Migration-Selection Balance

Migration–Selection Balance

When populations are spatially subdivided, gene flow (migration) and local selection create spatial patterns in allele frequencies called clines. The balance between these forces determines whether populations remain locally adapted or become homogenized.

Key Concepts

• Stepping-stone model: Populations arranged in a linear array with migration only between adjacent demes.
• Local adaptation: Different alleles are favored in different locations due to environmental variation.
• Gene flow: Migration homogenizes allele frequencies across space, opposing local selection.
• Cline width: The spatial scale over which allele frequency changes, approximately w ~ √(σ²/s) where σ² is dispersal variance and s is selection strength.
• F_ST: Measures genetic differentiation between populations. Low F_ST indicates high gene flow.

The Model

Each generation consists of three steps:

1. Selection: Within each deme, genotype fitnesses change allele frequencies. In the spatial gradient mode, allele A is favored on the left (fitness advantage s) and allele a is favored on the right.
2. Migration: A fraction m of individuals in each deme is replaced by migrants from adjacent demes (or both neighbors for interior demes).
3. Equilibrium: At equilibrium, a stable cline forms where selection and migration balance. The cline steepness depends on the ratio s/m.

Predictions

• Higher migration (m) → shallower clines, more homogenization, lower F_ST
• Stronger selection (s) → steeper clines, more local adaptation, higher F_ST
• When m >> s, migration dominates and clines are weak
• When s >> m, selection dominates and populations are locally adapted