Effective Population Size & Genetic Diversity Loss

Breeding Population

Census size N 60

Male fraction 50%

Reproductive skew V_k 2.0

Speed (gen/s) 2

Population Genetics

Ne ≥ 500 — genetically healthy

Effective size Ne

60.0

Ne / N ratio

100%

Gene diversity H

87.5%

Generation

Diversity vs. Generations

Actual H Predicted (const. Ne)

How it works

Genetic diversity is not lost according to the census population size N — it is lost according to the effective population size N_e, the size of an idealised population that would drift at the same rate as the real one. Two real-world effects shrink N_e below N:

Unequal sex ratio (Wright 1931):
  Ne(sex) = 4·Nm·Nf / (Nm + Nf)

Variance in offspring number (Crow & Morton 1955):
  Ne(var) = 4·N / (Vk + 2)     [Vk = variance/mean of offspring count]

Combined (independent factors):
  1/Ne ≈ 1/Ne(sex) + 1/Ne(var) − 1/N

Each generation this simulator draws N_e "effective parents" (with replacement) from the current population, then draws all N offspring from those parents — a small N_e means offspring share fewer parental lineages, so an allele's frequency swings more per generation. Gene diversity (Nei's expected heterozygosity) is measured directly from the simulated allele pool:

H = 1 − Σ pᵢ²           (pᵢ = frequency of allele i)
Expected decay: H(t) = H₀ · (1 − 1/(2Ne))^t

The dashed curve projects that decay formula forward from the current point using today's N_e; the solid curve is the actual simulated trajectory — they track closely but never match exactly, because the simulation is itself one stochastic draw from the same process the formula describes.

The 50/500 rule (Franklin 1980, Soulé 1980), a long-standing conservation-genetics rule of thumb: N_e below ~50 risks measurable inbreeding depression within a few generations; N_e below ~500 is too small to maintain the standing variation needed for long-term adaptive evolution. Try skewing the sex ratio or raising reproductive skew with N held fixed — N never changes, yet N_e and the diversity-loss rate both collapse.

Gen 0

Each sphere = one individual Colour = marker allele

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