Replicator Dynamics

Replicator dynamics model how population shares change according to relative fitness. Fitness may depend on the population composition, allowing outcomes including coexistence or cycles as well as dominance.

Replicator dynamics describe changes in a type's population share relative to average fitness. In the continuous model, the change rate is its current share multiplied by its fitness advantage. A rare type with an advantage therefore increases from a small base, while an absent type remains absent unless an additional mechanism introduces it.

Fitness can depend on the current population composition. A strategy that performs well when rare may lose its advantage when common, producing coexistence or cycling rather than one permanent winner. Applying the model to firms or ideas requires an explicit replication process and payoff measure; popularity alone does not establish usefulness or future dominance.

When to use it

When understanding competitive landscape evolution; when predicting which strategies will dominate; when finding contrarian opportunities in converging landscapes; when modeling cultural evolution.

How it can help

Specify what replicates, how payoffs affect copying, and whether fitness changes with population composition. Use the resulting dynamics to explore conditional trajectories rather than extrapolating current popularity.