Bottleneck Calculator

The bottleneck calculator estimates the genetic consequences when a population crashes to a small size and then recovers. A population bottleneck is a sharp, temporary reduction in the number of breeding individuals caused by events such as disease epidemics, habitat loss, overharvesting, natural disasters, or the founding of a new colony by a handful of migrants. While the population may rebound in raw numbers, the genetic damage done while it was small can persist for thousands of generations. This calculator quantifies that damage in the metrics conservation geneticists care about most: loss of heterozygosity, loss of allelic diversity, accumulated inbreeding, effective population size, and the time required to recover genetic variation.

You provide six inputs: the original population size before the crash, the reduced bottleneck size (the small number of breeders during the crisis), the duration of the bottleneck in generations, the recovery population size after the event, the initial expected heterozygosity, and the initial number of alleles segregating at a representative locus. From these the bottleneck calculator returns the severity classification, the per-generation and total heterozygosity lost, the expected number of alleles retained versus lost, the harmonic-mean effective population size, the inbreeding coefficient, and an estimate of how many generations of recovery are needed to rebuild diversity.

Because random genetic drift dominates in tiny populations, bottlenecks erode the genetic diversity that fuels adaptation. This conservation genetics tool makes those abstract risks concrete, helping students, wildlife managers, and breeders see why even a brief crash in census size can leave a long-lasting genetic signature in endangered species and managed herds alike.

The engine of the bottleneck calculator is the classic drift equation for the decay of heterozygosity in a finite population. Each generation, a population of effective size N loses a fraction 1/(2N) of its heterozygosity to genetic drift, because alleles are sampled randomly when only N individuals reproduce. Over t generations at the bottleneck size N_b, the retained heterozygosity is the initial value multiplied by (1 - 1/(2N_b))^t. The calculator reports this as final heterozygosity, the percentage retained, and the percentage lost.

For allelic diversity, the tool treats each of the k alleles as starting at an average frequency of 1/k. The probability that a given allele survives at least one round of sampling among the 2N_b gene copies present in the bottleneck is 1 - (1 - 1/k)^2N_b. Multiplying by k gives the expected number of alleles retained, and the remainder is the number lost. Rare alleles disappear far faster than heterozygosity, which is why bottlenecks reduce the number of alleles dramatically while average heterozygosity declines more slowly.

The bottleneck calculator also computes the effective population size across the whole episode using the harmonic mean of the sizes through the bottleneck and a fixed ten-generation recovery window. The harmonic mean is heavily weighted toward the smallest sizes, capturing the disproportionate genetic impact of the lowest point. Inbreeding accumulation is reported as F = 1 - (1 - 1/(2N_b))^t, and the recovery time is estimated as the generations needed for drift at the recovery size to reach 95% of equilibrium, using ln(0.05) / ln(1 - 1/(2N_f)).

The headline output of the bottleneck calculator is the population reduction percentage and a severity label. A reduction greater than 99.9% is classed as Extreme, greater than 99% as Severe, greater than 90% as Moderate, and milder crashes as Mild. Severity is judged by the ratio of bottleneck size to original size, because it is the proportional drop, not the absolute numbers, that governs how strongly drift bites.

The heterozygosity panel breaks the loss into three numbers: the loss per generation (1/(2N_b) expressed as a percentage), the cumulative percentage lost, and the percentage retained. Heterozygosity is the probability that two randomly chosen alleles differ, so it is the standard yardstick for genetic diversity. Even a severe bottleneck often retains most heterozygosity if it is brief, which is why duration matters as much as depth.

The allelic diversity panel shows alleles retained and alleles lost. This metric is far more sensitive than heterozygosity because rare alleles are easily purged by sampling. The population effects panel reports the harmonic-mean N_e, the inbreeding coefficient F, and the recovery time in generations. A high F warns of increased homozygosity and possible inbreeding depression, while a long recovery time signals that lost diversity will not return quickly even after census numbers rebound.

The bottleneck calculator is a working tool across conservation biology, wildlife management, and evolutionary teaching. Endangered species such as the cheetah, the northern elephant seal, and the Mauritius kestrel famously passed through bottlenecks that left them with strikingly low genetic diversity, and similar modelling guides recovery plans today.

• Endangered species management: Estimate how much diversity a captive or wild population will lose during a crash and target a minimum viable population size to keep heterozygosity loss acceptable.
• Founder effect analysis: A bottleneck of one generation models the founder event when a few individuals colonise new habitat or seed a captive breeding program.
• Reintroduction planning: Compare scenarios with different recovery sizes to see which rebuilds genetic variation fastest before release.
• Inbreeding risk assessment: Use the inbreeding coefficient F to flag populations at risk of inbreeding depression and reduced fitness.
• Teaching genetic drift: Demonstrate to students how census size, duration, and the (1 - 1/2N)^t relationship interact.

By translating census numbers into heterozygosity and allele loss, the bottleneck calculator connects field demography with the genetic health that ultimately determines a population's capacity to adapt and survive.

Several factors determine how badly a population bottleneck erodes genetic diversity, and the bottleneck calculator lets you explore each one. The single most important driver is the bottleneck size N_b: because the loss rate is 1/(2N_b), a population reduced to 10 breeders loses heterozygosity five times faster per generation than one reduced to 50. Depth of the crash matters more than the original size in absolute terms.

The second factor is duration. A single-generation crash, even an extreme one, may retain surprising diversity, whereas a prolonged bottleneck compounds drift generation after generation. This is why slow declines can be more genetically damaging than a quick crash followed by rapid recovery. The third factor is the initial allele count: populations rich in rare alleles lose far more alleles through a bottleneck than allele-poor populations, even though their heterozygosity may decline similarly.

Finally, the recovery size N_f governs how the population behaves afterward. A large recovery population freezes diversity at its post-bottleneck level and lets mutation slowly rebuild variation over many generations, while a population that stays small continues to lose diversity. The harmonic-mean effective size reported by the calculator captures the combined weight of these phases, reminding users that the smallest size in a population's history exerts an outsized and lasting influence on its genetic future.

The bottleneck calculator uses idealized neutral-locus population genetics, so its outputs are best read as informative estimates rather than exact predictions. The heterozygosity decay equation assumes a constant bottleneck size N_b, discrete non-overlapping generations, neutral alleles unaffected by selection, and no mutation or migration replenishing diversity during the crash. Real populations have overlapping generations, variable sizes, and family-size variation that can make the genetically effective size considerably smaller than the census count.

The allele-retention model assumes every allele begins at the same average frequency of 1/k. In reality allele frequencies are uneven, and rare alleles are lost even faster than this even-frequency assumption predicts, so the calculator may slightly understate allele loss for highly skewed frequency distributions. The harmonic-mean effective size uses a fixed ten-generation recovery window, a convenient simplification rather than a population-specific demographic history.

The recovery-time estimate describes drift dynamics toward a pseudo-equilibrium and does not include the slow input of new variation from mutation, which is what ultimately restores allelic richness over evolutionary timescales. Use this conservation genetics tool for teaching, scenario comparison, and first-pass risk screening, and pair it with individual-based simulation software and empirical molecular markers for management decisions affecting real endangered populations.