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Gene Flow & Population Structure

Migration and its effects on genetic differentiation

Try it: Continent-IslandF-Statistics

Gene Flow and Migration

Gene flow is the transfer of alleles between populations through migration. It is a homogenizing force — gene flow tends to make populations more similar to each other, counteracting the diversifying effects of drift and local selection.

Key insight: Gene flow reduces genetic differentiation between populations. Even a small amount of migration can prevent populations from diverging substantially.

Continent-Island Model

The simplest migration model assumes one-way gene flow from a large "continent" population to a small "island" population:

p'(island) = (1-m)p + m×p_C Island frequency after migration

Where m is the fraction of the island replaced by migrants each generation, and p_C is the continent allele frequency.

The change in island frequency is:

Δp = m(p_C - p) Change due to migration

Interactive Migration Dynamics

Adjust migration rate and population frequencies to see how the island population converges toward the continent frequency over time.

0.05
0.80
0.20

Island population approaches continent frequency. Half-life = ln(2)/m generations.

Rate of Convergence

Migration acts quickly compared to mutation but can be slower than selection. The deviation from equilibrium decays exponentially:

p(t) - p_C = (p₀ - p_C)(1-m)^t Exponential approach to equilibrium
t₁/₂ = ln(2) / m ≈ 0.693 / m Half-life of differentiation

With m = 0.1 (10% migration), the half-life is only ~7 generations. Even with m = 0.01, differentiation halves every 70 generations.

Island Model

Wright's island model considers multiple populations exchanging migrants symmetrically. Each population receives a fraction m of migrants from a common migrant pool with mean allele frequency p̄.

p'ᵢ = (1-m)pᵢ + m×p̄ Frequency in population i after migration

F-Statistics

Wright's F-statistics quantify genetic structure at different levels:

  • FIS: Inbreeding within subpopulations
  • FST: Differentiation among subpopulations
  • FIT: Total inbreeding relative to the whole population
F_ST = (H_T - H_S) / H_T Genetic differentiation index

Where HT is the expected heterozygosity of the total population and HS is the mean heterozygosity within subpopulations.

Migration-Drift Equilibrium

In finite populations, migration counters drift. At equilibrium under the island model:

F_ST ≈ 1 / (4Nm + 1) Equilibrium F_ST (island model)

The product Nm (effective number of migrants per generation) determines population structure:

  • Nm >> 1: Populations are essentially panmictic (FST ≈ 0)
  • Nm ≈ 1: Moderate differentiation (FST ≈ 0.2)
  • Nm << 1: Strong differentiation (FST approaches 1)
The famous "one migrant per generation" rule: If Nm ≥ 1, populations remain genetically cohesive. This is surprisingly little gene flow!

Wahlund Effect

When populations with different allele frequencies are pooled, the combined sample shows a deficiency of heterozygotes relative to Hardy-Weinberg expectations:

H_observed < 2p̄(1-p̄) Heterozygote deficiency from population structure

This apparent "inbreeding" is purely a sampling artifact — each subpopulation may be in HWE, but the pooled sample is not.

Gene Flow and Local Adaptation

Gene flow can prevent local adaptation by swamping locally beneficial alleles with maladaptive immigrants. The balance depends on the ratio m/s:

  • m << s: Selection overcomes migration; local adaptation possible
  • m ≈ s: Balance between forces; polymorphism maintained
  • m >> s: Migration swamps selection; no local adaptation

Real-World Patterns

Natural populations show a range of gene flow patterns:

  • Isolation by distance: Nearby populations more similar than distant ones
  • Stepping-stone model: Migration only between adjacent populations
  • Source-sink dynamics: Asymmetric flow from productive to marginal habitats
  • Hybrid zones: Narrow regions of contact between differentiated populations