Population Bottleneck Calculator

Calculate loss of genetic diversity and allele frequency changes through population bottlenecks.

Pre-bottleneck population size N₀

Bottleneck size Nb (minimum population)

Post-bottleneck size N1

Heterozygosity before H₀

0-1

Number of generations at bottleneck

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Why Duration Matters More Than Depth

Heterozygosity is lost at a rate of 1/(2N_e) per generation, so the loss compounds across every generation spent at low numbers.

H_t = H₀ × (1 − 1/(2N_e))^t

Bottleneck	Generations	Heterozygosity retained
N = 10	1	95%
N = 10	10	60%
N = 10	50	8%
N = 100	10	95%
N = 100	50	78%

A single generation at ten individuals costs only 5% of heterozygosity. Ten generations at the same size costs 40%. A brief severe crash is far less damaging than a prolonged moderate one — which is why rapid population recovery matters so much in conservation.

The Harmonic Mean

Effective size across generations is the harmonic mean, not the arithmetic mean, so the smallest value dominates. A population at 1,000 for nine generations and 10 for one has N_e of about 92 — far closer to the crash size than to the typical size.

This is why historical bottlenecks leave signatures long after numbers recover, and why census size today says little about genetic health.

Allelic Richness Falls Faster Than Heterozygosity

Measure	Sensitivity to bottleneck	Why
Allelic richness	Drops sharply	Rare alleles lost immediately
Heterozygosity	Declines slowly	Dominated by common alleles
Excess heterozygosity	Diagnostic signal	Detects recent bottlenecks

Rare alleles are lost first because few copies exist to sample, while heterozygosity depends on common alleles that survive. This produces a temporary excess of heterozygosity relative to allele number — the basis of the BOTTLENECK test for detecting recent crashes.

Cheetahs and northern elephant seals both show the long-term consequence: near-monomorphic MHC in cheetahs allows reciprocal skin grafts between unrelated individuals, and elephant seals recovered to over 200,000 animals from perhaps 20 founders while retaining almost none of their original variation.

Worked Examples

Example 1: Cheetah bottleneck: N0=10000, Nb=10, H0=0.8

H_after=0.8×(1-0.05)^1

Result: H=0.76 — one generation, 5% loss

Cheetahs have extremely low diversity from ~10,000 ya bottleneck

Example 2: Northern elephant seal: Nb=20, g=1

H_after=0.8×(1-0.025)

Result: H=0.78 per generation, but total loss over decades

Recovered from ~20 individuals in 1890s

Example 3: Depth versus duration

One generation at N = 10 versus ten generations at N = 10

Result: 95% versus 60% retained

Each generation multiplies the remaining heterozygosity by 0.95. A brief crash is far less costly than a sustained one.

Example 4: Detecting a recent bottleneck

Heterozygosity higher than allele number predicts

Result: Recent crash signature

Rare alleles vanish first, so heterozygosity temporarily exceeds what the remaining allelic diversity would generate at equilibrium.

Common Mistakes

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Judging a bottleneck by its depth alone

Loss compounds per generation. Ten generations at N = 10 costs 40% of heterozygosity while one generation costs 5%.

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Using the arithmetic mean for N_e

It is a harmonic mean, so the smallest value dominates. One crash generation can halve the long-term effective size.

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Assuming recovery in numbers restores diversity

Genetic variation returns only through mutation, over thousands of generations. Elephant seals number over 200,000 yet remain genetically depauperate.

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Monitoring heterozygosity alone

Allelic richness falls much faster because rare alleles are lost first. Heterozygosity understates recent losses.

Frequently Asked Questions

Harmonic mean Ne?

Effective population size for variable populations is dominated by the minimum: 1/N_e = Σ(1/N_t)/t. Even brief bottlenecks drastically reduce long-term N_e. 100 generations at N=10000 preceded by 1 generation at N=10: N_e≈19.8, not 10000.

Conservation implications?

Genetic erosion during bottleneck increases inbreeding, exposes recessive deleterious alleles, reduces adaptive potential. Minimum viable population (MVP) typically 50-500 to avoid inbreeding depression. 5000+ for long-term evolutionary potential.

How fast is heterozygosity lost?

At 1/(2N_e) per generation. At N_e = 10 that is 5% per generation, compounding across every generation at low numbers.

Why is effective size a harmonic mean?

Because loss compounds multiplicatively. A single low-size generation dominates the long-term average far more than an arithmetic mean would suggest.

Does population recovery restore genetic diversity?

No. Variation returns only through new mutation over thousands of generations. Northern elephant seals recovered numerically but not genetically.

Why does allelic richness fall faster than heterozygosity?

Rare alleles exist in few copies and are lost immediately, while heterozygosity depends on common alleles that survive the crash.