Evolutionary Branching & Adaptive Dynamics

Adaptive dynamics tracks how a trait evolves under natural selection via invasion fitness. At evolutionarily singular strategies, disruptive selection can cause the population to branch into two distinct morphs.

Controls

Competition width σ_c0.8

Carrying cap width σ_K1.0

Mutation step σ_m0.03

Population size200

Theory

K(x) = K₀ exp(−x²/2σ_K²)
a(x,y) = exp(−(x−y)²/2σ_c²)

Invasion fitness:
f(y,x̄) = r[1 − a(y,x̄)/K(y)]

Branching condition:
∂²f/∂y² > 0 at singular x*
⟺ σ_c < σ_K

(disruptive selection)