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Frequency-Dependent Selection

Why It Matters

When fitness depends on frequency, there's no single "best" strategy - optimal depends on what others are doing. This maintains diversity, creates oscillations, and makes prediction context-dependent. Recognizing frequency-dependence reveals why optimal strategies shift over time and why mimicking successful strategies can backfire.

The Key Move

When analyzing competitive dynamics, ask: does success of a strategy depend on how many others are using it? If rare strategies have advantage, expect diversity and oscillation. If common strategies have advantage, expect winner-take-all dynamics. This determines whether to follow the crowd or go contrarian.

Classic Application

Batesian mimicry. Harmless species mimic toxic species to avoid predation. But mimicry only works when mimics are rare - if mimics become common, predators learn the signal is unreliable and attack anyway. Negative frequency-dependence maintains low mimic frequency. The moment mimicry "succeeds," it becomes less advantageous.

Surprising Application

Investment strategies. A profitable trading strategy attracts imitators. As more traders use it, the opportunity disappears (prices adjust), reducing profitability. Negative frequency-dependence explains why published strategies often stop working - popularization is self-defeating. Contrarian strategies work precisely because few use them, but only until they become popular.

Failure Modes

  • Assuming all frequency-dependence is negative: positive frequency-dependence (bandwagons, network effects) is equally common and produces different dynamics.

  • Confusing frequency-dependence with density-dependence: frequency is about proportions; density is about absolute numbers. Different effects.

  • Ignoring timescales: frequency-dependent effects may be too slow to matter for decision-making, or too fast for equilibrium assumptions.

Go Deeper

  • Ayala & Campbell, "Frequency-Dependent Selection" - theoretical foundations
  • Maynard Smith, Evolution and the Theory of Games - game theory formalization