proportions?
Hardy–Weinberg assumes no mutation, not a constant mutation rate.
Correct answer: Constant mutation rate
Solving simple selection problems
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1
Write genotype fitnesses relative to the best genotype.
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2
Compute the post-selection genotype frequencies.
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3
Convert genotype frequencies to allele frequencies.
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4
Iterate across generations or analyze equilibrium behavior.
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5
Interpret whether selection is directional, balancing, or disruptive.
Why can migration oppose local adaptation?
The effect depends on the balance between selection and gene flow.
Correct answer: Because incoming alleles from other populations can reduce the frequency of locally favored alleles, lowering divergence between populations.