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Natural Selection

Differential fitness and allele frequency change

Try it: Selection SimFreq-Dependent

The Principle

Natural selection is the process by which individuals with certain heritable traits tend to survive and reproduce more successfully than others. At the genetic level, this translates to changes in allele frequencies over generations.

Key insight: Selection acts on phenotypes but changes genotype frequencies. The connection between phenotype and genotype (dominance, epistasis) shapes how selection operates on alleles.

Fitness and Selection

Fitness (w) measures the relative reproductive success of a genotype. By convention, we set the highest fitness to 1 and express others relative to it.

w_AA = 1, w_Aa = 1-hs, w_aa = 1-s Standard parameterization with dominance

Where:

  • s = selection coefficient (reduction in fitness of aa)
  • h = dominance coefficient (0 = recessive, 0.5 = codominant, 1 = dominant)

Change in Allele Frequency

The change in allele frequency per generation depends on current frequencies and fitness values:

Δp = pq[p(w_AA - w_Aa) + q(w_Aa - w_aa)] / w̄ General selection equation

Where w̄ = p²w_AA + 2pqw_Aa + q²w_aa is the mean population fitness.

Interactive Selection Dynamics

Adjust the fitness values below to see how selection changes allele frequencies. The curve shows Δp for each frequency p. Where the curve crosses zero, populations are at equilibrium.

1.00
1.00
0.80

Δp curve showing direction and magnitude of selection. Arrows indicate direction of change.

Selection Regimes

Directional Selection

When one allele has consistently higher fitness, selection drives it toward fixation. Try setting wAA = 1.0, wAa = 0.9, waa = 0.8 to see directional selection favoring A.

Balancing Selection

When heterozygotes have the highest fitness (overdominance), both alleles are maintained at a stable equilibrium. Try wAA = 0.9, wAa = 1.0, waa = 0.8.

p̂ = (w_Aa - w_aa) / (2w_Aa - w_AA - w_aa) Equilibrium frequency under overdominance

Disruptive Selection

When heterozygotes have the lowest fitness (underdominance), the equilibrium is unstable — populations evolve away from it toward fixation or loss.

Rate of Selection

How fast does selection work? The time to change frequency depends on dominance:

  • Dominant advantageous: Fast initial spread, slow to fix (rare recessives hard to remove)
  • Recessive advantageous: Slow initial spread (hides in heterozygotes), fast final fixation
  • Additive: Relatively constant rate throughout
t ≈ (1/s) × ln(p/q) for additive selection Approximate time to change frequency

Selection and Drift

In finite populations, selection competes with drift. The key parameter is Ns:

  • Ns >> 1: Selection dominates; advantageous alleles likely fix
  • Ns ≈ 1: Both forces matter; outcomes are probabilistic
  • Ns << 1: Drift dominates; alleles behave as if neutral

The probability of fixation for a new mutation with selective advantage s in a population of size N:

P(fix) ≈ 2s (for Ns >> 1) Probability of fixation for beneficial mutation
Even strongly advantageous mutations are often lost by drift when rare. A mutation with 10% advantage has only about 20% chance of eventual fixation.

Mutation-Selection Balance

Deleterious alleles persist in populations due to the balance between mutation (introducing them) and selection (removing them):

q̂ ≈ μ/s (recessive) or q̂ ≈ μ/hs (partially dominant) Equilibrium frequency of deleterious allele

This explains why many genetic diseases persist at low frequencies — they're continuously replenished by mutation even as selection removes them.