Evolutionary Singularity

An evolutionary singularity is a trait value at which the fitness gradient vanishes — meaning no small mutant can gain an immediate selective advantage by moving in either direction. In adaptive dynamics, singularities are the candidate endpoints of evolution, but their properties determine whether evolution actually stops there. A singularity may be convergence stable (nearby traits evolve toward it), evolutionarily stable (no nearby mutant can invade), or a branching point (convergence stable but not evolutionarily stable, leading to disruptive selection and diversification). The classification of singularities is one of the central achievements of adaptive dynamics theory. See also: Fitness Landscape, Adaptive dynamics, Dynamical Systems