Population Genetics I: Deterministic and Stochastic Change in Allele Frequencies

Manual: General · Subject: Evolutionary Biology

This lesson develops the quantitative machinery for selection, drift, mutation, and migration in finite populations.

Allele-frequency dynamics

Deterministic evolution

For a biallelic locus with allele frequency $p$ , selection changes allele frequencies according to genotype fitnesses. In simple cases, deterministic recursion equations show how advantageous alleles increase, how recessive mutations can persist, and how dominance modifies trajectories. In continuous time, analogous dynamics can be written as differential equations.

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Interpretation tip

Inference from allele-frequency change is always confounded by demography unless genealogical context is modeled explicitly.

Selection and drift

Selection is directional and can be weak or strong depending on the magnitude of $s$ . Drift introduces sampling variance on the order of $1/(2N_e)$ per generation in diploids. When $|s| \ll 1/(2N_e)$ , drift can dominate; when $|s| \gg 1/(2N_e)$ , selection is more likely to dominate.

Canonical forces and their signatures

Force	Typical signature
Selection	Consistent directional change tied to fitness differences
Drift	Random walk with variance increasing over time
Mutation	Introduction of new alleles, usually at low frequency
Migration	Allele-frequency shifts coupled to gene flow

When is drift most likely to overpower selection?

When

|s| \gg 1/(2N_e)

When

|s| \ll 1/(2N_e)

Only when mutation rate is zero Only in infinite populations

What does the Wright-Fisher model primarily capture?

Models of selection

Hard selection

Fitness affects absolute contribution to future generations
Population growth may change with environment

Soft selection

Fitness is often relative within local context
Total contributions can be normalized among competitors

Which parameter most directly controls the rate at which neutral heterozygosity is lost by drift?

N_e

s

r

Trait mean

Workflow for a simple allele-frequency analysis

1

Estimate allele frequencies across time points or populations.
2

Specify a population-genetic model for drift, selection, and migration.
3

Fit parameters by likelihood, Bayesian, or simulation-based inference.
4

Check identifiability and sensitivity to demographic assumptions.
5

Compare neutral and selection models using model selection or posterior predictive checks.

State the Hardy-Weinberg expectation for genotype frequencies at a biallelic locus with allele frequencies $p$ and $q$ .

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