Population Split Time Calculator

Calculate population split time from allele frequency differences and mutation rates.

FST between populations

Effective population size Ne

Mutation rate μ (per site per generation) (per site/gen)

Generation time (years) (years)

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What the Model Assumes

Estimating divergence time from F_ST uses a pure isolation model: two populations split from one ancestor and exchanged no genes afterwards. Differentiation then accumulates through drift alone.

F_ST ≈ 1 − e^−t/(2N_e)

Every assumption here is restrictive, and each failure biases the estimate in a predictable direction.

Assumption	If violated	Effect on estimate
No gene flow	Ongoing migration	Underestimates split time
Constant N_e	Bottleneck after split	Overestimates split time
Equal population sizes	Asymmetric sizes	Biased, direction depends
Neutral markers	Selection at some loci	Inflates or deflates F_ST

The first two matter most and pull in opposite directions. Continued migration keeps F_ST low, making populations look recently separated when they are not. A bottleneck accelerates drift, making them look anciently separated when they are not.

Why Modern Studies Use Coalescent Methods

Because those two effects are confounded in a single F_ST value, this estimator gives an order of magnitude rather than a date. Coalescent approaches use the full distribution of coalescence times across many loci, which lets divergence time, migration rate and population size history be estimated jointly rather than assumed.

Methods such as isolation-with-migration models, PSMC and MSMC can distinguish "split 50,000 years ago with ongoing gene flow" from "split 200,000 years ago in complete isolation" — two histories that produce the same F_ST and are indistinguishable by this calculation.

Generation time introduces further uncertainty. Converting generations to years for human studies has used values from 20 to 30 years, and that choice alone changes a date by 50%. Published estimates should always state the generation time assumed.

Worked Examples

Example 1: African/European: FST=0.15, Ne=10000, gt=25yr

T=-2×10000×ln(0.85)

Result: T=3250 gen × 25yr = 81,250 years

Rough estimate — actual divergence ~150-300kya

Example 2: Deep split FST=0.40

T=-20000×ln(0.6)=10219 gen

Result: 256,000 years — deeper divergence

High FST suggests long isolation or selection

Example 3: Two histories, one F_ST

Recent split with gene flow versus ancient split in isolation

Result: Indistinguishable by F_ST alone

Both produce the same differentiation. Only coalescent methods using the full distribution of gene genealogies can separate them.

Example 4: Generation time uncertainty

3,250 generations at 25 versus 29 years

Result: 81,250 versus 94,250 years

A 16% change in the assumed generation time propagates directly into the date, which is why the assumption must be stated.

Common Mistakes

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Treating the estimate as a date

It gives an order of magnitude under strong assumptions. Coalescent methods that model migration and population size explicitly give far better estimates.

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Ignoring ongoing gene flow

Migration keeps F_ST low, so populations still exchanging genes appear far more recently separated than they are.

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Assuming constant population size

A bottleneck after the split accelerates drift and inflates F_ST, making the divergence appear older.

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Not stating the generation time

Human studies have used 20 to 30 years. That choice alone shifts a calculated date by half as much again.

Frequently Asked Questions

Limitations of this model?

Assumes: isolation model (no gene flow), constant Ne, pure drift. Real: migration reduces FST (lower T estimate). Bottlenecks change Ne. Selection at FST outliers. Use MSMC, PSMC, or G-PhoCS for rigorous demographic inference from genomic data.

FST as split time proxy?

Useful for rough estimate when molecular clock unavailable. Better: use sequence divergence (Ks) with molecular clock. Or Bayesian coalescent methods with multiple loci. FST method: lower bound because gene flow reduces FST.

How reliable is F_ST-based split time?

It gives an order of magnitude at best. Gene flow and population size changes bias it in opposite directions and cannot be distinguished from a single value.

Why does gene flow underestimate divergence time?

Because migration continually homogenises allele frequencies, keeping F_ST low and making long-separated populations appear recently split.

What do coalescent methods add?

They use the distribution of coalescence times across many loci to estimate divergence time, migration rate and population size jointly rather than assuming them.

Why does generation time matter so much?

It converts generations to years directly. Using 20 versus 30 years changes a human divergence estimate by 50%.