Migration-Drift Balance Calculator

Calculate FST at migration-drift equilibrium and effective migration rate for population structure.

Migration rate m (per generation)

Fraction migrating per generation

Effective size of each subpopulation Ne

Number of subpopulations n

Observed FST

For Nm estimate

Please check your inputs and try again.

Why One Migrant Is Enough

Migration homogenises allele frequencies while drift differentiates them. At equilibrium the two balance, and the striking result is that the balance point depends on the absolute number of migrants, not the migration rate.

F_ST ≈ 1 / (4N_em + 1)

N_em	F_ST	Differentiation
0.25	0.50	Very strong
1	0.20	Moderate
5	0.048	Low
10	0.024	Very low

The reason population size drops out is that drift is stronger in small populations, but a single migrant also represents a larger proportion of them. The two effects cancel exactly, which is why one migrant per generation prevents substantial differentiation whether the population is 100 or 100,000.

This is Wright's one-migrant-per-generation rule, and it underpins conservation guidance on corridors between fragmented habitats.

Why the Rule Is a Guideline, Not a Target

The result assumes an idealised island model — equal population sizes, symmetric migration, no selection, and equilibrium reached. Real systems violate all four.

Assumption	Reality	Consequence
Equal-sized demes	Source–sink dynamics common	Asymmetric gene flow
Migrants reproduce	Many do not	Effective migration is lower
Equilibrium reached	Fragmentation is recent	F_ST still rising
Neutral markers	Selection at some loci	Biases the estimate

The second row matters most in conservation practice. Wright's m is effective migration — migrants that survive and breed. An individual that disperses but fails to reproduce contributes nothing genetically, so counting observed dispersers overestimates gene flow substantially.

For this reason, managers commonly aim for closer to ten effective migrants per generation rather than one, giving margin for the gap between observed dispersal and genetic contribution.

Worked Examples

Example 1: Islands: Ne=1000, m=0.01, n=5

Nem=10, FST=1/(1+4×10×(5/4)²)

Result: FST=0.0157 — low differentiation

10 migrants/gen: populations stay similar

Example 2: From FST=0.15, n=4

Nem≈2.5 migrants/gen

Result: Low gene flow: significant structure

Consistent with isolated island populations

Example 3: Why population size cancels

One migrant into a deme of 100 versus 100,000

Result: Same F_ST ≈ 0.20

Drift is far stronger in the small deme, but one migrant is also a far larger fraction of it. The two effects offset exactly.

Example 4: Observed versus effective migrants

Twenty dispersers observed, five breed successfully

Result: N_em = 5, not 20

Only reproducing migrants transmit alleles. Genetic estimates of gene flow are routinely lower than field observations of movement.

Common Mistakes

⚠️

Confusing observed dispersal with effective migration

Wright's m counts migrants that survive and reproduce. Individuals that move but do not breed contribute nothing genetically.

⚠️

Treating one migrant per generation as a management target

It is the threshold for avoiding severe differentiation, not a goal. Conservation practice typically aims considerably higher for safety margin.

⚠️

Assuming equilibrium in recently fragmented habitat

F_ST takes many generations to reach migration–drift balance. Recent fragmentation shows lower differentiation than the eventual equilibrium.

⚠️

Applying the island model to source–sink systems

The formula assumes symmetric migration between equal demes. Asymmetric flow between unequal populations gives quite different results.

Frequently Asked Questions

Wright's Nem rule?

FST ≈ 1/(1+4Nem) (two-island, large Ne). Nem=1: FST≈0.2 (notable structure). Nem=10: FST≈0.024 (little structure). Nem>10: populations nearly panmictic. Rule of thumb: >1 migrant per generation prevents major divergence by drift alone.

Real populations?

Island model oversimplified: stepping-stone, isolation-by-distance models more realistic. Contemporary gene flow vs historical structure. Landscape genetics: incorporates geography. FST outliers: candidate locally adapted loci beyond neutral expectations.

What is the one-migrant-per-generation rule?

Approximately one effective migrant per generation prevents substantial genetic differentiation, regardless of population size.

Why doesn't population size affect the threshold?

Because drift is stronger in small populations but a single migrant is also a larger proportion of them. The two effects cancel.

What counts as a migrant?

Only individuals that survive and reproduce in the new population. Observed dispersal overestimates effective migration, often substantially.

Should conservation aim for exactly one migrant?

No. That is the threshold for avoiding severe differentiation. Managers usually target closer to ten to allow for the gap between dispersal and successful breeding.