Balancing Selection: Heterozygote Advantage

Selection Coefficients

Against AA homozygote (s₁) 0.60

Against aa homozygote (s₂) 0.90

Population size (N) 150

Initial frequency of a (q₀) 0.10

Population State

Generation

Freq. of a, q

0.100

Equilibrium q*

0.400

Mean fitness w̄

1.000

How it works

Each generation is a discrete Wright-Fisher step. Genotypes assort by random mating under Hardy-Weinberg proportions, viability selection then removes individuals in proportion to their fitness disadvantage, and the survivors' gametes form a finite population of size N — the source of genetic drift.

Fitness:      w_AA = 1-s1,  w_Aa = 1,  w_aa = 1-s2
Mean fitness: w̄ = p²w_AA + 2pq·w_Aa + q²w_aa
Selection:    p' = (p²w_AA + pq·w_Aa) / w̄
Drift:        next-gen allele count ~ Binomial(2N, p')

Because the heterozygote Aa is fittest (overdominance / heterozygote advantage), selection pulls the population toward an internal equilibrium instead of fixing one allele:

q* = s1 / (s1 + s2)

s₁, s₂ sliders — how strongly each homozygote is selected against; together they set where q* lands.
Population size N — smaller populations sample the next generation's alleles noisily (drift), so the trajectory wobbles around q* instead of settling exactly on it; larger N tracks the deterministic curve closely.
q₀ slider — the starting frequency of allele a; the trajectory line shows convergence toward q* regardless of where it starts, as long as both s₁ and s₂ are positive.

Real-world example: the sickle-cell allele (HbS) is maintained at ~10-15% frequency in malaria-endemic regions because heterozygotes (HbA/HbS) resist severe malaria while HbA/HbA is more malaria-susceptible and HbS/HbS causes sickle-cell disease — the textbook case of balancing selection in a human population.

AA homozygote Aa heterozygote aa homozygote

Trajectory: q(t) vs generation · dashed = q*

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