Trait Substitution Sequence

A trait substitution sequence is the stepwise path by which a population adapts in adaptive dynamics, proceeding through a series of rare mutations and selective replacements. Each step begins with a mutant near the current resident trait; if its invasion fitness is positive, it spreads and becomes the new resident, shifting the population to a nearby point in trait space. Under assumptions of rare and small mutations, the sequence can be approximated by a deterministic differential equation that resembles gradient ascent on a landscape that moves as the population evolves. The sequence may converge to a stable strategy, diverge at an evolutionary branching point, or cycle indefinitely.